Thermophysical properties, interactions and structure in organic liquid mixtures including polar and/or associated compounds: N, N-dialkylamides, amines, 1-alkanols, ketones and organic carbonates

PROGRAMA DE DOCTORADO EN FÍSICA TESIS DOCTORAL THERMOPHYSICAL PROPERTIES, INTERACTIONS AND STRUCTURE IN ORGANIC LIQUID MIXTURES INCLUDING POLAR AND/OR ASSOCIATED COMPOUNDS: N,N-DIALKYLAMIDES, AMINES, 1-ALKANOLS, KETONES AND ORGANIC CARBONATES Presentada por Luis Fernando Hevia de los Mozos para optar al grado de Doctor por la Universidad de Valladolid Dirigida por: José Carlos Cobos Hernández Juan Antonio González López Isaías García de la Fuente A Marta. A mis padres, Luis y María del Mar. A mi padrino, Fernando. 5 Table of contents Table of contents ........................................................................................................................ 5 Agradecimientos/acknowledgements ..........................................................................................11 The structure of this Thesis ....................................................................................................... 13 Part I. Objectives and methodology ......................................................................... 15 Chapter 1. Introduction .........................................................................................................17 1.1. About this research group ...........................................................................................17 1.1.1. Members of GETEF ..................................................................................................17 1.1.2. Lines of research ........................................................................................................18 1.1.3. Collaboration with other research groups ..................................................................20 1.2. About this PhD Thesis ................................................................................................21 1.2.1. Experimental objectives ............................................................................................21 1.2.2. Theoretical objectives ................................................................................................ 23 1.2.3. Scientific activities related to the PhD Thesis ...........................................................24 1.2.4. Scientific production of the author ............................................................................24 1.2.5. Funding .....................................................................................................................29 1.3. Detail of the work at ICCF .........................................................................................29 1.3.1. September 2017 – December 2017 .............................................................................29 1.3.2. September 2018 – December 2018 ............................................................................. 31 1.3.3. Publication of the results ........................................................................................... 32 1.4. References ................................................................................................................... 32 Chapter 2. Mixing and excess functions ................................................................................. 33 2.1. Mixing functions .......................................................................................................... 33 2.2. Excess functions ..........................................................................................................36 2.3. Speed of sound ............................................................................................................37 2.4. Dielectric and refractive properties ..............................................................................37 2.4.1. Static relative permittivity ........................................................................................37 2.4.2. Refractive index ........................................................................................................38 TABLE OF CONTENTS 6 2.5. Redlich-Kister equation ............................................................................................... 39 2.6. References ................................................................................................................... 39 Chapter 3. Experimental equipment ...................................................................................... 41 3.1. Densidad y velocidad del sonido. Anton Paar DSA 5000 ............................................ 41 3.1.1. El método del tubo vibrante ..................................................................................... 41 3.1.2. El método del pulso .................................................................................................. 43 3.1.3. Características del Anton Paar DSA 5000 ................................................................ 44 3.1.4. Uso de un líquido de referencia ................................................................................. 44 3.1.5. Calibración ............................................................................................................... 45 3.1.6. Sistema test de volúmenes de exceso y compresibilidades isoentrópicas..................... 47 3.2. Índice de refracción. Bellingham + Stanley RFM970 ................................................... 51 3.2.1. Sistema test de índices de refracción ......................................................................... 54 3.3. Permitividad dieléctrica .............................................................................................. 55 3.3.1. El método del puente autoequilibrado en configuración 4TP ..................................... 55 3.3.2. Relación de la impedancia medida con la permitividad ............................................. 57 3.3.3. Montaje experimental ............................................................................................... 58 3.3.4. Compensación ........................................................................................................... 60 3.3.5. Procedimiento de medida y limpieza. Programas de control ...................................... 61 3.3.6. Resultados de la técnica ............................................................................................ 63 3.3.7. Sistema test de permitividad relativa ........................................................................ 63 3.4. Entalpía molar de exceso ............................................................................................ 66 3.4.1. Montaje experimental ............................................................................................... 66 3.4.2. Principio de medida del calorímetro .......................................................................... 68 3.4.3. Procedimiento de medida y calibración ..................................................................... 69 3.5. Referencias .................................................................................................................. 69 Chapter 4. Theoretical models ............................................................................................... 73 4.1. Prigogine-Flory-Patterson model ................................................................................. 73 4.1.1. Hypotheses for pure liquids ....................................................................................... 73 4.1.2. Hypotheses for binary mixtures ................................................................................ 74 4.1.3. Equations .................................................................................................................. 74 4.1.4. Estimation of the Flory energetic parameter ............................................................. 75 4.1.5. Study of the random mixing hypothesis .................................................................... 76 4.1.6. Patterson’s series expansions .................................................................................... 76 4.2. The ERAS model ........................................................................................................ 79 4.2.1. Hypotheses................................................................................................................ 79 4.2.2. Equations.................................................................................................................. 79 TABLE OF CONTENTS 7 4.3. Kirkwood-Fröhlich model ............................................................................................81 4.3.1. Dielectric behavior ....................................................................................................81 4.3.2. Long-range interactions and the local field hypothesis ...............................................82 4.3.3. Fröhlich’s fluctuation theory of dielectrics at zero field .............................................83 4.3.4. Macroscopic separation of induced and orientational contributions ...........................84 4.3.5. The Kirkwood-Fröhlich equation for pure polar fluids .............................................. 86 4.3.6. The adaptation of Kirkwood-Fröhlich model to mixtures ......................................... 87 4.3.7. Molar refraction and dispersive interactions ............................................................. 89 4.4. Appendix: derivation of Prigogine-Flory-Patterson equations ..................................... 90 4.4.1. Reduced and mixing functions .................................................................................. 90 4.4.2. Series expansion of the mixing functions .................................................................. 90 4.4.3. Series expansion of the free volume terms .................................................................92 4.4.4. Derivatives of the reduced temperature .....................................................................93 4.5. References ...................................................................................................................95 Part II. Copies of the published works ..................................................................... 97 Article 1. F. Hevia, A. Cobos, J.A. González, I. García de la Fuente, L.F. Sanz, Thermodynamics of Amide + Amine Mixtures. 1. Volumetric, Speed of Sound, and Refractive Index Data for N,N-Dimethylformamide + N-Propylpropan-1- amine, + N-Butylbutan-1-amine, + Butan-1-amine, or + Hexan-1-amine Systems at Several Temperatures. J. Chem. Eng. Data 61 (2016) 1468-1478. https://doi.org/10.1021/acs.jced.5b00802. Article 2. F. Hevia, A. Cobos, J.A. González, I.G. de la Fuente, V. Alonso, Thermodynamics of Amide + Amine Mixtures. 2. Volumetric, Speed of Sound and Refractive Index Data for N,N-Dimethylacetamide + N-Propylpropan-1- Amine, + N-Butylbutan-1-Amine, + Butan-1-Amine, or + Hexan-1-Amine Systems at Several Temperatures. J. Solution Chem. 46 (2017) 150-174. https://doi.org/10.1007/s10953-016-0560-0. Article 3. F. Hevia, J.A. González, I. García de la Fuente, L.F. Sanz, J.C. Cobos, Thermodynamics of amide + amine mixtures. 3. Relative permittivities of N,N- dimethylformamide + N-propylpropan-1-amine, + N-butylbutan-1-amine, + butan-1-amine, or + hexan-1-amine systems at several temperatures. J. Mol. Liq. 238 (2017) 440-446. https://doi.org/10.1016/j.molliq.2017.05.025. Article 4. F. Hevia, J.A. González, A. Cobos, I. García de la Fuente, L.F. Sanz, Thermodynamics of amide + amine mixtures. 4. Relative permittivities of N,N- dimethylacetamide + N-propylpropan-1-amine, + N-butylbutan-1-amine, + butan-1-amine, or + hexan-1-amine systems and of N,N-dimethylformamide + aniline mixture at several temperatures. Characterization of amine + amide systems using ERAS. J. Chem. Thermodyn. 118 (2018) 175-187. https://doi.org/10.1016/j.jct.2017.11.011. TABLE OF CONTENTS 8 Article 5. F. Hevia, J.A. González, A. Cobos, I. García de la Fuente, C. Alonso-Tristán, Thermodynamics of mixtures with strongly negative deviations from Raoult's law. XV. Permittivities and refractive indices for 1-alkanol + n-hexylamine systems at (293.15–303.15) K. Application of the Kirkwood-Fröhlich model. Fluid Phase Equilib. 468 (2018) 18-28. https://doi.org/10.1016/j.fluid.2018.04.007. Article 6. F. Hevia, A. Cobos, J.A. González, I. García de la Fuente, L.F. Sanz, Thermodynamics of mixtures with strongly negative deviations from Raoult's law. XVI. Permittivities and refractive indices for 1-alkanol + di-n-propylamine systems at (293.15–303.15) K. Application of the Kirkwood-Fröhlich model. J. Mol. Liq. 271 (2018) 704-714. https://doi.org/10.1016/j.molliq.2018.09.040. Article 7. F. Hevia, J.A. González, C. Alonso-Tristán, I. García de la Fuente, L.F. Sanz, Orientational effects in alkanone, alkanal or dialkyl carbonate + alkane mixtures and in alkanone + alkanone or + dialkyl carbonate systems. J. Mol. Liq. 233 (2017) 517-527. https://doi.org/10.1016/j.molliq.2017.03.014. Article 8. J.A. González, F. Hevia, C. Alonso-Tristán, I. García de la Fuente, J.C. Cobos, Orientational effects in mixtures of organic carbonates with alkanes or 1-alkanols. Fluid Phase Equilib. 449 (2017) 91-103. https://doi.org/10.1016/j.fluid.2017.06.012. Part III. Discussion and conclusions ....................................................................... 251 Chapter 5. Discussion of the results ..................................................................................... 253 5.1. Introduction .............................................................................................................. 253 5.1.1. Amide + amine liquid mixtures .............................................................................. 253 5.1.2. 1-Alkanol + amine liquid mixtures ......................................................................... 253 5.1.3. Experimental data .................................................................................................. 254 5.2. Discussion of amide + amine liquid mixtures ............................................................ 255 5.2.1. Excess molar enthalpies and volumes ...................................................................... 255 5.2.2. ERAS model results ................................................................................................ 258 5.2.3. Excess relative permittivities .................................................................................. 258 5.2.4. Kirkwood-Fröhlich model results ............................................................................ 259 5.3. Discussion of 1-alkanol + amine liquid mixtures ....................................................... 260 5.3.1. Excess relative permittivities .................................................................................. 260 5.3.2. Temperature dependence of the permittivity .......................................................... 263 5.3.3. Kirkwood-Fröhlich model results ............................................................................ 264 5.4. References ................................................................................................................. 277 Chapter 6. Conclusions ........................................................................................................ 287 TABLE OF CONTENTS 9 Part IV. Appendices ............................................................................................... 289 Appendix A. Excess molar enthalpies of amide + amine mixtures and ERAS model results .... 291 A.1. Introduction .............................................................................................................. 292 A.2. Experimental ............................................................................................................. 292 A.2.1. Materials ................................................................................................................ 292 A.2.2. Apparatus and procedure ....................................................................................... 292 A.3. Results.......................................................................................................................... 295 A.4. ERAS model .............................................................................................................. 299 A.4.1. Adjustment of ERAS parameters ........................................................................... 299 A.5. Discussion .................................................................................................................. 301 A.5.1. ERAS results .......................................................................................................... 303 A.6. Conclusions ............................................................................................................... 303 A.7. Supplementary material ............................................................................................. 304 A.8. Acknowledgements .................................................................................................... 305 A.9. References ................................................................................................................. 305 Appendix B. Dielectric and refractive properties of 1-alkanol + N,N,N-triethylamine mixtures and Kirkwood-Fröhlich results ................................................................................................. 311 B.1. Introduction .............................................................................................................. 312 B.2. Experimental ............................................................................................................. 313 B.2.1. Materials ................................................................................................................ 313 B.2.2. Apparatus and procedure ....................................................................................... 313 B.3. Results ...................................................................................................................... 315 B.4. Discussion .................................................................................................................. 323 B.4.1. Relative permittivities ............................................................................................ 324 B.4.2. Excess relative permittivities .................................................................................. 325 B.4.3. Temperature dependence of the permittivity .......................................................... 328 B.4.4. Molar refraction ...................................................................................................... 329 B.4.5. Aromaticity effect ................................................................................................... 330 B.4.6. Kirkwood-Fröhlich model ....................................................................................... 330 B.5. Conclusions ............................................................................................................... 332 B.6. Supplementary material ............................................................................................. 332 B.7. Acknowledgements .................................................................................................... 335 B.8. References ................................................................................................................. 335 Appendix C. Measurement and modeling of enthalpies of solution of SO2 and NO in water .... 345 C.1. Introduction .............................................................................................................. 345 C.2. Experimental ............................................................................................................. 346 17 Equation Section (Next) Chapter 1. Introduction 1.1. About this research group The Applied Physics Department of the Faculty of Science of the University of Valladolid (in Spanish, Departamento de Física Aplicada de la Facultad de Ciencias de la Universidad de Valladolid) has a remarkably wide experience in the study of thermodynamic properties of nonelectrolyte liquid mixtures. These studies started in the 1970s with works by M.A. Villamañán [1] and J.C. Cobos [2, 3], supervised by C. Casanova –members then of the so-called Fundamental Physics Department– and collaborations with the Santiago de Compostela (Spain), Marseille and Clermont-Ferrand (France) Universities. In the mid-1980s, I. García de la Fuente [4] and J.A. González [5] began here as PhD students and, since then, never took their research activity apart from J.C. Cobos. They founded in 1994 the research group GETEF (‘Grupo Especializado en Termodinámica de los Equilibrios entre Fases’, which can be translated as ‘Group Specialized in Thermodynamics of Phase Equilibria’). The work in this PhD Thesis has been developed within the framework of this research group. 1.1.1. Members of GETEF Since the creation of the group, many researchers have been part of it: • The Professors: ▪ D. José Carlos Cobos Hernández. ▪ D. Isaías García de la Fuente. ▪ D. Juan Antonio González López. ▪ D. José Ricardo Páramo Vela. ▪ Dña. Cristina Alonso Tristán (University of Burgos). • The PhD: ▪ D. Juan María Fernández Martínez. ▪ D. Francisco Javier Carmona del Río. ▪ D. Nicolás Riesco Fernández. ▪ Dña. Susana Villa Vallejo. ▪ D. Ismael Mozo Ruiz. ▪ D. Iván Alonso Miguel. CHAPTER 1 18 ▪ D. Víctor Alonso Gómez. ▪ D. Luis Felipe Sanz del Soto. • The PhD students: ▪ D. Francisco Javier Arroyo Maestu. ▪ D. Rubén Martínez Díez. ▪ Dña. Marta Fernández Régulez. ▪ D. Juan Lobos Martín. ▪ Dña. Ángela Mediavilla Trabada. ▪ Dña. Ana Cobos Huerga. ▪ D. Luis Fernando Hevia de los Mozos. • The Bachelors: ▪ Juan Francisco Rodríguez Cogollos. ▪ Dña. María Aboy Cebrián. ▪ D. Tomás Romero Albillos. ▪ D. Miguel Ángel Rubio Hernández. ▪ D. Andrés Serna Gutiérrez. 1.1.2. Lines of research The research activity of the group is defined by a general line, which gives the group its name, and seven specific lines according to it. 1.1.2.1 General line of research The general line can be summarized as thermodynamic study of phase equilibria in gaseous, liquid and solid mixtures. The main experimental projects performed according to this line include the assembly and commissioning of experimental equipment: • A Tian-Calvet microcalorimeter. • A densimeter Anton Paar DMA 602. • A densimeter and sound analyzer Anton Paar DSA 5000. • A self-constructed experimental device for the determination of liquid-liquid and solidliquid equilibria by the observation of the phenomenon of critical opalescence. • A refractometer Bellingam + Stanley RFM970. • An experimental setup for the determination of relative permittivity including an Agilent 4294A High Precision Impedance Analyzer, 40 Hz to 110 MHz and an Agilent 16452 Liquid Test Fixture. • A differential scanning calorimeter TA Instruments DSC Q2000. Among the theoretical works carried out, the following must be highlighted: • Application of the DISQUAC (DISpersive-QUAsiChemical) model to liquid mixtures. • Application of the UNIFAC (UNIQUAC Functional-group Activity Coefficients) model, in its different versions, to liquid mixtures. • Application of the Flory model to liquid mixtures. • Application of the ERAS (Extended Real Associated Solution) model to liquid mixtures. • Application of the Kirkwood-Buff formalism for concentration fluctuations to liquid mixtures. INTRODUCTION 19 • Application of the Bhatia-Thornton formalism for concentration fluctuations to liquid mixtures. • Application of the Kirkwood-Fröhlich model for dielectrics to liquid mixtures. 1.1.2.2 Specific lines of research 1. Experimental study of associated mixtures. • Alcohol + hydrocarbon. • Alcohol + ether. • Hydroxy ether + hydrocarbon. • Hydroxy ether + ether. • Hydroxy ether + alcohol. • Hydroxy ether + hydroxy ether. • Primary or secondary amine + hydrocarbon. • Primary or secondary amine + ketone. • Amine + alcohol. • Amide + primary or secondary amine. 2. Experimental study of mixtures with purely dipolar interactions. • Ether + alkane. • Ketone + alkane. • Ketone + ether. • Organic carbonate + organic solvents. • Alkyl anhydride + organic solvents. • N,N,N-trialkylamine + alkane. • Amide + alkane. • N,N-dialkylamide + ketone. 3. Investigation of the behavior of the excess heat capacity for several fundamental theories of mixtures. • Experimental study of mixtures whose excess molar isobaric heat capacity shows a W-shaped dependence (double minimum) with concentration. • Theoretical study of W-shaped concentration dependence in excess heat capacities. First step: Strictly Regular Solution Theory. Second step: Flory Theory. 4. Application of theories based on group-contribution methods to characterize the thermodynamic properties of mixtures. • Systematic application of the DISQUAC model (purely physical theory with no association or solvation parameters) to justify the properties of all types of mixtures and phase equilibria. • Application of group-contribution models to predict vapor-liquid equilibrium and excess functions in multicomponent liquid mixtures. 5. Study of models based on the random mixing hypothesis. • Application of the Flory model to characterize orientational effects in mixtures of polar compounds with hydrocarbons or other polar compounds. • Analysis of the limitations of the Flory model with the purpose to improve the ERAS model. 6. Application of association models to explain the thermodynamic properties and phase equilibria in associated mixtures. CHAPTER 1 20 • Systematic application of the ERAS model. • Comparison of the results from the ERAS model with those from groupcontribution models. 7. Application of theories of fluctuations of concentration to study orientational and structural effects in mixtures. In particular: • The Kirkwood-Buff formalism, following Ben Naim’s method. • The Bhatia-Thornton formalism. 1.1.2.3 Other lines of research • An a priori mathematical analysis of the Wilson equation. • Determination of solid-liquid equilibria of mixtures that can form complexes in condensed phase with a Setaram DSC 111 calorimeter. • Calibration of a vibrating-tube densimeter R.-K.-Wood-type and density measurement of pure liquids and mixtures at high temperature and pressure. • Development of a latent-heat cover for greenhouses in Castilla y León. • Thermodynamic study of basic structural units in polymers (oligomers) in solution. • Determination of critical exponents from liquid-liquid equilibrium coexistence curves. • Study of the influence of the combinatory term on the prediction of thermodynamic properties of mixtures containing long-chain molecules. • Experimental study and modeling of solid-solid first-order phase transitions in mixtures of alcohols with different organic solvents. • Study of biologically interesting liquid mixtures. 1.1.3. Collaboration with other research groups GETEF has been continuously collaborating with many universities and research centers, such as: 1.1.3.1 National centers • Dr. M.A. Villamañán and collaborators (co.). Laboratorio de Termodinámica. Departamento de Ingeniería Energética y Fluidomécanica. E.T.S. de Ingenieros Industriales. Universidad de Valladolid. • Dra. M.J. Cocero and co., Dr. A. Cartón and co. Departamento de Ingeniería Química. Universidad de Valladolid. • Dr. R. Bravo and co. Departamento de Física Aplicada. Universidad de Santiago de Compostela. • Dr. A. Lainez, Dr. J.A.R. Renuncio and co. Departamento de Química-Física I. Universidad Complutense de Madrid. • Dr. S. Otín and co., Dr. P. Pérez and co., and Dr. C. Lafuente and co. Departamento de Química-Física y Química Orgánica. Universidad de Zaragoza. • Dra. C. Alonso Tristán. Departamento de Ingeniería Electromecánica. Escuela Politécnica Superior. Universidad de Burgos. • Dra. Mª Purificación Cuadrado Curto. Departamento de Química Orgánica. Universidad de Valladolid. INTRODUCTION 21 1.1.3.2 Foreign centers • Prof. J.-P.E. Grolier, A.H. Roux, G. Roux-Desgranges, Prof. J.R. Quint, Prof. J.-Y. Coxam, K. Ballerat-Busserolles and co. Université Blaise-Pascal. Clermont-Ferrand (France). • Prof. E. Wilhelm. Institut für Physikalische Chemie. Universität Wien. Vienna (Austria). • Prof. U. Domanska and Prof. T. Hofman. Department of Chemistry. Physical Chemistry Division. Faculty of Chemistry. Warsaw University of Technology. Warsaw (Poland). • Prof. S.W. Campbell. Department of Chemical Engineering. University of South Florida. Tampa, Florida (USA). • Prof. J.P. M. Trusler y Dr. A. Fenghour. Chemical Engineering and Chemical Technology Department. Imperial College. London (UK). • Dr. N. Riesco. Department of Earth Science and Engineering. Imperial College. London (UK). • Prof. J. Gmehling. Technische Chemie Department. Carl von Ossietzky Universität. Oldenburg (Germany). • Dr. I. Mozo. Universidad de Yachay. Imbabura (Ecuador). In addition, more sporadic collaborations have existed, as those with Dra. Magda Sampaio (Universidade de Lisboa, Portugal) or with Dr. A. Ait-Kaci (Université des sciences et de la technologie Houari-Boumediene, Dar el Beïda, Algeria). 1.2. About this PhD Thesis This PhD Thesis continues the exhaustive scientific work carried out by GETEF, not only following their general research lines but also the specific ones. This PhD Thesis began in October 2015 as a continuation of a Master Thesis [6] developed in the same research group in 2014-2015. It started as the first systematic investigation of thermophysical properties of amide + amine liquid mixtures, but soon its scope became wider. Not only it reached other kinds of experimental and theoretical lines of research, but it also was enriched with two international research stays at the ‘Institut de Chimie de Clermont- Ferrand’ (ICCF), in ‘Université Clermont Auvergne’, with the group MAG (‘Mécanismes d’Absorption des Gaz’), directed by Jean-Yves Coxam. 1.2.1. Experimental objectives The experimental contribution consists essentially of the measurement of thermophysical properties of binary liquid mixtures of biologically interesting molecules. Particularly: • Measurement of thermophysical properties of amide + amine mixtures (Articles 1 to 4, Appendix A). These include calorimetric, volumetric, dielectric and refractive properties. • Measurement of dielectric and refractive properties of 1-alkanol + isomeric amine mixtures (Articles 5 to 6, Appendix B). The considered amines are hexan-1-amine (HxA), N-propylpropan-1-amine (DPA) and N,N,N-triethylamine (TEA). The work continues the investigation carried out by S. Villa in her PhD Thesis [7] and is complementary to L.F. Sanz and V. Alonso’s PhD Theses [8, 9]. It allows to study the effect of the replacement of a strongly polar compound (amide) by an associated liquid (1-alkanol). CHAPTER 1 22 Complementarily, other experimental works were performed during the first of the stays in Clermont-Ferrand (Appendix C, [10]). More precisely: • Measurement of the enthalpy of solution of sulfur dioxide in water and in electrolyte aqueous solutions of sodium chloride and sodium sulfate. • Measurement of the enthalpy of solution of nitric oxide in water. The details of the measurements performed can be seen in Table 1.1. It must be noted that the isobaric heat capacity measurements have not been included in this Thesis, as their analysis is not yet finished. Table 1.1: Experimental work performed in this PhD Thesis. The properties determined are (see Chapter 2): density (  ), speed of sound (c), isentropic compressibility ( S  ), isobaric thermal expansion coefficient ( p  ), excess molar volume ( E m V ), excess isentropic compressibility ( E S  ), excess speed of sound ( E c ), excess isobaric thermal expansion coefficient ( E p  ), refractive index at the sodium D-line ( D n ), excess refractive index at the sodium D-line ( E D n ), relative permittivity at 1 MHz ( r  ), excess relative permittivity at 1 MHz ( E r  ), excess molar enthalpy ( E m H ), volumetric heat capacity ( , mmpp CVc  = ), molar isobaric heat capacity ( ,mp C ), excess molar isobaric heat capacity ( E ,mp C ), enthalpy of solution ( solH ). Device Location Measured properties Derived properties Mixtures Anton Paar DSA5000 GETEF  , c S  , p  , E m V , E S  , E c , E p  DMF + BA, HxA, DPA or DBA DMA + BA, HxA, DPA or DBA Bellingham + Stanley RFM970 GETEF D n E D n DMF + BA, HxA, DPA or DBA DMA + BA, HxA, DPA or DBA HxA + 1OH, 3OH, 4OH, 5OH or 7OH DPA + 1OH, 3OH, 4OH, 5OH or 7OH TEA + 1OH, 3OH, 4OH, 5OH or 7OH Agilent 4294A and 16452A GETEF r  E r  DMF + BA, HxA, DPA, DBA or aniline DMA + BA, HxA, DPA or DBA HxA + 1OH, 3OH, 4OH, 5OH or 7OH DPA + 1OH, 3OH, 4OH, 5OH or 7OH TEA + 1OH, 3OH, 4OH, 5OH or 7OH Setaram BT2.15 MAG E m H DMF + BA, HxA, DPA or DBA DMA + BA, HxA, DPA or DBA Setaram Micro DSC III and Micro SC MAG p c  ,mp C , E ,mp C DMF + BA, HxA, DPA or DBA DMA + BA, HxA, DPA or DBA The organic liquids used are: N,N-dimethylformamide (DMF), N,N-dimethylacetamide (DMA), butan-1-amine (BA), hexan-1-amine (HxA), N-propylpropan-1-amine (DPA), N-butylbutan-1-amine (DBA), N,N,N-triethylamine (TEA), aniline, methanol (1OH), 1-propanol (3OH), 1-butanol (4OH), 1-pentanol (5OH) and 1-heptanol (7OH). INTRODUCTION 23 Device Location Measured properties Derived properties Solutions Setaram C80 MAG solH SO2 + H2O, NaCl(aq) or Na2SO4(aq) NO + H2O The salts dissolved in water (H2O) are: sodium chloride (NaCl) and sodium sulfate (Na2SO4). The gases dissolved in water and electrolyte aqueous solutions are: sulfur dioxide (SO2) and nitric oxide (NO). 1.2.2. Theoretical objectives In addition to the exhaustive experimental work of this Thesis, a significant amount of theoretical investigations has been conducted. Some of them are related to the knowledge and interpretation of properties of amide or 1-alkanol + amine liquid mixtures: • Application of DISQUAC to justify excess molar enthalpies and heat capacities of amide + amine liquid mixtures (in progress). • Application of the ERAS model to reproduce excess molar volumes and enthalpies of amide + amine liquid mixtures (Appendix A). • Application of the Prigogine-Flory-Patterson model to describe excess molar volumes of amide + amine liquid mixtures (Article 2). • Application of the Kirkwood-Fröhlich model to interpret the permittivity for the liquid mixtures studied experimentally (amide + amine and 1-alkanol + amine, see Table 1.1; Articles 1 to 6, Appendix B). Nevertheless, other works were thought to open the scope of the Thesis: • Investigation of orientational (i.e. non-random) effects in alkanone, alkanal or dialkyl carbonate + alkane mixtures and in alkanone + alkanone or + dialkyl carbonate liquid mixtures by means of experimental data (excess molar enthalpies, volumes or isobaric heat capacities, and liquid-liquid equilibria) and the application of the Prigogine-Flory- Patterson model to describe excess molar enthalpies and volumes (Article 7). • Investigation of orientational effects in mixtures of organic carbonates with alkanes or 1- alkanols by means of experimental data (excess molar enthalpies, volumes, isobaric heat capacities, entropies or permittivities, internal pressures and liquid-liquid equilibria) and several theoretical approaches: the Prigogine-Flory-Patterson model to describe excess molar enthalpies and volumes, the Bhatia-Thornton concentration-concentration structure factor formalism, and the Kirkwood-Fröhlich model (Article 8). • Study of the dielectric behavior of binary liquid mixtures involving 1‒alkanols and strongly polar compounds (benzonitrile, nitrobenzene, ethanenitrile, nitromethane, sulfolane or dimethyl sulfoxide), using experimental data available in the literature. Application of the Kirkwood‒Fröhlich model to these mixtures (Chapter 5, [11]). • Review of the Thermodynamics and Statistical Physics of homogeneous dielectric media. Clarification of the macroscopic and microscopic hypothesis characterizing existing theories. Proposal of a consistent classification of microscopic models of dielectrics within the general modern scheme of Equilibrium Thermodynamics and Statistical Physics. In particular, careful study of the implicit macroscopic and microscopic assumptions in the Kirkwood-Fröhlich model and clear derivation of its equations as a fluctuation theory at zero electric field (Chapter 4). CHAPTER 1 24 Finally, it must be mentioned that some theoretical work was done to complement the experimental work carried out in Clermont-Ferrand, namely: • Study, programming and modeling to predict the enthalpy of solution of sulfur dioxide in water and comparison of the calculations with measured and literature data (Appendix C). 1.2.3. Scientific activities related to the PhD Thesis Conference attendance: • 14th Joint European Thermodynamics Conference (JETC). Budapest University of Technology and Economics, Department of Energy Engineering (BME, DEE). 21/05/2017 – 25/05/2017, Budapest, Hungary. • Cutting-Edge Technology for Carbon Capture, Utilization and Storage (CETCCUS). Institut de Chimie de Clermont-Ferrand, France; Sphere Technology Connection, Calgary, Canada; CALNESIS, Riom, France. 24/09/2017 – 27/09/2017, Clermont-Ferrand, France. • Thermodynamique des Équilibres Entre Phases (TEEP). Institut de Chimie de Clermont-Ferrand; Laboratoire des Multimatériaux et Interfaces, Lyon; CALNESIS, Clermont-Ferrand. 07/12/2017 – 08/12/2017, Clermont-Ferrand, France. • 23rd International Congress of Chemical and Process Engineering (CHISA 2018 Prague). Czech Society of Chemical Engineering. 25/08/2018 – 29/08-2018, Prague, Czech Republic. International courses: • Summer School and Workshop in Calorimetry 2017: Calorimetry and thermal methods in material science. Institut de Recherches sur la Catalyse et l'Environnement de Lyon (IRCELYON); Association de Calorimétrie et Effets Thermiques en Catalyse (ACETC); Societé Chimique de France; CNRS. 1.2.4. Scientific production of the author Scientific articles: 1. J.A. González, F. Hevia, A. Cobos, I.G.d.l. Fuente, C. Alonso-Tristán, Thermodynamics of mixtures containing a very strongly polar compound. 11. 1-Alkanol + alkanenitrile systems. Thermochim. Acta 605 (2015) 121-129. https://doi.org/10.1016/j.tca.2015.02.021 2. A. Cobos, F. Hevia, J.A. González, I. García De La Fuente, C. Alonso Tristán, Thermodynamics of amide + ketone mixtures. 1. Volumetric, speed of sound and refractive index data for N,N-dimethylformamide + 2-alkanone systems at several temperatures. J. Chem. Thermodyn. 98 (2016) 21-32. https://doi.org/10.1016/j.jct.2016.02.016 3. F. Hevia, A. Cobos, J.A. González, I. García de la Fuente, L.F. Sanz, Thermodynamics of Amide + Amine Mixtures. 1. Volumetric, Speed of Sound, and Refractive Index Data for N,N-Dimethylformamide + N-Propylpropan-1-amine, + N-Butylbutan-1-amine, + Butan-1-amine, or + Hexan-1-amine Systems at Several Temperatures. J. Chem. Eng. Data 61 (2016) 1468-1478. https://doi.org/10.1021/acs.jced.5b00802 INTRODUCTION 25 4. F. Hevia, A. Cobos, J.A. González, I.G. de la Fuente, V. Alonso, Thermodynamics of Amide + Amine Mixtures. 2. Volumetric, Speed of Sound and Refractive Index Data for N,N-Dimethylacetamide + N-Propylpropan-1-Amine, + N-Butylbutan-1-Amine, + Butan-1-Amine, or + Hexan-1-Amine Systems at Several Temperatures. J. Solution Chem. 46 (2017) 150-174. https://doi.org/10.1007/s10953-016-0560-0 5. C. Alonso Tristán, J.A. González, F. Hevia, I. García de la Fuente, J.C. Cobos, Liquid– Liquid Equilibria for Systems Containing 4-Phenylbutan-2-one or Benzyl Ethanoate and Selected Alkanes. J. Chem. Eng. Data 62 (2017) 988-994. https://doi.org/10.1021/acs.jced.6b00803 6. F. Hevia, J.A. González, C. Alonso-Tristán, I. García de la Fuente, L.F. Sanz, Orientational effects in alkanone, alkanal or dialkyl carbonate + alkane mixtures and in alkanone + alkanone or + dialkyl carbonate systems. J. Mol. Liq. 233 (2017) 517-527. https://doi.org/10.1016/j.molliq.2017.03.014 7. F. Hevia, J.A. González, I. García de la Fuente, L.F. Sanz, J.C. Cobos, Thermodynamics of amide + amine mixtures. 3. Relative permittivities of N,N-dimethylformamide + N- propylpropan-1-amine, + N-butylbutan-1-amine, + butan-1-amine, or + hexan-1-amine systems at several temperatures. J. Mol. Liq. 238 (2017) 440-446. https://doi.org/10.1016/j.molliq.2017.05.025 8. J.A. González, F. Hevia, C. Alonso-Tristán, I. García de la Fuente, J.C. Cobos, Orientational effects in mixtures of organic carbonates with alkanes or 1-alkanols. Fluid Phase Equilib. 449 (2017) 91-103. https://doi.org/10.1016/j.fluid.2017.06.012 9. J.A. González, C.A. Tristán, F. Hevia, I.G. De La Fuente, L.F. Sanz, Thermodynamics of mixtures containing aromatic nitriles. J. Chem. Thermodyn. 116 (2018) 259-272. https://doi.org/10.1016/j.jct.2017.09.027 10. A. Cobos, J.A. González, F. Hevia, I.G.D. La Fuente, C.A. Tristán, Thermodynamics of amide+ketone mixtures. 2. Volumetric, speed of sound and refractive index data for N,N-dimethylacetamide+2-alkanone systems at several temperatures. Application of Flory's model to tertiary amide+n-alkanone systems. J. Mol. Liq. 248 (2017) 286-301. https://doi.org/10.1016/j.molliq.2017.10.007 11. F. Hevia, J.A. González, A. Cobos, I. García de la Fuente, L.F. Sanz, Thermodynamics of amide + amine mixtures. 4. Relative permittivities of N,N-dimethylacetamide + N- propylpropan-1-amine, + N-butylbutan-1-amine, + butan-1-amine, or + hexan-1-amine systems and of N,N-dimethylformamide + aniline mixture at several temperatures. Characterization of amine + amide systems using ERAS. J. Chem. Thermodyn. 118 (2018) 175-187. https://doi.org/10.1016/j.jct.2017.11.011 12. J.A. Gonzalez, F. Hevia, L.F. Sanz, I. García de la Fuente, C. Alonso-Tristán, Thermodynamics of mixtures containing a very strongly polar compound. 12. Systems with nitrobenzene or 1-nitroalkane and hydrocarbons or 1-alkanols. Fluid Phase Equilib. 471 (2018) 24-39. https://doi.org/10.1016/j.fluid.2018.04.022 CHAPTER 1 32 1.3.3. Publication of the results The results obtained in both periods are being prepared for publication at the time of writing this manuscript, and they are shown in the appendices. 1.4. References [1] M.Á. Villamañán, Estudio termodinámico de mezclas líquidas alcohol + éter. Tesis Doctoral, 1979. Departamento de Física Fundamental, Facultad de Ciencias, Universidad de Valladolid. [2] J.C. Cobos, Montaje y puesta a punto de un microcalorímetro Tian-Calvet. Trabajo de Licenciatura, 1979. Departamento de Física Fundamental, Facultad de Ciencias, Universidad de Valladolid. [3] J.C. Cobos, Estudio termodinámico de mezclas líquidas de alcoxietanoles con disolventes orgánicos. Tesis Doctoral, 1987. Departamento de Física Aplicada II, Facultad de Ciencias, Universidad de Valladolid. [4] I. García de la Fuente, Estudio termodinámico de mezclas líquidas de carbonatos con disolventes orgánicos. Tesis Doctoral, 1987. Departamento de Física Aplicada II, Facultad de Ciencias, Universidad de Valladolid. [5] J.A. González, Estudio termodinámico de las mezclas líquidas de cetonas con alcanos mediante el modelo DISQUAC. Comparación de las predicciones del modelo UNIFAC. Tesis Doctoral, 1987. Departamento de Física Aplicada II, Facultad de Ciencias, Universidad de Valladolid. [6] F. Hevia, Estudio experimental y teórico de mezclas binarias de amidas y aminas. Trabajo Fin de Máster, 2015. Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid. [7] S. Villa, Contribución experimental y teórica al estudio de las propiedades termodinámicas de mezclas líquidas formdas por aminas y alcanos o 1-alcoholes. Tesis Doctoral, 2003. Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid. [8] L.F. Sanz, Estudio experimental y teórico de mezclas líquidas binarias formadas por 1- alcoholes y ciclohexilamina. Tesis Doctoral, 2016. Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid. [9] V. Alonso, Estudio experimental de propiedades termofísicas de mezclas binarias formadas por 1-alcohol + alcano, + éter lineal o + amina aromática primaria. Tesis Doctoral, 2016. Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid. [10] F. De Los Mozos, K. Ballerat-Busserolles, B. Liborio, N. Nénot, J.-Y. Coxam, Y. Coulier, Calorimetric and Densimetric Data to Help the Simulation of the Impact of Annex Gases Co-Injected with CO2 During Its Geological Storage, in The Three Sisters: Acid Gas Injection, Carbon Capture and Sequestration, and Enhanced Oil Recovery, Y. Wu, J.J. Carroll, and Y. Hu, Editors. 2019, Scrivener Publishing and John Wiley & Sons: USA. p. 39-54. [11] J.A. González, F. Hevia, L.F. Sanz, I.G. De La Fuente, J.C. Cobos, Characterization of 1-alkanol + strongly polar compound mixtures from thermophysical data and the application of the Kirkwood-Buff integrals and Kirkwood-Fröhlich formalisms. Fluid Phase Equilib. 492 (2019) 41-54. https://doi.org/10.1016/j.fluid.2019.03.012 33 Equation Section (Next) Chapter 2. Mixing and excess functions Thermodynamics of heterogeneous and multicomponent systems is of the greatest importance. Not only is it of great theoretical significance, but it also has many scientific and industrial applications. As a consequence, it is used every day by physicists, chemists and engineers. It covers a very wide range of subjects, and therefore an extensive treatment is beyond the scope of this chapter. Thus, it is intended to briefly summarize most of the topics used along this Thesis. In addition, the basic concepts are assumed known by the reader. In Table 2.1 we give the notation used for some thermodynamic properties used in the text, and also their expressions for an ideal mixture in the sense explained below. 2.1. Mixing functions A mixing process at constant pressure (and temperature) is understood as a thermodynamic process in which certain amounts of several pure substances (homogeneous and monocomponent systems), which at a given pressure and temperature are in the same state of aggregation, transform into an only homogeneous and multicomponent system (called a mixture) at the same pressure and temperature. As a result of intermolecular forces existing among the different structural units (atoms, molecules…) of the substances involved, the properties of the mixture cannot be obtained as a simple consequence of the properties of the pure substances separately: they are emergent properties. Thus, the extensive properties of the mixture will not be, in general, the sum of the extensive properties of the separate components. This leads to the concepts of molar property of the mixture, partial molar properties and molar mixing properties. Let X denote an extensive property of the mixture, T the temperature, p the pressure, i n the amount of substance of component i, i i nn= the total amount of substance of the mixture and ii x n n= the mole fraction of component i. The molar property of the mixture, m X , and the partial molar property of component i, m,i X , are defined by: mX Xn = (2.1) m, ,,ji i i T p n XX n  =    (2.2) CHAPTER 2 34 Table 2.1: Notation and ideal thermodynamic functions (see sections 2.2 to 2.4). Meaning of symbols: T, temperature; R, universal gas constant; i x , mole fraction of component i,  =m, id miii x VV , volume fraction of component i; i M , molar mass of pure component i; subscript “m”, molar quantity. Extensive property Symbol ( X ) id m X id m X Volume V 0 m,ii xV Entropy S −ln i i xxR −  m, ln iiii Rx S x x Gibbs function G ln i i xR xT +  m, ln iiii R xTxG x Helmholtz function F ln i i xR xT +  m, ln iiii R xTx F x Internal energy U 0 m,ii xU Enthalpy H 0 m,ii xH Isobaric heat capacity p C 0 m,ii p xC Isochoric heat capacity V C ( )        −       2 id id m m i 2, , , d p i i T pi Ti TV V x ( )   −= 2 id id id id m,m id ,m id id ppS p TT TV C C Intensive property Symbol ( X ) id X Isobaric thermal expansion coefficient  p  ,ipi Isothermal compressibility coefficient  T  ,iTi Isentropic compressibility coefficient  S ( )   − 2 id id m id id ,m p T p TV C Density  id m ii xM V Speed of sound c ( )  − id id 12 S Relative permittivity  r  r,ii Refractive index (at the sodium D-line) D n ( )  12 2 D,ii n Due to extensivity (homogeneity of degree one of the extensive state variables): ,m m i i i X x X= (2.3) The molar mixing property or function (at constant pressure) is defined as: ( ) ( ) ( ) m m m, , , , , , i i i X T p x X T p x x X T p=− (2.4) where x denotes the set of mole fractions needed to specify the composition and ( ) m, , i X T p is the molar property of the pure compound i. MIXING AND EXCESS FUNCTIONS 35 Particularly important is the well-known fact that the mixing molar volume, ( ) m,,xV Tp , is not zero. Therefore, there exists a contribution to all mixing properties at constant pressure that arises from the volume variation of the system. It depends on several factors, such as the nature and strength of intermolecular forces, the size and shape of the molecules and the supramolecular structural units, and their reorganization to form the mixture. This contribution can be quantified rigorously by means of the variation of pressure ( ) ,,p T p x that the system should experience in order to keep the volume constant: ( ) ( ) ( ) ( ) ( ) m m, m m , , , , , , , , , i i i T p T p x x xV T p T p x T pV p V xV+ = = −  (2.5) It is useful to define a mixing process at constant volume (and temperature), which is different from the constant pressure mixing only because the final state is not defined by the same pressure as before mixing, but by a volume equal to the sum of the volumes of the pure substances (at the initial pressure) separately. The molar mixing properties at constant volume are defined by: ( ) ( ) ( ) ( ) m, m m, , , , , , ,, Vi i i X T p x X T p Tp p x x x X T p= + −  (2.6) The volume variation contribution: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) m m, mm m m m m m m, , , , , , , , , , , ,, , ,, VV T p x X T p x X T p x X T p x X T p T p x x X T V x p X V x X VT − =−  =     + = − − (2.7) can be calculated with a very good degree of approximation by expanding ( ) m m m,,T VXxV−  in powers of m V . To second order, it is: ( ) 22 mm m2 mm mm ,, 1 2 Tx Tx VXX X V V VV        −      (2.8) In the majority of cases, it is easier to evaluate the derivatives in equation (2.8) in terms of derivatives with respect to p. The following expressions are useful for that purpose: mm m, , m 1 TTx Tx V XX Vp    =−       (2.9) ( )   22 m m, , m ,, m m m 2 2 2 m 11 Tx Tx TT T xx T T X X X V Vpp Vp V            =−                       (2.10) We give below the most used mixing functions at constant volume up to the first nonzero term of the series expansion: ( ) 2 m, m m m 1 2 VT F G V V     +  (2.11) m, m m p VT S S V      −  (2.12) m, m m p VT U H T V      −  (2.13) CHAPTER 2 36 2.2. Excess functions In many situations it is useful to compare the mixing functions with those of a very simple mixture model that is well known and understood. Such a model is termed ideal mixture. We will use the Lewis-Randall model, defined by a mixing molar Gibbs function id m G given by: id mln i i i xG RT x= (2.14) which is the mixing molar Gibbs function of a mixture of ideal gases (R is the universal gas constant). More details about ideal states can be found in the usual literature of the subject (e.g. [1-3]); here we are only interested in a summary of the properties used throughout this Thesis. The rest of the mixing properties of the ideal mixture can be calculated from id m G . They are tabulated in Table 2.1. Since id m0V= , ideal mixing properties at constant volume are the same as those at constant pressure. To perform the mentioned comparison of real and ideal quantities, we define the excess molar functions at constant pressure: E id id mmm mm XXX X X−−=   = (2.15) and the corresponding excess molar functions at constant volume: m, E id m, mVV XXX −=   (2.16) Between these two classes of functions there is a relationship: m, Em E m m, mVV VXX X XX  −=− =    (2.17) which allows to use the results for the molar mixing functions already obtained to calculate the excess molar functions at constant volume. Particularly, and since m E m V V=  : ( ) 2 E E E m, m m m 1 2 VT F G V V  + (2.18) E E E m, m m p VT S S V   − (2.19) E E E m, m m p VT U H T V   − (2.20) Although it does not make sense to define an intensive property of mixing, it does to talk about the deviation from ideality of an intensive property. By extension of equation (2.15), they are also called excess functions. The excess of an intensive property X is therefore defined by: E id X X X= − (2.21) where id X is the value of the property in an ideal mixture. There has been considerable confusion about the ideal value of some thermodynamic properties, but the procedure to obtain them is actually very simple: one only has to use general thermodynamic relations starting from the definition of ideal mixture. MIXING AND EXCESS FUNCTIONS 37 2.3. Speed of sound The propagation of sound waves in a fluid is, strictly speaking, a non-equilibrium phenomenon. There is, however, a sufficiently approximated method to analyze the situation in the framework of near-equilibrium Thermodynamics. When the speed of the fluid particles (macroscopic portions of fluid treatable as mechanical points) is sufficiently small, the local equilibrium hypothesis can be applied. More precisely, the speed of the fluid particles has to be smaller than p   , where p  is the amplitude of the pressure oscillation and  is the amplitude of the associated density oscillation. Both oscillations are assumed very small compared to their equilibrium values. Wave equations are characterized by the presence of a quantity having the dimensions of velocity. This quantity will be called wave velocity. The wave velocity represents the speed at which the wave would propagate with the same properties in a medium if there were no absorption or dispersion. It must be noted that, in the general case, wave velocity does not represent a phase velocity or a group velocity. In fact, in the presence of absorption or dispersion a wave packet does not preserve its shape as it moves forward, which makes it difficult to give a precise meaning to the group velocity. When there are no dispersion or absorption, both the phase velocity of a monochromatic wave and the group velocity of a wave packet are equal to the wave velocity. It is well-known that the sound in a fluid has a wave velocity, c, given by the Newton- Laplace equation [4]: 2 1 Sc  = (2.22) Consequently, the measurement of  and c allows to obtain the value of S  . In order to consider the speed of a pulse through the fluid (see section 3.1) as the wave velocity, the effect of absorption and dispersion must be negligible. This is the case when the length traveled by the pulse is sufficiently small, provided there are no important resonance processes at the range of frequencies covered by the pulse. 2.4. Dielectric and refractive properties 2.4.1. Static relative permittivity For a dielectric to be considered in thermodynamic equilibrium, it has to be linear and homogeneous, and the true electric field 1 ( E ) has to be static and uniform everywhere outside the conductors responsible of the presence of the field. Thermodynamics of systems under the action of an electric field can be made on the basis of different kinds of thermodynamic potentials. In other words, one can use different “energies” to derive the rest of the thermodynamic potentials by Legendre transformation [5]. Caution must always be exercised, since not all of them are adaptable to different situations and, more importantly, they are not necessarily consistent with the general formalism of Statistical Physics. Particularly popular is the function G whose differential is given by: 1 For more details about dielectric behavior and all the physical quantities used along section 2.4, see section 4.3. CHAPTER 2 38 ii i dG SdT Vdp M dE nd  = − + − +  (2.23) where M is the macroscopic dipole moment of the dielectric and i  is the chemical potential of species i. Actually, this should be a natural choice if we want to work with a mixing process at constant T, p and E . Nevertheless, there are sound reasons to be careful with the function G , since it is obtained by Legendre transformation of an “energy” which does not have a clear physical meaning. The reasons are the following: • The use of MEd as the electric work term, in which E is the field already modified by the polarization of the dielectric (see section 4.3), does not define an internal energy. To clarify its meaning, we exclude at first expansion work. The term MEd can be obtained from the following steps: (i) treat the volume of the dielectric as a constant, rather than a thermodynamic variable; (ii) consider the total work on the system (including the conductors) needed to modify the field produced by the conductors, 0 ()VE E Pd   + [5], where P is the polarization (macroscopic density of dipole moment); (iii) subtract the exact differential 0 ( )EdVE   = ( ) 2 02d VE  , obtaining the desired result. MEd defines de adiabatic variation of an “energy” (let us call it U ), which is the difference between two contributions: (i) an energy including the internal energy of the dielectric and all the electrostatic energy of the system and conductors; and (ii) a quantity 2 02VE  having the dimensions of energy but, as argued by Landau and Lifshitz [5], not representing the energy of any of the parts of the system (including the conductors). In the mentioned conditions, U has an exact differential: ii i EddU TdS M dn  =++ (2.24) from which equations of state can be derived consistently. • The addition of the expansion work term to different electric work approaches can lead to different expressions of the entropy variation with a change of the electric field at constant temperature and pressure. In fact, this simple addition is an approximation, as the forces on a dielectric inside the influence of an electric field do not simply reduce to the external uniform pressure exerted by a non-dielectric medium [5]. One must proceed with caution after including expansion work, because some approximations are not fully consistent and may lead to contradictions if their consequences are led sufficiently far. Being warned of this, we will follow the usual treatments of the subject and define the ideal mixture (at constant T, p and E ) by an extension of equation (2.14): id mln i i i G RT xx= (2.25) This gives id m0M= . Using the relationship between M and the relative permittivity, r  , one obtains id r  as given in Table 2.1. An equivalent definition has been given by Reis et al. [6]. 2.4.2. Refractive index The refractive index is related to the propagation of electromagnetic waves in the system. Non-static electromagnetic fields make the system undergo a non-equilibrium process. Electric MIXING AND EXCESS FUNCTIONS 39 and magnetic losses always exist, to some extent, in variable electromagnetic fields; in other words, the imaginary parts of the dielectric permittivity and magnetic permeability do not vanish, strictly speaking, for any value of the frequency different from zero. However, there exist regions of frequencies where the imaginary parts are very small compared to the real parts, called transparency ranges [5]. For sufficiently weak fields, in these regions it is possible to neglect the absorption and, in a similar way to the case of sound waves, apply the local equilibrium hypothesis. The weakness of the field guarantees that the local thermodynamic properties remain practically uniform and at their equilibrium values. Then the static result can be extrapolated to some extent to define the ideal value of the refractive index for a mixture at constant T, p, and E (Table 2.1). This definition relies on the fact that for non-magnetic fluids the refractive index at a certain frequency is given by the square root of the relative permittivity at that frequency. 2.5. Redlich-Kister equation In the present section we assume that the system is a binary mixture, like the liquid mixtures studied in this Thesis. The Redlich-Kister (RK) equation is a polynomic equation proposed by O. Redlich and A.T. Kister [7] to adjust the experimental data of an excess function ( E X ) as a function of the composition. A RK equation with m terms is of the form: ( ) ( ) ( ) ( ) 11 1 2 1 2 1 1 RK E1 00 1 2 1 mm ii ii ii X x x A x x x x A x −− == = − = − −  (2.26) Each term of the sum includes the factor 12 xx , and therefore the sum vanishes for the pure compounds. Moreover, it is expressed in terms of powers of 12 xx− so that, if the order of the components is exchanged, the only change in the coefficients is the sign of those corresponding to odd powers. The coefficients are determined by an unweighted linear least-squares regression. The number of necessary coefficients has been decided by applying an F-test of additional term [8] at a 99.5% confidence level. The standard deviation of the fit is calculated from the equation: ( ) ( ) E E E cal, exp 12 2 , 1 1N j jj XX Nm X  =  =   − −   (2.27) where the index j takes one value for each of the N experimental data E exp,j X , and E cal,j X is the corresponding value of the excess property calculated from equation (2.26). 2.6. References [1] W.E. Acree, Thermodynamic Properties of Nonelectrolyte Solutions. Academic Press, Orlando, Florida, USA, 1984. [2] J.M. Prausnitz, R.N. Lichtenthaler, E. Gomes de Azevedo, Termodinámica Molecular de los Equilibrios de Fases. 3ª ed. Prentice-Hall, Madrid, España, 2000. [3] J.M. Smith, H.C. Van Ness, M.M. Abott, Introducción a la Termodinámica en Ingeniería Química. 5ª ed. Mc-Graw Hill/Interamericana, México, 1997. CHAPTER 2 40 [4] O. Kiyohara, C.J. Halpin, G.C. Benson, Ultrasonic velocities, compressibilities, and heat capacities for binary mixtures of benzene, cyclohexane, and tetrachloromethane at 298.15 K. J. Chem. Thermodyn. 10 (1978) 721-730. https://doi.org/10.1016/0021- 9614(78)90130-1 [5] L.D. Landau, E.M. Lifshitz, Electrodinámica de los Medios Continuos. Curso de Física Teórica. Vol. 8. Reverté, 1981. [6] J.C.R. Reis, T.P. Iglesias, G. Douhéret, M.I. Davis, The permittivity of thermodynamically ideal liquid mixtures and the excess relative permittivity of binary dielectrics. Phys. Chem. Chem. Phys. 11 (2009) 3977-3986. https://doi.org/10.1039/B820613A [7] O. Redlich, A.T. Kister, Algebraic Representation of Thermodynamic Properties and the Classification of Solutions. Ind. & Eng. Chem. 40 (1948) 345-348. https://doi.org/10.1021/ie50458a036 [8] P.R. Bevington, D.K. Robinson, Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill, New York, 2000. 41 Equation Section (Next) Chapter 3. Experimental equipment In this chapter we describe the experimental devices used to perform the measurements, the working principles on which they are based, the calibration methods and, if convenient, the work done to check their proper functioning. 3.1. Densidad y velocidad del sonido. Anton Paar DSA 5000 El instrumento utilizado para la medida de la densidad y de la velocidad del sonido es el densímetro y analizador del sonido Anton Paar DSA 5000 (Figura 3.1). Este dispositivo contiene dos celdas de medida conectadas en serie (Figura 3.2), que permiten determinar simultáneamente estas dos propiedades para una misma muestra líquida. En una celda se mide la densidad mediante el método del tubo vibrante, mientras en la otra se determina la velocidad del sonido mediante el método del pulso. Figura 3.1: Anton Paar DSA 5000. Figura 3.2: Esquema de la celda de medida del Anton Paar DSA 5000. 3.1.1. El método del tubo vibrante El Anton Paar DSA 5000 es un densímetro de tubo vibrante [1, 2]. Existen muchas variantes de este tipo de densímetros, que difieren en diversos aspectos como la forma de excitación del tubo, la forma de detección de la frecuencia y amplitud de resonancia, métodos correctivos, etc. Celda densidad Termómetro Pt-100 Salida de la muestra Entrada de la muestra Celda velocidad del sonido CHAPTER 3 48 Tabla 3.6: Datos experimentales de la densidad,  , velocidad del sonido, c, volumen molar de exceso, E m V , y compresibilidad isoentrópica de exceso, E S  , del sistema ciclohexano (1) + benceno (2) en función de la fracción molar de ciclohexano, x1, a temperatura T = 298.15 K y presión p = 0.1 MPa. x1  /g·cm-3 c/m·s-1 E m V /cm3·mol-1 E S  /TPa-1 0.0519 0.866375 1291.3 0.1248 4.5 0.1033 0.859227 1284.2 0.2456 9.2 0.1512 0.853003 1279.1 0.3274 12.1 0.1999 0.846823 1273.9 0.4094 15.2 0.2463 0.841175 1269.4 0.4746 17.9 0.3141 0.833238 1263.8 0.5568 21.0 0.3487 0.829321 1261.2 0.5935 22.4 0.4012 0.823670 1257.6 0.6272 24.1 0.4539 0.818274 1254.9 0.6423 24.7 0.4977 0.813844 1252.8 0.6585 25.3 0.5558 0.808373 1250.8 0.6441 24.9 0.6204 0.802460 1249.3 0.6242 23.7 0.6598 0.799064 1248.4 0.5939 23.0 0.7045 0.795342 1247.9 0.5502 21.4 0.7519 0.791510 1247.8 0.4970 19.3 0.8097 0.787078 1248.2 0.4113 16.0 0.8433 0.784533 1248.2 0.3626 14.4 0.8960 0.780821 1249.4 0.2558 10.2 0.9475 0.777363 1251.0 0.1363 5.5 Incertidumbres estándar: ( ) uT = 0.01 K; ( ) up = 1 kPa; ( ) 1 ux = 0.0010; ( ) uc = 0.4 m·s-1; ( ) E m u V = (0.010 E m,max V + 0.005 cm3·mol-1). Incertidumbres estándar relativas: ( ) r u  = 0.0012; ( ) E rS u  = 0.015. Los valores de su volumen molar de exceso, E m V , se han obtenido con diferentes técnicas de medida, dando resultados consistentes entre sí. Handa y Benson [2] realizaron el ajuste de 164 puntos experimentales a la temperatura de 298.15 K y presión atmosférica, correspondientes a las determinaciones dilatométricas de Stokes et al. [25], de Tanaka et al. [26] y de Kumaran y McGlashan [27]. Asimismo, establecieron los valores de este E m V que se aceptan como patrón. Por otro lado, también existe para este sistema una variedad de medidas de la compresibilidad isoentrópica de exceso, E S  . Los líquidos puros utilizados son los mismos que los del calibrado, y por tanto su origen y pureza pueden consultarse en la Tabla 3.1. En la Tabla 3.5 se muestran las propiedades físicas de los compuestos puros obtenidas en este trabajo y se comparan con los valores existentes en la literatura. En la Tabla 3.6 se recogen los datos experimentales correspondientes al sistema ciclohexano (1) + benceno (2). En la Tabla 3.7 pueden verse los resultados del ajuste de los EXPERIMENTAL EQUIPMENT 49 datos de E m V y E S  a una ecuación de Redlich-Kister. En la Figura 3.3 se representan los resultados del E m V junto con los de otros trabajos anteriores, y en la Figura 3.4 se comparan todos ellos con el ajuste patrón de Handa y Benson. Los resultados de E S  se comparan con los de otros trabajos en la Figura 3.5. También se midieron las propiedades de este sistema a las temperaturas de 293.15 K y 303.15 K. Estas propiedades, junto con el cálculo de la velocidad del sonido de exceso y el coeficiente de dilatación térmica de exceso, pueden consultarse en un trabajo anterior [28] y no se documentarán aquí. Tabla 3.7: Coeficientes de ajuste de los datos experimentales de la propiedad E F a una ecuación de Redlich-Kister (ecuación (2.26)), y desviación estándar del ajuste, E ()F  (ecuación (2.27)), a temperatura T = 298.15 K y presión p = 0.1 MPa. Propiedad E F T/K A0 A1 E ()F  E m V /cm3·mol-1 298.15 2.621 0.09 0.004 E S  /TPa-1 298.15 100.4 7.2 0.2 Figura 3.3: Volumen molar de exceso, E m V , del sistema ciclohexano (1) + benceno (2) en función de la fracción molar de ciclohexano, x1. Símbolos, resultados experimentales: este trabajo (●), V. Alonso () [4], I. Alonso () [6], Mozo () [5]. Línea sólida, ajuste de Redlich-Kister de los puntos de este trabajo. CHAPTER 3 50 Figura 3.4: Diferencias entre los datos experimentales del volumen molar de exceso, E m V , y el ajuste patrón de Handa y Benson [2], E m,H&B V , del sistema ciclohexano (1) + benceno (2) en función de la fracción molar de ciclohexano, x1. Símbolos, resultados experimentales: este trabajo (●), V. Alonso () [4], I. Alonso () [6], Mozo () [5]. Líneas sólidas, diferencias de ±1%. Figura 3.5: E S  del sistema ciclohexano (1) + benceno (2) en función de la fracción molar de ciclohexano, x1. Símbolos, resultados experimentales: este trabajo (●), V. Alonso () [4], I. Alonso () [6], Mozo () [5], Tamura et al. (○) [29]. Línea sólida, ajuste de Redlich-Kister de los puntos de este trabajo. EXPERIMENTAL EQUIPMENT 51 3.2. Índice de refracción. Bellingham + Stanley RFM970 El dispositivo utilizado para la medida del índice de refracción es el refractómetro Bellingham + Stanley RFM970 (Figura 3.6 y Figura 3.7). Figura 3.6: Bellingham + Stanley RFM970. Figura 3.7: Detalle de la zona de medición del Bellingham + Stanley RFM970. Las muestras de líquido, de 10 μL, se toman con una micropipeta y se vierten sobre el prisma de medición de zafiro artificial, que tiene un índice de refracción de 1.7681 para la longitud de onda de medida (véase más abajo). La placa del prisma es de acero inoxidable y está rodeada por un plato de goteo de plástico PEEK, que tiene una buena resistencia química y ofrece aislamiento térmico. La temperatura es controlada por módulos Peltier con una precisión de 0.03 K y una estabilidad de 0.05 K, entre 273.15 K y 353.15 K. La prensa (tapa del prisma) minimiza las variaciones de temperatura, y evita la entrada de luz ambiental durante la medida. El conjunto se encuentra insertado en un armazón de espuma de poliuretano expandido de baja densidad, que aporta una buena resistencia y estabilidad mecánicas. El instrumento mide el índice de refracción a la longitud de onda de la línea D del sodio (  589 nm), D n , entre los valores 1.30 y 1.70, con una precisión de 8·10-5, mediante un método basado en la detección del ángulo límite (Figura 3.8). La fuente de luz, que no es más que un diodo LED de la longitud de onda deseada, emite luz hacia la muestra. Debido a los diferentes ángulos de incidencia en la interfaz prisma-muestra, algunos rayos se refractan hacia la muestra y otros sufren reflexión total en la cara interior del prisma. Estos últimos salen a través de otra cara del prisma y, mediante un objetivo, son enfocados hacia un circuito integrado sensible a la luz (una matriz de fotodiodos). Cierta región queda iluminada por estos rayos, mientras que la correspondiente a los rayos que no han sufrido reflexión total (por haberse refractado a través de la muestra) queda oscura. En otras palabras, idealmente existe una línea correspondiente al ángulo límite que separa la zona oscura de la zona iluminada en la matriz de fotodiodos. Es posible por tanto determinar este ángulo y, conociendo el índice de refracción del prisma, hallar el índice de refracción de la muestra. En realidad, esta línea en muchas ocasiones no está perfectamente definida, pero el fabricante indica [30] que el equipo incorpora un software que determina de forma razonablemente objetiva la posición de esa hipotética línea. Prensa Armazón Orificio de entrada de aire de refrigeración Placa del prisma Plato de goteo Prisma CHAPTER 3 52 Figura 3.8: Esquema del método de medida utilizado por los refractómetros automáticos digitales Bellingham + Stanley como el RFM970. Incluso bajando la prensa del refractómetro, la evaporación de parte de la muestra durante la medida causa que no sea lo suficientemente estable. Esto, que ya se aprecia en la medida de compuestos puros, resulta decisivo cuando se trata de mezclas. La diferencia en las presiones de vapor de los componentes se traduce en una variación de la composición durante el proceso, lo que resulta en errores sistemáticos de magnitud importante. Por ello, se ha incorporado a la prensa un tapón de teflón que, sin entrar en contacto con la muestra líquida, minimiza el volumen de aire con el que está en contacto y evita en lo posible su evaporación. Las medidas realizadas con este tapón han demostrado alcanzar la estabilidad requerida [4]. Tras la medida, se retira la muestra del prisma con un trozo de papel. Para limpiar el prisma, primero se aplica con la pipeta una cantidad aproximada de 20 μL de metanol 2 . Después, con papel secante, se frota suavemente tanto el prisma como la placa de acero inoxidable. Seguidamente, con un paño limpiador de lentes, se frota para eliminar restos adheridos a la superficie del prisma y en los bordes de la placa del prisma. Por último, se utiliza aire comprimido para terminar de secar y eliminar restos de papel que hayan podido quedar en el prisma. Antes de pasar a la siguiente medida, hay que asegurarse de que tanto el prisma como la placa de acero están completamente limpios y secos y de que no hay sobre ellos ningún resto sólido. Si el tapón o la prensa han tocado la muestra, o han acumulado parte de la condensación del vapor formado durante la medida, hay que limpiarlos de forma similar. La calibración del refractómetro se realiza cada vez que se enciende el instrumento o se cambia la temperatura de medida 3 , y se lleva a cabo mediante dos líquidos patrón, identificados por el aparato como muestra “cero” (para la cual se ha usado isoctano) y muestra “intervalo” (tolueno) [12]. La calibración con la muestra “intervalo” es recomendable y el valor de su índice de refracción ha de ser superior al del de la muestra “cero”, además de asegurar un buen intervalo índices de refracción. 2 Si la muestra no se mezcla bien con el metanol, es posible que haga falta realizar antes con otro disolvente el proceso descrito en este párrafo. Sin ir más lejos, para las medidas con 1-heptanol realizadas en esta tesis fue necesario limpiar con 1-propanol antes de proceder con el metanol. 3 Es posible saltar este paso si se desea conservar el valor de calibración anterior. EXPERIMENTAL EQUIPMENT 53 Tabla 3.8: Índice de refracción, D n , de los líquidos puros utilizados en el sistema test a temperatura T y presión p = 0.1 MPa. Propiedad T/K Ciclohexano Benceno Este trabajo Literatura Este trabajo Literatura D n 293.15 1.42638 1.42638 [14] 1.50117 1.50112 [10] 298.15 1.42367 1.42363 [14] 1.42360 [31] 1.49797 1.49792 [10] 303.15 1.42080 1.4210 [32] 1.49471 1.4949 [33] Incertidumbres estándar: ( ) uT = 0.01 K; ( ) up = 1 kPa; ( ) D un = 0.00008. Tabla 3.9: Índice de refracción, D n , y la correspondiente función de exceso, E D n , del sistema ciclohexano (1) + benceno (2) en función de la concentración de ciclohexano ( 1 x , fracción molar; 1  ; fracción de volumen) a temperatura T = 298.15 K y presión p = 0.1 MPa. 1 x 1  D n 5E D 10 n 1 x 1  D n 5E D 10 n 0.0519 0.0624 1.49251 –93 0.5590 0.6066 1.44916 –419 0.1048 0.1246 1.48717 –174 0.6204 0.6653 1.44501 –395 0.1512 0.1781 1.48281 –220 0.6598 0.7023 1.44237 –382 0.1999 0.2331 1.47819 –279 0.7045 0.7436 1.43956 –353 0.2463 0.2844 1.47405 –317 0.7519 0.7866 1.43673 –312 0.3141 0.3577 1.46818 –364 0.8097 0.8381 1.43341 –255 0.3487 0.3944 1.46507 –404 0.8481 0.8717 1.43127 –215 0.4058 0.4538 1.46040 –432 0.8960 0.9129 1.42879 –150 0.4539 0.5027 1.45676 –433 0.9475 0.9564 1.42617 –82 0.4977 0.5465 1.45348 –435 Incertidumbres estándar: ( ) uT = 0.01 K; ( ) up = 1 kPa; ( ) 1 ux = 0.0010; ( ) 1 u  = 0.004; ( ) D un = 0.00008. Incertidumbre expandida (nivel de confianza 0.95): ( ) E cD Un = 0.0002. Tabla 3.10: Coeficientes de ajuste de los datos experimentales del índice de refracción de exceso E 5 E D 10 nF = a una ecuación de Redlich-Kister (ecuación (2.26)), y desviación estándar del ajuste, E ()F  (ecuación (2.27)), a temperatura T = 298.15 K y presión p = 0.1 MPa. Propiedad E F T/K A0 A1 E ()F  5E D 10 n 298.15 –1720 77 7 CHAPTER 3 54 Figura 3.9: Índice de refracción de exceso, E D n , del sistema ciclohexano (1) + benceno (2) en función de la fracción de volumen de ciclohexano, 1  . Símbolos, resultados experimentales: este trabajo (●), González et al. () [31], Tasic et al. () [34], Ridgway y Butler () [35], Iglesias et al. (x) [36], Piñeiro et al. (○) [37]. Línea sólida, ajuste de Redlich-Kister de los puntos de este trabajo. La comprobación del calibrado puede hacerse con agua destilada, pues la experiencia ha demostrado su gran reproducibilidad. Si bien hay que tener cuidado ya que, debido a su elevada tensión superficial, la gota puede adoptar formas variopintas para las cuales se producen reflexiones parásitas que hacen que el resultado de la medida sea absurdo. A este respecto, es conveniente indicar que el indicador de calidad de la medida, que se puede leer en la pantalla, debe ser lo más próximo a 100 posible. Según el fabricante, la calidad es un valor arbitrario que se utiliza para describir el valor de una lectura. El valor de la calidad se deriva del patrón óptico producido al colocar una muestra en el prisma. Un valor alto indica un patrón óptico bien definido, lo que facilita la resolución de la señal; un valor bajo indica un patrón menos bien definido y por lo tanto una lectura menos fiable. El valor de la calidad de la muestra “cero” del calibrado se fija automáticamente a 100, lo cual se puede utilizar como una referencia con la que comparar otras muestras medidas. 3.2.1. Sistema test de índices de refracción Aunque menos documentado que el E m V , existen diversas fuentes bibliográficas que aportan el D n del sistema ciclohexano (1) + benceno (2) a la temperatura de 298.15 K y presión atmosférica. Al no existir ningún patrón aceptado de forma general, se ha escogido este sistema para comprobar la viabilidad de la determinación de D n y su propiedad de exceso, E D n , con este refractómetro. De igual manera que con el E m V , también se midió este sistema a las temperaturas de 293.15 K y 303.15 K [28], pero aquí solo se mostrarán las medidas a 298.15 K. EXPERIMENTAL EQUIPMENT 55 De nuevo, el origen y pureza de los líquidos utilizados se encuentra en la Tabla 3.1. La Tabla 3.8 muestra el índice de refracción de estos líquidos puros, mientras que los datos experimentales de D n y E D n pueden consultarse en la Tabla 3.9. Los resultados del ajuste de Redlich-Kister de los datos de E D n se muestran en la Tabla 3.10. En la Figura 3.9 se representan estos resultados de E D n y se comparan con los de otros autores. 3.3. Permitividad dieléctrica El método de medida de la permitividad que se ha empleado se basa en la determinación de la impedancia de una muestra de líquido en un condensador de placas plano-paralelas mediante el método del puente autoequilibrado. Para ello se dispone de un baño termostático Lauda RE 304, en el cual se sumerge una celda de medida de permitividades Agilent 16452A Liquid Test Fixture. La celda se conecta a un analizador de impedancias Agilent 4294A Precision Impedance Analyzer, 40 Hz to 110 MHz a través de unos cables coaxiales denominados Agilent 16048G Test Lead. El esquema del montaje experimental puede verse en la Figura 3.10. Ahora se procede a explicar el principio de medida y cada uno de los elementos del montaje. Figura 3.10: Esquema del montaje experimental. 3.3.1. El método del puente autoequilibrado en configuración 4TP El método del puente autoequilibrado es uno de los métodos más utilizados para medir impedancia. Tiene la ventaja de cubrir con mucha precisión y exactitud un intervalo de frecuencias bastante amplio (desde 20 Hz hasta 120 MHz) y también un intervalo de impedancias muy grande (incluso para valores muy pequeños). Aunque para ello no sirve cualquier configuración de medida. Al elevar la frecuencia, aparecen impedancias residuales y parásitas que afectan al resultado. Si, además, la frecuencia es suficientemente elevada, la teoría de circuitos de baja frecuencia deja de ser aplicable y hay que tener en cuenta la distribución de los parámetros eléctricos a lo largo de la línea. Para minimizar todos estos efectos, puede usarse la denominada configuración 4TP (Four-terminal pair configuration), que se caracteriza por las siguientes peculiaridades: CHAPTER 3 56 Figura 3.11: Vista esquemática del método del puente autoequilibrado en configuración 4TP. Los conductores exteriores de los cables coaxiales se encuentran conectados por la parte más cercana a la impedancia problema. Las flechas con línea continua paralelas a los hilos representan la “corriente de la señal de test”, mientras que las de línea discontinua representan la “corriente de retorno” (aunque no debe olvidarse que es una corriente alterna). El detector de cero actúa sobre el generador de la parte derecha de la figura, que produce la corriente de realimentación. • Four-terminal: Utiliza cables diferentes para llevar la corriente de la señal de test (denominados HCUR y LCUR) que para la determinación del voltaje (HPOT y LPOT). Esto permite eliminar las resistencias de contacto y otras impedancias parásitas. Los terminales denominados con una H se conectan al punto de potencial “alto” del circuito, mientras que los designados con una L miden en el punto de potencial “bajo”. • Pair: Los cables son coaxiales y por sus conductores exteriores circula la “corriente de retorno”; no están conectados a tierra, aunque lo están entre sí por su parte final (la que va conectada a la impedancia problema). El campo magnético en el exterior del cable se anula, minimizando así el efecto de la inducción mutua entre cables CUR y POT. Mediante un voltímetro vectorial se determina la diferencia de potencial entre los conductores interiores y exteriores; este método diferencial también ayuda a eliminar el efecto de la inducción mutua. Teniendo las anteriores particularidades en mente, pasamos a describir esquemáticamente (y omitiendo muchos detalles, para los que el lector es referido a la literatura del fabricante [38-40]) el método de medida (Figura 3.11). El objetivo del puente autoequilibrado es igualar la corriente r I que circula por la resistencia r R con la corriente x I que circula por la impedancia problema, Z . Para ello, cuando por el detector de cero pasa una corriente, se genera 4 una señal que se retroalimenta hacia r R para compensar esa corriente no equilibrada. El proceso debe converger 4 Para generar esta señal se utilizan componentes electrónicos de gran precisión. A grandes rasgos, dos detectores de fase separan la corriente (compleja) que sale del detector de cero en componentes perpendiculares. Las señales de salida de los detectores de fase pasan por un integrador (filtro pasa-baja) y se envían a un modulador vectorial que crea las componentes de la señal que se va a retroalimentar. Aunque el bucle tenga errores de fase, la componente de la corriente no equilibrada debida a estos errores es también detectada y compensada para anular el error en la corriente de la resistencia. EXPERIMENTAL EQUIPMENT 57 hasta que la corriente por el detector de cero es exactamente nula. Cuando el puente se ha equilibrado, el voltaje en la resistencia vale r r r rx V I R I R== y la impedancia problema puede calcularse como: r r xx x VV ZR IV == (3.7) donde x V es el voltaje en la impedancia problema. Los voltajes complejos x V y r V se determinan con un voltímetro vectorial. La resistencia r R recibe el nombre de “resistencia de intervalo” (range resistor) y es un elemento clave del circuito, pues determina el intervalo de impedancias que se puede medir. Se selecciona de entre varias en función del orden de magnitud de la impedancia problema. 3.3.2. Relación de la impedancia medida con la permitividad La impedancia problema es un condensador de placas plano-paralelas. Teóricamente, la impedancia de un condensador ideal con placas de área A separadas una distancia d (muy pequeña en relación su tamaño) y relleno de un dieléctrico de permitividad relativa compleja r  cuando está sometido a una tensión alterna de frecuencia angular  es: condensador id 0r eal d Zj A    = (3.8) La impedancia del mismo condensador vacío es: condensador ideal,0 0 d Zj A  = (3.9) Y en consecuencia r  puede obtenerse como: condensador ideal,0 condensador rideal Z Z  = (3.10) Sin embargo, existen capacidades parásitas debido, entre otras cosas, a que el tamaño de las placas no es infinito. Por ello, si en la ecuación (3.10) se sustituyen las impedancias reales, 0 Z (en vacío) y Z (con muestra), en lugar de las respectivas ideales, se obtendrá un valor rm  que diferirá del valor real r  : 0 rm r Z Z  = (3.11) Para eliminar el efecto de la capacidad parásita, Agilent propone en el manual de uso de la celda un factor de corrección que varía entre 1 (para el vacío) y  1.030 (para valores altos de rm  ): rm r rm rm 100 97.0442 2.9558    =+ (3.12) Se puede modelar esta impedancia como una resistencia y una capacidad en paralelo. Así, puede escribirse: p p 11 ZR Cj  =+ (3.13) CHAPTER 3 64 Tabla 3.12: Permitividad relativa, r  , a temperatura T y presión p = 0.1 MPa de los compuestos puros utilizados en el sistema test. Propiedad T/K Dietil carbonato Decano Este trabajo Literatura [46] Este trabajo Literatura [46] r  288.15 2.835 2.83 2.011 2.01 298.15 2.835 2.83 1.997 2.00 308.15 2.839 2.83 1.987 1.98 Incertidumbres estándar: ( ) uT = 0.01 K; ( ) up = 1 kPa; ( ) rr u  = 0.003. Tabla 3.13: Permitividad relativa, r  , y la correspondiente función de exceso, E r  , del sistema dietil carbonato (1) + decano (2) en función de la concentración de dietil carbonato ( 1 x , fracción molar; 1  ; fracción de volumen) a temperatura T y presión p = 0.1 MPa. 1 x 1  r  E r  1 x 1  r  E r  T/K = 288.15 0.1089 0.0706 2.052 –0.017 0.6008 0.4832 2.353 –0.056 0.2090 0.1410 2.101 –0.026 0.7047 0.5972 2.448 –0.055 0.3115 0.2194 2.153 –0.039 0.8027 0.7165 2.555 –0.046 0.4079 0.2997 2.211 –0.047 0.8976 0.8449 2.676 –0.031 0.5058 0.3887 2.276 –0.055 T/K = 298.15 0.1089 0.0706 2.037 –0.019 0.6008 0.4835 2.347 –0.055 0.2090 0.1412 2.090 –0.025 0.7047 0.5975 2.444 –0.054 0.3115 0.2196 2.144 –0.037 0.8027 0.7168 2.554 –0.044 0.4079 0.3000 2.202 –0.046 0.8976 0.8450 2.672 –0.033 0.5058 0.3890 2.269 –0.054 T/K = 308.15 0.1089 0.0707 2.027 –0.020 0.6008 0.4838 2.335 –0.064 0.2090 0.1413 2.073 –0.034 0.7047 0.5978 2.434 –0.062 0.3115 0.2198 2.129 –0.045 0.8027 0.7170 2.546 –0.052 0.4079 0.3002 2.188 –0.055 0.8976 0.8452 2.672 –0.035 0.5058 0.3893 2.257 –0.062 Incertidumbres estándar: ( ) uT = 0.01 K; ( ) up = 1 kPa; ( ) 1 ux = 0.0010; ( ) 1 u  = 0.004. Incertidumbre estándar relativa: ( ) rr u  = 0.003. Incertidumbre combinada relativa (nivel de confianza 0.95): ( ) E rc r U  = 0.02. EXPERIMENTAL EQUIPMENT 65 Tabla 3.14: Coeficientes de ajuste de los datos experimentales de la permitividad relativa de exceso EE r F  = a una ecuación de Redlich-Kister (ecuación (2.26)), y desviación estándar del ajuste, E ()F  (ecuación (2.27)), a temperatura T y presión p = 0.1 MPa. Propiedad E F T/K A0 A1 A2 E ()F  E r  288.15 –0.213 –0.107 –0.05 0.0012 298.15 –0.206 –0.10 –0.07 0.002 308.15 –0.242 –0.106 –0.073 0.0006 Figura 3.15: Permitividad relativa de exceso, E r  , del sistema dietil carbonato (1) + decano (2) en función de la fracción de volumen de dietil carbonato, 1  , a temperatura T y presión p = 0.1 MPa. Símbolos, resultados experimentales: este trabajo (●), V. Alonso () [4], Mosteiro et al. () [46]. Línea sólida, ajuste de Redlich-Kister de los puntos de este trabajo. T/K = 288.15 T/K = 298.15 T/K = 308.15 CHAPTER 3 66 En la Tabla 3.11 puede consultarse el origen y pureza de los compuestos puros usados. Su permitividad relativa, r  , puede verse en la Tabla 3.12. Los datos experimentales de r  de las mezclas y su correspondiente magnitud de exceso, E r  , se encuentran en la Tabla 3.13. Los datos de E r  se han ajustado a una ecuación de Redlich-Kister, y la Tabla 3.14 recoge los coeficientes y desviación estándar de los ajustes. Estos resultados se representan en la Figura 3.15 junto con los resultados de V. Alonso y de Mosteiro et al. para su comparación. 3.4. Entalpía molar de exceso Las entalpías molares exceso (o de mezcla) se han medido mediante un calorímetro Setaram BT2.15 adaptado a una celda para calorimetría de flujo. Estas medidas se llevaron a cabo durante la estancia de realizada en 2018 en el Institut de Chimie de Clermont-Ferrand. 3.4.1. Montaje experimental El esquema del montaje experimental puede verse en la Figura 3.16. El calorímetro Setaram BT2.15 consta de un gran bloque calorimétrico y dos orificios, en los que se pueden alojar dos celdas, una de medida y una de referencia. Los orificios están rodeados de sendas termopilas (termopares conectados en serie) que detectan el flujo de calor entre las celdas y el bloque calorimétrico. Este último se aloja en una camisa interna que puede rellenarse con un líquido refrigerante, como por ejemplo nitrógeno líquido. Los fluidos circulan por tubos de acero inoxidable de 1.6 mm de diámetro exterior y 1.0 mm de diámetro interior, y son inyectados en el sistema mediante sendas bombas de jeringuilla modelo Teledyne ISCO 260 D Syringe Pump, que están conectadas a su vez a un controlador Teledyne ISCO D-Series Pump Controller. Las diferentes concentraciones se obtienen variando los flujos proporcionados por las bombas. El flujo en volumen puede variarse desde 1 μL·min-1 hasta 25 mL·min-1, con una incertidumbre estándar relativa del 0.5%. La capacidad de las bombas es de 266.05 mL, y pueden regularse hasta una presión de 52 MPa con una incertidumbre estándar relativa del 2%. Para asegurar la estabilidad del flujo molar y con ello la fracción molar, los fluidos en las bombas se mantienen a una temperatura constante de 298.15 K mediante un baño termostático Fisher Scientific Polystat 36, con una estabilidad de 0.03 K. La presión en el sistema se mantiene constante mediante un regulador de presión colocado a la salida del recorrido del flujo. La presión relativa a la presión atmosférica se mide junto con la temperatura ambiente por medio de un transductor Keller conectado al ordenador. Este sensor puede medir hasta 40 MPa con una incertidumbre estándar relativa del 0.25%. Para controlar la temperatura del bloque calorimétrico, se enfría inicialmente haciendo circular un fluido termostatado a 10 K por debajo de la temperatura del experimento, usando un baño ultra-criostático Julabo FL1201. Después se regula la temperatura calentando el bloque mediante una unidad Setaram G11 Universal Controller con una estabilidad de 0.01 K La temperatura de los fluidos inyectados se ajusta a la temperatura de trabajo del calorímetro mediante un prerrefrigerador externo y un precalentador interno. El prerrefrigerador externo se encuentra encima del bloque calorimétrico y está conectado en serie al compartimento por donde circula el fluido que enfría el bloque calorimétrico y al baño Julabo FL1201. El precalentador interno se encuentra dentro del bloque calorimétrico; suministra la potencia necesaria para alcanzar la temperatura exacta del experimento por medio de cartuchos EXPERIMENTAL EQUIPMENT 67 calefactores, y su temperatura se controla mediante una resistencia de platino conectada a un controlador PID Fluke Hart Scientific 2200 con una estabilidad de 0.01 K. Se ha trabajado con una única celda, prescindiendo del montaje diferencial. La celda está diseñada de modo que los fluidos se comienzan a mezclar en un punto en la parte inferior, y después hacen un largo recorrido en espiral hasta que llegan de nuevo a la parte superior. Con esto se busca que todo el proceso de mezcla se produzca en la celda y pueda ser detectado completamente por la termopila. La señal (fuerza electromotriz) de la termopila correspondiente se mide con un multímetro digital de 6 ½ dígitos Keysight 34401A. Éste está conectado a un ordenador a través de un puerto GPIB y, con ayuda de un programa en lenguaje VEE, se representa en tiempo real la señal en función del tiempo y se guarda en archivos de texto. Figura 3.16: Esquema del montaje experimental utilizado para la medida de la entalpía de mezcla. CHAPTER 3 68 3.4.2. Principio de medida del calorímetro La calorimetría de flujo se basa en la medida del flujo de calor que se produce en la celda de medida cuando se introducen a través de ella unos flujos de materia constantes en el tiempo y se espera hasta alcanzar el estado estacionario. El efecto térmico a medir se produce en una zona del bloque calorimétrico que puede dividirse en tres partes: • La parte exterior, que se mantiene a una temperatura regulada constante. • La parte interior, donde se encuentra la celda de medida y de donde procede el flujo de calor que se desea medir. • La parte intermedia, donde se encuentra la termopila. Se admitirán como válidas las siguientes hipótesis en el estado estacionario: • Las temperaturas de la parte exterior y la parte interior son uniformes a lo largo de toda su longitud. En consecuencia, en el estado estacionario se produce una diferencia de temperatura entre ambas partes que es constante y uniforme. • A una temperatura exterior fija, el flujo de calor total entre la parte interior y la exterior es proporcional a la diferencia de temperaturas entre ellas. Esta proporcionalidad puede entenderse de forma similar a la ley de Fourier de conducción del calor. • A una temperatura exterior fija, la fuerza electromotriz producida en la termopila por efecto Seebeck es proporcional a la diferencia de temperatura entre la parte interior y la parte exterior. En virtud de estas relaciones de proporcionalidad, es evidente que la fuerza electromotriz (señal de la termopila), S, deberá ser proporcional al flujo de calor, P: S kP= (3.17) donde la sensibilidad, k, será una función de la temperatura de la parte exterior, es decir, de la temperatura a la que se regule el calorímetro. Esta constante se determina con una calibración adecuada. Básicamente, la calibración puede realizarse o bien de forma puramente eléctrica, suministrando una potencia eléctrica con un elemento calefactor (típicamente una resistencia de platino), o bien mediante un ajuste de los datos de la medida de un sistema patrón cuya entalpía molar de exceso sea conocida. La entalpía de exceso, E m H , cuando se introduce un flujo molar 1 n del líquido (1) y uno 2 n del líquido (2) a través de la celda se determina como sigue. Si los líquidos no se mezclaran al pasar por la celda, se produciría un flujo de calor LB P y una correspondiente señal en la termopila LB S que serían próximos a cero. Esta señal se denomina línea de base, y corresponde a la señal que se produce al entrar los líquidos sin mezclarse con esos flujos molares. Al producirse la mezcla, el flujo de calor tomará un valor P, correspondiente a una señal S generada en la termopila, y se tendrá: ( ) LB 12 m2 ELB 1 P P S S Hn n k n n −− == ++ (3.18) La fracción molar del componente i, i x , se calcula como: 12 i in xnn =+ (3.19) EXPERIMENTAL EQUIPMENT 69 Y los flujos molares i n se relacionan con los flujos volumétricos programables en las bombas, i V , a través de la masa molar i M y de la densidad del compuesto, i  , a la presión de trabajo y a la temperatura a la que se encuentran en las bombas (regulada por el baño termostático): i i ii V nM  = (3.20) 3.4.3. Procedimiento de medida y calibración Tanto para la calibración como para las medidas el procedimiento a seguir es similar. Antes de introducir nuevos líquidos en las bombas, éstas se limpian llenándolas con etanol y haciéndolo fluir hacia el sistema. Una vez hecho esto, se procede a secar cada una de las bombas (primero una y después la otra). Para ello, se conecta nitrógeno seco a presión a la entrada de bomba y se deja fluir por el sistema durante un tiempo prudencial (20 minutos suele ser suficiente). Durante ese tiempo, conviene crear “pulsos” de sobrepresiones cerrando y abriendo la válvula de salida de la bomba, ya que esto ayuda a secar gotas que se hayan quedado adheridas. Después se procede a llenar las bombas con los líquidos. Antes de empezar a medir, se debe hacer fluir cada uno de los líquidos hasta que la línea hasta la celda esté llena con ellos. Para realizar una medida (o tomar la línea de base), se ajustan los flujos de las bombas a los valores deseados y se espera hasta el estado estacionario, es decir, a que el promedio de la señal de la termopila sea constante en el tiempo. En esta Tesis se han determinado las entalpías de exceso de mezclas binarias amida + amina a presión de 0.1 MPa y temperatura de 298.15 K. La sensibilidad del calorímetro a esta temperatura se ha determinado tomando como patrón los datos de Ott et al. [47, 48] de la entalpía de exceso del sistema etanol + agua. La calibración arrojó un resultado para la sensibilidad de k = 32.0 mV·mW-1, estimándose una incertidumbre estándar relativa del 2%. Teniendo en cuenta la incertidumbre de los flujos, de la densidad, de la sensibilidad y de la señal de la termopila, se estima que la incertidumbre estándar relativa de la entalpía de exceso es, a lo sumo, del 5%. Valores del 5% se han alcanzado solamente en el caso de señales muy pequeñas correspondientes a los extremos de concentración, mientras que típicamente suelen presentarse valores del 3%. La incertidumbre estándar relativa de la fracción molar se estima en un 0.4%. 3.5. Referencias [1] O. Kratky, H. Leopold, H. Stabinger, Determination of density of liquids and gases to an accuracy of 10-6 g/cm3, with a sample volume of only 0.6 cm3. H. Z. Angew. Phys. 27 (1969) 273-277. [2] Y.P. Handa, G.C. Benson, Volume changes on mixing two liquids: A review of the experimental techniques and the literature data. Fluid Phase Equilib. 3 (1979) 185-249. https://doi.org/10.1016/0378-3812(79)85010-4 [3] O. Kiyohara, G.C. Benson, Determination of Excess Volumes of Cyclohexane + Benzene Mixtures with a Mechanical Oscillator Densimeter. Can. J. Chem. 51 (1973) 2489-2491. https://doi.org/10.1139/v73-373 [4] V. Alonso, Estudio experimental de propiedades termofísicas de mezclas binarias formadas por 1-alcohol + alcano, + éter lineal o + amina aromática primaria. Tesis Doctoral, 2016. Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid. CHAPTER 3 70 [5] I. Mozo, Estudio experimental y teórico de mezclas binarias de n-butan-1-ol, di-n- butiléter y celosolvas. Tesis Doctoral, 2010. Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid. [6] I. Alonso, Estudio experimental y teórico de mezclas binarias de aminas y cetonas. Tesis Doctoral, 2014. Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid. [7] T.J. Fortin, A. Laesecke, M. Freund, S. Outcalt, Advanced calibration, adjustment, and operation of a density and sound speed analyzer. J. Chem. Thermodyn. 57 (2013) 276- 285. https://doi.org/10.1016/j.jct.2012.09.009 [8] U. Kaatze, E. Frieder, L. Karl, Ultrasonic velocity measurements in liquids with high resolution—techniques, selected applications and perspectives. Meas. Sci. Technol. 19 (2008) 062001. https://doi.org/10.1088/0957-0233/19/6/062001 [9] D. Schneditz, T. Kenner, H. Heimel, H. Stabinger, A sound ‐ speed sensor for the measurement of total protein concentration in disposable, blood ‐ perfused tubes. J. Acoust. Soc. Am. 86 (1989) 2073-2080. https://doi.org/10.1121/1.398466 [10] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic solvents: physical properties and methods of purification. Wiley, New York, 1986. [11] K. Tamura, K. Ohomuro, S. Murakami, Speeds of sound, densities, and isentropic compressibilities of {xC7H16 + (1 − x)C6H6} at 293.15 and 303.15 K. J. Chem. Thermodyn. 16 (1984) 121-125. https://doi.org/10.1016/0021-9614(84)90143-5 [12] K.N. Marsh, Recommended reference materials for the realization of physicochemical properties. Blackwell Scientific Publications, Oxford, UK, 1987. [13] J. Nath, Speeds of sound in and isentropic compressibilities of (n-butanol+n-pentane, or n-hexane, or n-heptane, or n-octane, or 2,2,4-trimethylpentane, or carbon tetrachloride) at T=293.15 K. J. Chem. Thermodyn. 29 (1997) 853-863. https://doi.org/10.1006/jcht.1997.0200 [14] A. Rodrıguez, J. Canosa, J. Tojo, Physical properties of the binary mixtures (diethyl carbonate + hexane, heptane, octane and cyclohexane) from T=293.15 K to T=313.15 K. J. Chem. Thermodyn. 35 (2003) 1321-1333. https://doi.org/10.1016/S0021- 9614(03)00096-X [15] M. Nishimoto, S. Tabata, K. Tamura, S. Murakami, Thermodynamic properties of the mixture of methoxyethanol and cyclohexane: Measurements at the temperatures 293.15, 298.15 and 303.15 K above and below UCST. Fluid Phase Equilib. 136 (1997) 235-247. https://doi.org/10.1016/S0378-3812(97)00128-3 [16] K. Tamura, S. Murakami, Speeds of sound, isentropic and isothermal compressibilities, and isochoric heat capacities of {xc-C6H12 + (1 − x)C6H6} from 293.15 to 303.15 K. J. Chem. Thermodyn. 16 (1984) 33-38. https://doi.org/10.1016/0021-9614(84)90072-7 [17] H. Doi, K. Tamura, S. Murakami, Thermodynamic properties of aqueous solution of 2- isobutoxyethanol at T = (293.15, 298.15, and 303.15) K, below and above LCST. J. Chem. Thermodyn. 32 (2000) 729-741. https://doi.org/10.1006/jcht.1999.0645 [18] M. Dzida, S. Ernst, Speed of Sound in Propan-1-ol + Heptane Mixtures under Elevated Pressures. J. Chem. Eng. Data 48 (2003) 1453-1457. https://doi.org/10.1021/je030136n [19] A.J. Treszczanowicz, Y.P. Handa, G.C. Benson, Excess volumes and isentropic compressibilities of decan-1-ol + 2,2-dimethylbutane and + 2,2,4-trimethylpentane. J. Chem. Thermodyn. 14 (1982) 871-881. https://doi.org/10.1016/0021-9614(82)90161-6 [20] J. Nath, Speeds of sound in and isentropic compressibilities of (n-butanol + n-pentane) at T=298.15 K, and (n-butanol + n-hexane, or n-heptane, or n-octane, or 2,2,4- EXPERIMENTAL EQUIPMENT 71 trimethylpentane) at T=303.15 K. J. Chem. Thermodyn. 30 (1998) 885-895. https://doi.org/10.1006/jcht.1998.0358 [21] B. Orge, A. Rodríguez, J.M. Canosa, G. Marino, M. Iglesias, J. Tojo, Variation of Densities, Refractive Indices, and Speeds of Sound with Temperature of Methanol or Ethanol with Hexane, Heptane, and Octane. J. Chem. Eng. Data 44 (1999) 1041-1047. https://doi.org/10.1021/je9900676 [22] E. Junquera, G. Tardajos, E. Aicart, Speeds of sound and isentropic compressibilities of (cyclohexane + benzene and (1-chlorobutane + n-hexane or n-heptane or n-octane or ndecane) at 298.15 K. J. Chem. Thermodyn. 20 (1988) 1461-1467. https://doi.org/10.1016/0021-9614(88)90041-9 [23] L.M. Trejo, M. Costas, D. Patterson, Effect of molecular size on the W-shaped excess heat capacities: oxaalkane-alkane systems. J. Chem. Soc. Faraday. Trans 87 (1991) 3001- 3008. https://doi.org/10.1039/FT9918703001 [24] J.P.E. Grolier, G. Roux-Desgranges, M. Berkane, E. Jiménez, E. Wilhelm, Heat capacities and densities of mixtures of very polar substances 2. Mixtures containing N, N-dimethylformamide. J. Chem. Thermodyn. 25 (1993) 41-50. https://doi.org/10.1006/jcht.1993.1005 [25] R.H. Stokes, B.J. Levien, K.N. Marsh, A continuous dilution dilatometer the excess volume for the system cyclohexane + benzene. J. Chem. Thermodyn. 2 (1970) 43-52. https://doi.org/10.1016/0021-9614(70)90062-5 [26] R. Tanaka, O. Kiyohara, P.J. D'Arcy, G.C. Benson, A Micrometer Syringe Dilatometer: Application to the Measurement of the Excess Volumes of some Ethylbenzene Systems at 298.15K. Can. J. Chem. 53 (1975) 2262-2267. https://doi.org/10.1139/v75-317 [27] M.K. Kumaran, M.L. McGlashan, An improved dilution dilatometer for measurements of excess volumes. J. Chem. Thermodyn. 9 (1977) 259-267. https://doi.org/10.1016/0021- 9614(77)90045-3 [28] F. Hevia, Estudio experimental y teórico de mezclas binarias de amidas y aminas. Trabajo Fin de Máster, 2015. Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid. [29] K. Tamura, K. Ohomuro, S. Murakami, Speeds of sound, isentropic and isothermal compressibilities, and isochoric heat capacities of {xc-C6H12+(1−x)C6H6}, x{CCl4+(1−x)C6H6}, and x{C7H16+(1−x)C6H6} at 298.15 K. J. Chem. Thermodyn. 15 (1983) 859-868. https://doi.org/10.1016/0021-9614(83)90092-7 [30] Bellingham+Stanley, Technical Bulletin R001: Principles of Refractometry. [31] B. González, I. Domínguez, E.J. González, Á. Domínguez, Density, Speed of Sound, and Refractive Index of the Binary Systems Cyclohexane (1) or Methylcyclohexane (1) or Cyclo-octane (1) with Benzene (2), Toluene (2), and Ethylbenzene (2) at Two Temperatures. J. Chem. Eng. Data 55 (2010) 1003-1011. https://doi.org/10.1021/je900468u [32] D. Gómez-Díaz, J.C. Mejuto, J.M. Navaza, Physicochemical Properties of Liquid Mixtures. 1. Viscosity, Density, Surface Tension and Refractive Index of Cyclohexane + 2,2,4-Trimethylpentane Binary Liquid Systems from 25 °C to 50 °C. J. Chem. Eng. Data 46 (2001) 720-724. https://doi.org/10.1021/je000310x [33] A.K. Nain, Refractive Indices of Binary Mixtures of Tetrahydrofuran with Aromatic Hydrocarbon at Temperatures from (288.15 to 318.15) K. J. Chem. Eng. Data 53 (2008) 850-853. https://doi.org/10.1021/je700564c CHAPTER 3 72 [34] A.Z. Tasic, B.D. Djordjevic, D.K. Grozdanic, N. Radojkovic, Use of mixing rules in predicting refractive indexes and specific refractivities for some binary liquid mixtures. J. Chem. Eng. Data 37 (1992) 310-313. https://doi.org/10.1021/je00007a009 [35] K. Ridgway, P.A. Butler, Physical properties of the ternary system benzene-cyclohexane- hexane. J. Chem. Eng. Data 12 (1967) 509-515. https://doi.org/10.1021/je60035a012 [36] M. Iglesias, B. Orge, J. Tojo, Speeds of sound, densities, refractive indices, and isentropic compressibilities of {x1C6H6 + x2c-C6H12 + (1 - x1 - x2)C6H5Cl} at the temperature 298.15 K. J. Chem. Thermodyn. 26 (1994) 1179-1185. https://doi.org/10.1006/jcht.1994.1137 [37] Á. Piñeiro, P. Brocos, A. Amigo, M. Pintos, R. Bravo, Prediction of Excess Volumes and Excess Surface Tensions from Experimental Refractive Indices. Phys. Chem. Liq. 38 (2000) 251-260. https://doi.org/10.1080/00319100008030275 [38] Agilent-Technologies, Agilent 4294A Precision Impedance Analyzer Service Manual, Third Edition. 2009. [39] Agilent-Technologies, Agilent 4294A Precision Impedance Analyzer Operation Manual, Seventh Edition. 2003. [40] Keysight-Technologies, Impedance Measurement Handbook, Sixth Edition. 2016. [41] Agilent-Technologies, Agilent 4294A Precision Impedance Analyzer - Technical overview. [42] L.F. Sanz, Estudio experimental y teórico de mezclas líquidas binarias formadas por 1- alcoholes y ciclohexilamina. Tesis Doctoral, 2016. Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid. [43] G.-Z. Jia, K.-M. Huang, L.-J. Yang, X.-Q. Yang, Composition-Dependent Dielectric Properties of DMF-Water Mixtures by Molecular Dynamics Simulations. Int. J. Mol. Sci. 10 (2009) 1590-1600. https://doi.org/10.3390/ijms10041590 [44] G.-Z. Jia, Q. Jie, W. Feng, Hydrogen bond analysis in alcohol (1-Propanol, 2-Propanol and Glycerol)-DMF mixtures based on dielectric spectroscopy. J. Mol. Struct. 1100 (2015) 354-358. https://doi.org/10.1016/j.molstruc.2015.07.065 [45] G.-Z. Jia, J.-C. Liu, The hydrogen bonding dynamics and cooperative interactions of DMAC–water mixture studied by dielectric relaxation spectroscopy. Phys. Chem. Liq. 52 (2014) 608-617. https://doi.org/10.1080/00319104.2014.890896 [46] L. Mosteiro, E. Mascato, B.E. de Cominges, T.P. Iglesias, J.L. Legido, Density, speed of sound, refractive index and dielectric permittivity of (diethyl carbonate + n -decane) at several temperatures. J. Chem. Thermodyn. 33 (2001) 787-801. https://doi.org/10.1006/jcht.2000.0779 [47] J.B. Ott, C.E. Stouffer, G.V. Cornett, B.F. Woodfield, R.C. Wirthlin, J.J. Christensen, U.K. Deiters, Excess enthalpies for (ethanol + water) at 298.15 K and pressures of 0.4, 5, 10, and 15 MPa. J. Chem. Thermodyn. 18 (1986) 1-12. https://doi.org/10.1016/0021- 9614(86)90036-4 [48] J.B. Ott, G.V. Cornett, C.E. Stouffer, B.F. Woodfield, C. Guanquan, J.J. Christensen, Excess enthalpies of (ethanol+water) at 323.15, 333.15, 348.15, and 373.15 K and from 0.4 to 15 MPa. J. Chem. Thermodyn. 18 (1986) 867-875. https://doi.org/10.1016/0021- 9614(86)90121-7 73 Equation Section (Next) Chapter 4. Theoretical models The theoretical models used to analyze and interpret experimental data of liquids and liquid mixtures are briefly presented. The physical hypotheses and the final equations are stated. References to the original works are given for the interested reader. Special emphasis is put on the concepts behind the Kirkwood-Fröhlich model for dielectrics. Some equations of the model are derived using a new approach, clearer than the original and subsequent works. 4.1. Prigogine-Flory-Patterson model The Flory model [1-5] is a purely physical theory. It is essentially a theory of the Van der Waals type, taking into account free volume and also attractive intermolecular interactions. The main feature of the Flory model is the random mixing hypothesis, and serves as a tool to evaluate if orientational (i.e., non-random) effects are relevant in the mixtures. 4.1.1. Hypotheses for pure liquids In the Flory model, a liquid, occupying the volume V , is formed by N molecules (of mean volume m/v V N= ), each of which is divided into r segments. The mean volume of a segment is denoted sm //v V rN v r== . A segment is an arbitrarily chosen isomeric portion of the molecule; its precise definition is left open and may be adapted to circumstances. The core volume of a molecule is defined as ms v rv  = , where s v is the core volume of a segment. Each segment is endowed with s contacts. The interactions considered are: (i) An attractive intermolecular interaction between pairs of contacts, with a mean potential energy per pair of the form s /v  − , where  is a positive constant of the liquid considered. (ii) A repulsive interaction, leading to a free volume term in the partition function [6]. (iii) The effect of the rest of the intramolecular interactions is treated assuming [7] that the 3r degrees of freedom of a molecule can be divided into two uncoupled categories, i.e., internal (not appreciably affected by neighbors in the liquid, and therefore dependent only on temperature) and external (dependent on molar volume as well as on temperature). For fluids with densities of liquids, the intramolecular potentials associated with the latter degrees of freedom are supposed to merely restrict the degrees of freedom per molecule from 3r to an effective number of 3rc . The constant 1c would take into account the restrictions on the precise location of a segment by its neighbors in the same chain. Some parameters of the model are better replaced by the reduction parameters p and T , defined together with the reduced parameters of CHAPTER 4 80 ( ) ( ) 3 ,, m, m, ,, 33 43 ppii iip i p i T VVT       −  = −+  + (4.31) ( ) ( ) , m, 1 2 1 2 2 4 2 4 1 2 11 i i i p i ii i i K K K vh KV RT  −     −− =   ++ (4.32) ( ) ,, 1 , 2 ,i p p T ii i ip i ii pV v TT h       −    = − −      (4.33) 43 13 1 i i i V TT V =− (4.34) If the pure compound is not self-associated, then i v  , i h  , i K are zero. Note that in such a case the above relations reduce to those of the Flory model with 0p . The mixing rules for the reduction parameters are the same as in the Flory model (equations (4.4) to (4.8)). In the context of this model, i s is the so-called surface-to-volume ratio of molecule i, and i  and i  are the reduction volume fraction and the surface fraction respectively. The total relative molecular volumes and surfaces of the compounds were calculated additively on the basis of the group volumes and surfaces recommended by Bondi [15]. Using i s calculated in this way, AB S is automatically determined. We must remark that i  and i  are different quantities from the homologous ones in the Flory model because, although they are obtained using the same equations, the reduction volumes are defined differently (as has been previously mentioned). The thermal equation of state (4.2) from the Flory model holds for both the pure compounds and the mixture, provided the reduction parameters are obtained from equations (4.31) to (4.34). Another important quantity in the model is the volume fraction of monomeric species of i in the mixture, 1i  . They can be calculated numerically from the following system of two equations: ( ) ( ) ABm,A 1B 1A m,B 1B 12 A AB A 11 1 VK VK K      =+   − − (4.35) ( ) AB B1B 1A 1A 1B 2A B 11 1 K K K     =+  − − (4.36) The volume fractions of monomeric species in the pure compounds, 0 1i  , are: 0 12 142 1 2 ii i i K K K  + − + = (4.37) We will focus only on the equations to calculate E m H and E m V . These are obtained from: ( ) E E E m m,phys m,chem ,F F F F H V= + = (4.38) THEORETICAL MODELS 81 The physical contributions, E m,phys F , are obtained in the same way as in the Flory model but with the variables defined in this section. The chemical contributions, E m,chem F , are calculated from: ( ) ( ) ( ) ( ) ( ) * 0 * 0 A A A B B B A * A AB AB E m,chem 1A 1A 1B 1B 1B 1A m,B m,A 1B BBA1B 1 1 V V x x x v K v K K KKV vK V        = − + −  −    +−  + (4.39) ( ) ( ) ( ) ( ) ( ) * 0 * 0 A A A B B B A * A AB E m,chem 1A 1A 1B 1B E m,chem 1B 1A m,B m,A A1B 1B B2 B AB 1 1 H x x V V x h K h K p K hK KK V VV         − + = − + − − +− (4.40) Parameters adjustable to excess properties are: i K , AB K , i h  , AB h  , i v  , AB v  and AB X . The number of adjustable parameters can be reduced by fitting the parameters i K , i h  and i v  of a self-associated compound to E m H and E m V data of its mixture with an appropriate inert compound, or to enthalpy of vaporization data. The molar enthalpy of vaporization, v m,i H , of a pure compound in the ERAS model is calculated as: vm m, ,12 2 41 ii i ii ii i K Hh pV KT KV R  + − +  = +− (4.41) 4.3. Kirkwood-Fröhlich model 4.3.1. Dielectric behavior In the presence of an external electric field, a dielectric gives rise to a macroscopic dipole moment, due to some well-defined physical processes: • Induced polarization, which includes the polarization mechanisms due to the elastic displacement of charges under the field. There are two classes of induced polarization: electronic polarization, in which the electron cloud surrounding atomic nuclei moves in the opposite sense to the field, and atomic (or ionic) polarization, by which ions of different charge sign in a molecule or crystal are displaced in opposite senses from their equilibrium positions. • Orientational polarization, due to the partial orientation of the permanent dipole moments in the presence of a field. It is not present in nonpolar substances. • Interfacial polarization, present in many non-homogeneous (multiphasic, porous, polycrystalline, with crystal defects…) materials, arises because of the motion of free charge across the interphases subject to the action of the field. It is possible to decompose the high complexity of the dielectric response of a system in such a way because the characteristic time of each of the polarization mechanisms described above is different. For a static field, all of them work at the same time and it is not possible to physically distinguish among them. In contrast, harmonic fields excite only some of these contributions depending on the value of their frequency. CHAPTER 4 82 More precisely, in the case of time-varying fields, the fact that matter shows a nonzero response time implies the existence of a delay of the polarization with respect to the electric field. The weak-field linear relationship between polarization and field must then account for the value of the field in all the earlier instants of time, therefore taking an integral form. The linear relation is simplified to a simple proportionality after a Fourier expansion, thus defining the complex relative permittivity. This is a very well-known fact from electromagnetic theory. But it is worthwhile to summarize the main properties of this frequency-dependent function. The imaginary part is related to energy dissipation and remains close to zero except for some absorption peaks in regions where notable phenomena occur. The first group of them are relaxation processes, in which interfacial or orientational polarization stop contributing. In contrast, in resonance processes ions or electrons absorb energy when their vibration enters into resonance under the action of the field at a critical frequency. For frequencies higher than the resonances, the induced polarization mechanisms associated to these charges stop contributing. These absorption peaks of the imaginary part as a function of frequency are significantly wider in relaxation than in resonance, since the latter are due to electronic or ionic transitions between discrete energy levels. The real part is approximately constant in certain frequency ranges, in which well-defined polarization mechanisms are in operation, and varies in the regions in which the aforementioned absorption peaks appear. It is at frequencies immediately higher than these peaks where the polarization mechanisms related to them are uncoupled from the excitation caused by the field. Thus, interfacial polarization has a very high response time, as the distances that the free charge has to cover are large compared to atomic and molecular lengths; therefore, it only contributes at very low frequencies (and in non-homogeneous materials). Orientational polarization usually ceases to contribute in the microwave region, since at higher frequencies the dipoles cannot rotate at the speed imposed by the external field. Atomic polarization typically has peaks in the infrared, and electronic polarization in near-infrared, visible and ultraviolet. Electrons in internal shells have characteristic frequencies of the order of 1019 Hz (X-ray) and, for this reason, any electromagnetic wave having a frequency above it does not cause any absorption or polarization effects. 4.3.2. Long-range interactions and the local field hypothesis From now on, we will restrict ourselves to homogeneous materials, where only orientational and induced polarization need be considered. Also, thermodynamic equilibrium requires that the electric field be static and uniform in all the space outside the conductors that cause it. Furthermore, we will consider the dielectric to be isotropic. The considerations from now on will then apply for homogeneous and isotropic fluids (liquids, vapors and gases) under static and uniform fields. The action of a static electric field on a dielectric produces the emergence of a macroscopic polarization. The polarization or density of macroscopic dipole moment, P , is related to the true field E inside the dielectric by: ( ) 0r1PE  =− (4.42) where r  is the relative permittivity of the dielectric and 0  the vacuum permittivity. Each portion of the dielectric shows a macroscopic dipole moment having its own field acting on the surroundings. This is of major importance, as long-range interactions between THEORETICAL MODELS 83 different parts of the dielectric cannot be neglected and need be considered even at macroscopic distances. As Fröhlich explains [16], this can be seen explicitly in the fact that dielectric thermodynamic properties (in a somewhat extended sense) depend on the shape of the dielectric [17]. The development of a rigorous microscopic model, solvable from the point of view of Statistical Physics, is then a hardly viable task. This fact led to the development of local field models. According to the local field hypothesis, we take a portion of an infinitely large dielectric in a cavity of a given volume V, assuming that: • The existence of long-range interactions can be ignored if in the thermodynamic relations the external field is replaced by an effective external field G E (the local field, also called cavity field). • The outside of the cavity is treated as a dielectric continuum with the same dielectric properties as the complete system. The field G E is the result of the superposition of: (i) the external field, and (ii) the field produced by this dielectric continuum in the cavity, assuming that the cavity is empty 6 . Typically, a spherical cavity is considered for these models. It has the great advantage of having a scalar polarizability (i.e., the polarizability tensor 7 of the cavity is proportional to the identity tensor), and thus the local field is parallel to the polarization. Standard electrostatic calculations [16, 18] lead to: r r 3 , 21 G E gE g   == + (4.43) 4.3.3. Fröhlich’s fluctuation theory of dielectrics at zero field Let M denote the macroscopic dipole moment of the cavity, and E M its component in the direction of the field. Starting from the local field hypothesis applied to a spherical cavity, Fröhlich [16] evaluates the mean value of 2 M at zero field. We propose here a direct form to obtain it, more consistent with the usual formalism of Statistical Mechanics. Taking into account the isotropy of the dielectric (at zero field), and that 0 E M = 0 (the brackets 0 denote averaging at zero field), general fluctuation equations 8 lead to: ( )( ) 22 00 rr 0r 0 BB 1 2 1 33E EGT M M k T k T V M E    −+  = = =       (4.44) Equation (4.44) is called the Fröhlich equation ( B k denotes Boltzmann’s constant). It is exact in the framework of the hypothesis given above. To further develop it, he generalizes the procedure employed by Kirkwood for systems composed of rigid dipoles [19]. Let us assume that 6 The emptiness of the cavity for the evaluation of this field is essential for the next steps to be correct. We give below more details about this (see section 4.3.4). 7 The polarizability tensor relates the total macroscopic dipole moment of a dielectric with the applied external field. The external field is not the same as the true field ( E ), the latter resulting from the superposition of this external field and the field due to the polarization of the dielectric. 8 For these fluctuation equations to hold, the energy appearing in the thermodynamic relations needs to be the internal energy. Therefore, it is essential to this treatment that the thermodynamic force conjugated to the macroscopic dipole moment be the external field, and not the true field. CHAPTER 4 84 the cavity is composed of N “units” (molecules, or other groups of atoms) such that each unit makes the same average contribution to the polarization in an external field. After some calculations, the following formula is obtained: 1 2 00 M N m m = (4.45) In equation (4.45), m denotes the dipole moment of a unit, m is the dipole moment of the whole cavity when it is polarized by one of its units kept at a constant configuration with dipole moment of value m , and 1 0 denotes averaging over the configurations of a single unit at zero field. The meaning of m is subtle. It can be shown [16] that: (i) m is affected by short-range interactions and it is independent of the position of the unit with dipole moment m inside the sphere, provided its distance from the surface is large enough to allow its interaction with the outside to be treated on a macroscopic basis (the number of units for which this is not valid can be made very small compared with N as long as the cavity is sufficiently large); (ii) the result is the same either if m is treated as a point dipole or as a uniformly polarized sphere. From these considerations, it follows that a region makes a contribution to m only if the average dipole moment induced in it by m cannot be obtained by treating m as a point dipole or a uniformly polarized sphere. Therefore, the deviations of m from m are due, essentially, to shortrange forces and the deviation of the shape of the molecules from a sphere. For mixtures containing different kinds of units, the treatment is the same as above taking into account the additivity of the dipole moments of the units. If the mixture contains i N units of kind i, equation (4.45) must be replaced by: 1 2 00 iii i M N m m =  (4.46) where, obviously, i m denotes the dipole moment of a unit of type i, and i m is the dipole moment of the whole cavity when it is polarized by one of the i-type units kept at a constant configuration with dipole moment of value i m . 4.3.4. Macroscopic separation of induced and orientational contributions In order to further simplify the task of obtaining a formula for the relative permittivity, it is possible to perform a macroscopic approximation to separate the induced and orientational contributions to the polarization. To do it, the induced contribution is treated macroscopically assuming a relation with the high-frequency relative permittivity, r   , which is the relative permittivity at a frequency at which only the induced polarizability contributes. For nonpolar fluids rr  = , while for polar fluids it is frequently estimated from the refractive index at optical wavelengths, n , using the formula 2 r1.1n  = [20]. There are two methods to do this macroscopic separation. One of them is described in Fröhlich’s book [16] and also by Chelkowski [18], and it is widely used in the literature on dielectrics 9 . A second and more consistent treatment, also due to Fröhlich [21], is the one to be described here (but presented in a different way from the original reference), and from it we will derive all the possible variations of the model. 9 In fact, it was used to discuss some results obtained in this Thesis regarding amide + amine mixtures. THEORETICAL MODELS 85 It must be noted, however, that the first approach (not described here) leads to the same results in the context of pure fluids and one-fluid or c-fluid models (see sections 4.3.5 and 4.3.6.1) for mixtures of polar compounds. However, if we try to derive a model like the one described in section 4.3.6.2 (which is obtained there using the second approach), it does not reduce to the equations from Onsager’s model [16, 18] (and it should) when spherical molecules and negligible short-range interactions are assumed (see below). In this second method, the induced polarizability ( ind  ) of the sphere is defined from the same relation as the total polarizability of the sphere [16] (  ): r 0r 1 32 V   − =+ (4.47) (which is called macroscopic Clausius-Mossoti relation 10 ) but replacing r  by r   : ind 0r r 1 32 V      − =+ (4.48) Then, the orientational polarizability ( or  ) is assumed additive with ind  and defined by or ind    =− . To understand the subsequent definition of the orientational ( or M ) and induced ( ind M ) contributions to M , we must first make some clarifications regarding the correct use of the polarizability for the case of our cavity, which is immersed in the dielectric continuum. If the cavity were in vacuum, it would possess a dipole moment vac e EM  = , where e E is the external field. However, if the cavity is inside the dielectric, its dipole moment is not 11 G E  , but ( ) G R EME  =+ . The reaction field, R E , added is the field in the cavity due to the fact that the presence of the dipole moment of the dielectric inside the sphere modifies the polarization of the surrounding medium. It can be calculated from electrostatics [16, 18], giving: ( ) r r0 21 1 , , 2 1 3 R E fM f V   − == + (4.49) Now we can proceed to the definition of or M as the sum of two contributions: (i) the orientational contribution due to the total field inside the sphere, ( ) or G R EE  + ; (ii) the induced contribution due to the reaction field or fM of this orientational contribution, ind or fM  . We see that in this way or M includes all the effects derived from the orientational contribution to the polarization. This definition of the orientational contribution differs from that given in the first of the mentioned two methods. Now, since by definition ind or M M M=+ , we have: ( ) ( ) ind ind ind i dind o nr GG M E fM M E ff M    = + = +− (4.50) ( ) or io ornr d G M E fM Mf  +=+ (4.51) 10 An analogous relation (the “microscopic” Clausius-Mossoti relation) is obtained in a simple model due to Lorentz for the polarizability of spherical nonpolar molecules with no short-range forces. In contrast, equation (4.47) is macroscopic and exact. 11 Here, the local field G E plays the role of the “external” field, not caused by the portion of dielectric inside the cavity, because it is calculated assuming that the cavity is empty. CHAPTER 4 86 Or, solving the equations: ( ) ( ) ind rr 0 ind r ind r 112 12 GG EE f MV         − =+− + = (4.52) ( ) ( ) ( ) ( ) ( ) 2 or rr 0 ind r o r r r r 2 11 1 3 2 GG MVEE ff         −− −+ == + (4.53) Finally, following an analogous procedure to the one used to calculate 2 0 M , we obtain straightforwardly the orientational ( or 2 0 M ) and induced ( ind 2 0 M ) contributions: ( ) ( ) rr B ind 2 00 r r 12 1 2 3M k T V       + + − = (4.54) ( ) ( ) ( ) or r2 rr B0 rr 2 0r 2 1 2 M k T V      −+ =+ (4.55) These equations were obtained by Fröhlich [21] using another formalism. Perhaps this development can help to clarify the concepts behind his work. 4.3.5. The Kirkwood-Fröhlich equation for pure polar fluids If the fluid is made of polar molecules, we can develop or 2 0 M assuming that there is only one type of unit and: int or 1 2 00 int MN   = (4.56) Equation (4.56) is analogous to (4.45), but instead of m and m we use their orientational contributions int  and int   . In order to be consistent with the above definition of or M , int  must include not only the value of the permanent dipole moment of the unit inside the dielectric, but also an induced contribution due to the reaction field from the surroundings of the unit caused by its presence in the cavity. The quantity int  is normally called internal dipole moment of the unit immerse in its own medium. If the short-range interactions reach z neighbors from int  , then; int int int, 1 z k k     = =+  (4.57) where int,k  is the internal dipole moment of the kth neighbor. Substituting in (4.56) and taking into account the isotropy of the dielectric, one reaches the result: 2 K in or 2t 0 M Ng  = (4.58) where THEORETICAL MODELS 87 0 K1 c1 osgz  =+ (4.59) is the so-called Kirkwood correlation factor.  is the relative angle between the dipole int  and its neighbors. Consequently, the value of K g allows to distinguish among three kinds of behavior: • If K g = 1, then short-range interactions and the non-spherical shape of the units have no effect on the average relative orientation of neighboring permanent dipoles. • If K g > 1, there is a trend to parallel orientation of neighboring dipoles. • If K g < 1, the trend is to antiparallel orientation. Since in practical situations int  is not known, it should be calculated in relation to the permanent dipole moment in vacuum,  . To do this, we should subtract the influence of all the surroundings, inside and outside the cavity, which is not an easy task. To make an estimation, it is assumed that the reaction is mostly due to the outside of the cavity. Therefore,  will be estimated by simply subtracting from int  the induced contribution due to the reaction field from the outside of the cavity caused by its presence in the cavity. In other words, we approximate int int indf     += . This gives: rr int rr 2 2 12 3       + + + = (4.60) After combining equations (4.55), (4.58) and (4.60), we finally obtain: ( )( ) ( ) rr mrr B0 K22 Ar r 2 9 2 k T V gN       −+ = + (4.61) ( A N is Avogadro’s constant). Equation (4.61) is called the Kirkwood-Fröhlich equation. Using experimental data, it is straightforward to evaluate K g of pure fluids. Neglecting shortrange interactions and assuming the molecules spherical, K g must be equal to 1 and one obtains the Onsager equation. 4.3.6. The adaptation of Kirkwood-Fröhlich model to mixtures 4.3.6.1 Models with global separation of the orientational contribution The first family of models generalizing equation (4.61) to mixtures separate the induced and orientational contributions to the polarization of the mixture globally (i.e., all the components “together”). In other words, they start from equation (4.55), with different variations. Therefore, they will only make sense if there is at least one polar component, as otherwise there would be no orientational contribution. The first and most direct possibility is to interpret the quantities of the right-hand side of equation (4.55) as referring to the mixture. It is the natural and least artificial extension of equation (4.55) to mixtures. An analogous development to the one performed to get to equation (4.61) leads to: CHAPTER 4 88 ( ) ( )( ) ( ) rrr 2B0 K, K, r 2 Ar m r 2 9 1 2 i ii i ij i iij jN k T V x g g             −+  + − =   +   (4.62) where i  is the dipole moment of species i under vacuum, and 0 K, 1 cs1 o jij ij gz  =+ is the Kirkwood correlation factor for an i-type central molecule interacting with j z j-type neighbors and whose dipole moments are oriented relatively to the central molecule with an angle ij  . The application of equation (4.62) is not easy, as it contains a whole set of unknown compositiondependent parameters K,ij g . However, particularly for an ideal mixture of ideal gases (pointlike and non-interacting molecules), all the K,ij g must be equal to 1 and the system behaves as if it were a pure ideal gas with a dipole moment  given by: 22 i ii x  = (4.63) For a mixture including only one polar compound (1), the left-hand side of equation (4.62) reduces to 2 1 K,11 1 xg  and it is possible to obtain K,11 g from experimental data. It can also be used to determine experimentally 1  by measuring volumetric, dielectric and refractive properties of the mixture at high dilution ( 10x ), where K,1 1g can be assumed 12 . The second possibility, called one-fluid approach [22], assumes that the mixture is composed of a hypothetic fluid behaving as a Kirkwood-Fröhlich pure compound, whose units are located in spherical cavities of molar volume m V (= molar volume of the mixture) and embedded in a continuum with the properties of the mixture at the same composition. The equation defining this model is, therefore, the same as that for the pure fluids but with an “effective” dipole moment dependent on the composition. The dipole moment under vacuum of these units,  , is taken as that of a Kirkwood-Fröhlich ideal mixture of ideal gases, and then it is obtained from equation (4.63). The justification of this choice is quite convincing from equations (4.62) and (4.63). Reis and Iglesias argue other reasons [22], but they might add more confusion to the subject. This model has been used in this Thesis to gain insight into the experimental results of mixtures of two polar liquids. The K g obtained in this way can be interpreted as an averaged measure of the dipole relative orientation. A third possibility, proposed by Reis and Iglesias [22], is the so-called c-fluid approach (where c is the number of polar components of the mixture), in which c hypothetical fluids are assumed to behave as Kirkwood-Fröhlich pure compounds. The hypothetical fluid i is defined as made by molecules of component i located in spherical cavities of molar volume m,i V (= partial molar volume of component i) and embedded in a continuum with the properties of the mixture at the same composition 13 . The Kirkwood correlation factor of fluid i ( K,i g ) is, therefore: 12 We must remark here that  int must be affected by the environment of the unit inside the cavity, and that equation (4.60) does not include this contribution. Therefore, it should not be surprising to obtain slightly different results for  1 depending on the nonpolar solvent used. 13 Formally, this means that in the definition of  ind (equation (4.48)) we must replace   r by the highfrequency relative permittivity of pure component i,   r,i . THEORETICAL MODELS 89 ( )( ) ( ) rr B0 K, 22 A r, r, m, r,r 2 9 2 ii i i i i V gN kT       −+ = + (4.64) 4.3.6.2 Models treating additively orientational and induced contributions Instead of taking the separation of the global orientational contribution as the starting point, another of the possible generalizations of the Kirkwood-Fröhlich equation for mixtures is to assume that the value of 2 0 M given by equation (4.44) can be obtained additively from the induced and orientational contributions of hypothetical fluids in the mixture, in a number equal to the number of components. The hypothetical fluid i is defined in the same way as in the cfluid model described just above. This kind of model has been particularly popular for the description of binary mixtures of a polar compound (1) and a nonpolar compound (2), for which the final result is: ( ) ( ) ( ) ( ) ( ) ( ) m,1 m,2 2 2 r,1 r,2 r r,1 A 1 1 K,1 r 2 r B 0 r ,1 r ,2 m12 r, r1 rr 33 2 1 2 1 2 11 22 9 VV N x g Vxx kT           + −+ −− − = − ++ + (4.65) Equation (4.65) reduces to Onsager’s equation for such mixtures [16] in the limit of spherical molecules and absence of short-range interactions (see above). It has been used to determine experimentally 1  from high dilution measurements ( 10x , K,1 1g ) [23], proceeding as already described in section 4.3.6.1. It is also the formula normally taken to define the Kirkwood correlation factor in such (polar + nonpolar) mixtures 14 . 4.3.7. Molar refraction and dispersive interactions In section 4.3.4 we defined an induced polarizability ind  for the macroscopic sphere. Analogously, we can define its electronic polarizability, e  , by: 2 e02 1 32 n Vn  − =+ (4.66) Here, the squared refractive index at optical frequencies, 2 n , plays the role of the permittivity at such frequencies (for non-magnetic substances). A widely used related quantity is the socalled molar refraction (or molar refractivity), m R , defined by: e 2A1 mm 20 1 3 2 N n RV n   − == + (4.67) Since ee 1N  = is the molecule-averaged electronic contribution to the polarizability of the macroscopic sphere, m R can be interpreted as a measure of the dispersion forces present in the fluid. 14 We note here that a procedure based on equation (4.62) might be more appropriate, as fewer approximations are involved in its derivation. In order to apply (4.62), a reasonable estimation of   r of such polar + nonpolar mixtures needs to be proposed. CHAPTER 4 96 [22] J.C.R. Reis, T.P. Iglesias, Kirkwood correlation factors in liquid mixtures from an extended Onsager-Kirkwood-Frohlich equation. Phys. Chem. Chem. Phys. 13 (2011) 10670-10680. https://doi.org/10.1039/C1CP20142E [23] M. El-Hefnawy, K. Sameshima, T. Matsushita, R. Tanaka, Apparent Dipole Moments of 1-Alkanols in Cyclohexane and n-Heptane, and Excess Molar Volumes of (1-Alkanol + Cyclohexane or n-Heptane) at 298.15 K. J. Solution Chem. 34 (2005) 43-69. https://doi.org/10.1007/s10953-005-2072-1 Part II Copies of the published works Thermodynamics of amide + amine mixtures. 1. Volumetric, speed of sound and refractive index data for N,N-dimethylformamide + N-propylpropan-1-amine, + N-butylbutan-1-amine, + butan-1-amine, or + hexan-1- amine systems at several temperatures Fernando Hevia, Ana Cobos, Juan Antonio González*, Isaías García de la Fuente, Luis Felipe Sanz G.E.T.E.F., Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid, Paseo de Belén, 7, 47011 Valladolid, Spain *e-mail: [email protected]a.es; Tel: +34 983 423757 Abstract Values of density (  ), speed of sound (c) and refractive index ( D n ) for N,N-dimethylformamide (DMF) + N-propylpropan-1-amine (DPA) or + butan-1-amine (BA) mixtures at (293.15-303.15) K, and for DMF + N-butylbutan-1-amine (DBA) or hexan-1-amine (HxA) mixtures at 298.15 K are reported. Density and speed of sound measurements were conducted using a vibrating-tube densimeter and sound analyzer, Anton Paar model DSA5000; refractive index, D n , values were obtained by means of a RFM970 refractometer from Bellingham+Stanley. The experimental  , c and D n values have been used to determine excess molar volumes, E m V , excess adiabatic compressibilities,  E S , excess speeds of sound, E c , excess thermal expansion coefficients,  E p , and excess refractive indices, E D n . This set of data show the existence of interactions between unlike molecules and of structural effects in the mixtures under study. E m V values of solutions including linear secondary amines are lower than those of mixtures with linear primary amines. In fact, the contribution to E m V from the breaking of amine-amine interactions is larger for the latter systems. Calculations on Rao’s constant point out that there is no complex formation between the mixture components. Dispersive interactions have been analyzed by means of the molar refraction. It is shown that solutions with DPA or HxA are characterized by similar dispersive interactions and that they mainly differ in dipolar interactions. Adapted with permission from F. Hevia, A. Cobos, J.A. González, I. García de la Fuente, L.F. Sanz, Thermodynamics of amide + amine mixtures. 1. Volumetric, speed of sound and refractive index data for N,N-dimethylformamide + N-propylpropan-1-amine, + N-butylbutan-1-amine, + butan-1-amine, or + hexan-1-amine systems at several temperatures, J. Chem. Eng. Data 61 (2016) 1468-1478. https://doi.org/10.1021/acs.jced.5b00802. Copyright 2016 American Chemical Society. 99 J. Chem. Eng. Data 61 (2016) 1468-1478 1. Introduction N,N-dimethylformamide (DMF) is a very polar liquid (3.7 D [1]) which is able to dissolve many organic substances, as it is an aprotic protophilic compound with excellent donor-acceptor properties. Consequently, this amide has many technical applications. For example, it is used for the production of acrylic fibers, plastics, pesticides or surface coatings [2]. In the oil industry, due to its good properties as selective extractant, it is used for the extraction of aromatic and saturated hydrocarbons and of compounds containing nitrogen [3, 4]. In addition, it results very effective in nanotechnology [5-7]. Interestingly, the detailed knowledge of liquid mixtures containing the amide functional group is essential for the understanding of complex molecules of biological interest [8]. In this context, DMF is useful as a model compound for peptides. The aqueous solution of DMF is a simple biochemical model of biological aqueous solutions [9, 10]. On the other hand, the significant local order characteristic of pure DMF and of other N,N- dialkylamides, related to the existence of strong dipole-dipole interactions [11], makes their theoretical study of high interest [12]. Primary and secondary amines are polar molecules (see below) which can also form hydrogen bonds giving self-associated complexes or, with the appropriate group, heterocomplexes [13-15]. Amines are also very common in Biology. In fact, the breaking of amino acids releases amines; neurotransmitters as dopamine or histamine are amines [16, 17], and the polymer DNA is usually bound to proteins which contain several amine groups [18]. In addition, many of the cations and anions of the technically important ionic liquids are related to amine groups [19]. We start this series of articles reporting density,  , data, speeds of sound, c, and refractive indices, D n , at (293.15 K-303.15) K for DMF mixtures with N-propylpropan-1-amine (DPA) or butan-1-amine (BA), and at 298.15 K for DMF systems with N-butylbutan-1-amine (DBA) or hexan-1-amine (HxA). A literature survey shows that there are no such data for the systems under study. In contrast, volumetric [4, 20], D n [4], vapor-liquid equilibrium [21] or excess molar enthalpy [22] ( E m H ) measurements are available for the DMF + aniline mixture. Data on E m H are also available for the N-methylethanamide + HxA system at 363.15 K [23]. The large and negative E m H value at equimolar composition for this mixture (–1005 J·mol-1) [23], and for the DMF + aniline system at 298.15 K (–2946 J·mol-1) [22] reveal the existence of strong interactions between unlike molecules in amide + amine mixtures. 2. Experimental section Materials. All the compounds were used without further purification. Table 1 contains information regarding their source and purity, and Table 2 shows their physical properties,  D , , cn , thermal expansion coefficient,  p , adiabatic compressibility,  S , and isothermal compressibility,  T . The values listed in Table 2 are in good agreement with the data available in the literature. Apparatus and procedure. Binary mixtures were prepared by mass in small vessels of about 10 cm3, using an analytical balance HR-202 (weighing accuracy 0.01 mg), with all weighings corrected for buoyancy effects. The standard uncertainty in the final mole fraction is estimated to be 0.0008. Molar quantities were calculated on the basis of the relative atomic mass table of 2015 issued by the Commission on Isotopic Abundances and Atomic Weights (IUPAC) [24]. 100 https://doi.org/10.1021/acs.jced.5b00802 Table 1. Sample description. Chemical name CAS number Source Purification method Mole fraction purity Analysis method N,N-dimethylformamide (DMF) 68-12-2 Fluka none  0.995 GCa N-propylpropan-1-amine (DPA) 142-84-7 Fluka none  0.99 GCa N-butylbutan-1-amine (DBA) 111-92-2 Aldrich none  0.995 GCa butan-1-amine (BA) 109-73-9 Sigma--Aldrich none  0.99 GCa hexan-1-amine (HxA) 111-26-2 Aldrich none  0.995 GCa a Gas-liquid chromatography. Temperatures were measured using Pt-100 resistances, calibrated according to the ITS-90 scale of temperature, against the triple point of water and the melting point of Ga. The repeatability of the equilibrium temperature measurements is 0.01 K. The standard uncertainties for this quantity are 0.02 K and 0.03 K for  and D n measurements, respectively (see below). Densities and speeds of sound of both pure liquids and of the mixtures were measured by means of a vibrating-tube densimeter and sound analyzer, Anton Paar model DSA 5000, automatically thermostated within 0.01 K. A detailed description of the calibration of the apparatus has been given in an earlier work [25]. The repeatability of the  measurements is 5·10-3 kg·m-3, while the relative standard uncertainty of the measurements is estimated to be 0.12%. The determination of the speed of sound is based on the measurement of the propagation time of short acoustic pulses (3 MHz center frequency [26]), which are repeatedly transmitted to the sample. The repeatability and standard uncertainty of the c measurements are, respectively, 0.1 and 0.4 m·s-1. The experimental technique was checked through the determination of E m V and E c of the (cyclohexane + benzene) mixture at (293.15-303.15) K. Our results and published values [27-29] are in good agreement. The standard uncertainty in E m V is (0.012 E m,max V + 0.005 cm3·mol-1), where E m,max V stands for the maximum experimental value of E m V with respect to the mole fraction. The standard uncertainty of E c is estimated to be 0.8 m·s-1. Refractive indices were measured using a refractometer model RFM970 from Bellingham+Stanley, with the temperature controlled by means of Peltier modules. The measurement technique is based on the optical detection of the critical angle at the wavelength of the sodium D line (589.6 nm). Calibration of the apparatus was undertaken using 2,2,4- trimethylpentane and toluene at (293.15-303.15) K, the working temperatures, as indicated by Marsh [30]. The temperature stability is 0.02 K, the repeatability of the D n measurements is 0.00004 and the relative standard uncertainty is 0.0015. 3. Equations The densimeter and sound analyzer Anton Paar DSA 5000 allows to obtain in straight form  , the molar volume, m V , the coefficient of thermal expansion, ( )( )    = −  1 pp T and the 101 J. Chem. Eng. Data 61 (2016) 1468-1478 Table 2. Physical properties of pure compounds at temperature T and pressure p = 0.1 MPa. a Property T/K DMF DPA DBA BA HxA  * /g·cm-3 293.15 0.948881 0.948922b 0.738194 0.738188c 0.759695 0.759571c 0.737048 0.764423 298.15 0.944081 0.944163b 0.733618 0.733683c 0.755525 0.755457c 0.732231 0.7327d 0.760073 0.76013e 303.15 0.939361 0.939390b 0.729098 0.729087c 0.751458 0.751329c 0.727452 0.755848 c*/m·s-1 293.15 1476.8 1477.8b 1209.4 1209c 1261.1 1261.2c 1268.3 1324.0 298.15 1457.2 1458.5b 1458.6g 1187.7 1198f 1241.5 1248f 1246.0 1247.8d 1303.6 1304.7e 303.15 1438.2 1439b 1440.3g 1167.2 1174f 1222.5 1227f 1224.6 1227f 1283.6 1285f  * p /10-3K-1 298.15 1.008 1.010g 1.240 1.29h 1.090 1.12h 1.311 1.314f 1.128 1.13e  * S /TPa-1 293.15 483.2 485b 926.2 926.5f 827.7 843.4 746.3 298.15 498.8 498.7i 497.9b 966.3 947f 858.7 849f 879.7 876.6d 774.2 773e 303.15 514.7 514b 512.9g 1006.7 992f 890.4 883f 916.7 912f 802.9 800f  * T /TPa-1 298.15 659.4 650h 662j 1216.4 1183f 1059.4 1039f 1151.9 1145f 974.6 975e *mp C /J·mol-1·K-1 298.15 146.05k 252.84h 302f 188l 252l * D n 293.15 1.43055 1.43047h 1.4281m 1.40432 1.4043h 1.41724 1.4177h 1.40060 1.40106n 298.15 1.42828 1.42817h 1.4280j 1.40139 1.4053f 1.41488 1.4152h 1.39786 1.3987h 1.41577 1.4160f 303.15 1.42603 1.4267o 1.4271j 1.39883 1.4022f 1.41253 1.4143f 1.39500 1.3978f 1.39744n a  * , density; * c , speed of sound;  * p , isobaric thermal expansion coefficient;  * S , adiabatic compressibility;  * T , isothermal compressibility; *mp C , isobaric molar heat capacity; and * D n , refractive index. Standard uncertainties, u , are: ( ) =0.02uT K (for * D n values, ( ) =0.03uT K); ( ) =1up kPa; ( ) = *0.4u c m·s-1. Relative standard uncertainties, r u , are: ( )  = r*0.0012u ; ( )  = * r0.028 p u ; ( )  = * r0.002 S u ; ( )  = * r0.015 T u ; ( ) = * r0.0015 D un . bRef. [67]; cRef. [68]; dRef. [69]; eRef. [70]; fRef. [71]; gRef. [72]; hRef. [73]; iRef. [74]; jRef. [75]; kRef. [76]; lRef. [77]; mRef. [78]; nRef. [79]; oRef. [80]. 102 https://doi.org/10.1021/acs.jced.5b00802 isentropic compressibility,  S . As in other previous applications,  p values were determined assuming that  changes linearly with T. In addition,  S can be determined from the Newton- Laplace equation assuming that the absorption of the acoustic wave is negligible:  =2 1 Sc (1) The values id F of a given thermodynamic property, F, for an ideal mixture at the same temperature and pressure as the investigated solution, are calculated by means of the wellestablished equations [31-33]: =+ id * * 1 1 2 2 F x F x F ( =mm ,p F V C ) (2)  =+ id * * 1 1 2 2 F F F (  =, pT F ) (3) where * i F is the value of the property F of pure component i, and mp C is the molar isobaric heat capacity. In equation (3),  =* id mmi i i xV V represents the volume fraction of component i, where * mi V is the molar volume of that component. Ideal values of  S and c are calculated from the expressions [31]:   =− id id 2 m id id id m () p ST p TV C (4)   =   1/2 id id id 1 S c (5) being  =+ id id 1 1 2 2 m ()x M x M V (Mi, molar mass of the i component). Finally, the ideal values of D n are determined using the equation proposed by Reis et al. [34]: ( ) ( )   =+   id * * D D1 2 1/2 22 D21 n n n (6) The excess functions are then determined from the equation: =− E id F F F (  =mD , , , , Sp F V c n ) (7) 4. Experimental results Values, at the considered temperatures, of  and c vs. 1 x , the mole fraction of DMF, are collected in Table 3, while D n results are shown in Table 4. Derived properties, as excess functions, are given in the supporting information: E m V (Table S1);  p and  E p at 298.15 K (Table S2);  E S and E c at 298.15 K (Table S3) and E D n (Table S4). These results are shown graphically in Figures 1-7. We have not found data available in the literature for comparison. The current data were fitted by unweighted least-squares polynomial regressions to the Redlich- Kister equation: 103 J. Chem. Eng. Data 61 (2016) 1468-1478 Table 3. Densities,  , and speeds of sound, c, for N,N-dimethylformamide (1) + amine (2) mixtures at temperature T and pressure p = 0.1 MPa. a 1 x  /g·cm-3 c /m·s-1 1 x  /g·cm-3 c /m·s-1 DMF (1) + DPA (2) ; T/K = 293.15 K 0.0600 0.745894 1218.2 0.4974 0.815656 1299.2 0.1071 0.752141 1225.0 0.5487 0.825989 1312.0 0.1560 0.758933 1232.9 0.6562 0.849651 1342.1 0.1975 0.764870 1239.3 0.7514 0.873097 1373.4 0.2490 0.772540 1248.1 0.8216 0.892212 1399.8 0.3099 0.782194 1259.4 0.8501 0.900523 1411.2 0.3463 0.788151 1266.2 0.9025 0.916508 1433.3 0.3985 0.797199 1276.9 0.9486 0.931283 1453.4 0.4480 0.806192 1287.6 DMF (1) + DPA (2) ; T/K = 298.15 K 0.0626 0.741577 1196.9 0.5386 0.819199 1288.9 0.1083 0.747697 1204.0 0.6082 0.833997 1307.9 0.1544 0.754025 1211.2 0.6527 0.844084 1321.1 0.2541 0.768732 1228.1 0.7477 0.867448 1352.4 0.3148 0.778293 1239.3 0.8063 0.883226 1374.0 0.3609 0.786012 1248.3 0.9020 0.911457 1413.1 0.4077 0.794223 1258.2 0.9482 0.926367 1433.5 0.4966 0.810800 1278.5 DMF (1) + DPA (2) ; T/K = 303.15 K 0.0453 0.734885 1174.0 0.5415 0.815193 1270.3 0.1034 0.742550 1183.0 0.6016 0.827909 1286.6 0.1963 0.755529 1198.0 0.6517 0.839209 1301.4 0.2582 0.764775 1208.8 0.7502 0.863388 1334.0 0.3559 0.780614 1227.6 0.8498 0.890941 1372.0 0.4099 0.790030 1239.0 0.9000 0.906165 1393.2 0.4565 0.798539 1249.4 0.9498 0.922203 1415.2 DMF (1) + DBA (2) ; T/K = 298.15 K 0.0642 0.761171 1246.4 0.5574 0.823977 1307.9 0.1134 0.765782 1250.5 0.5996 0.831688 1316.3 0.1647 0.770882 1255.0 0.6514 0.842013 1328.1 0.2121 0.775872 1259.5 0.6869 0.849571 1336.8 0.2734 0.782835 1266.1 0.7361 0.860924 1350.4 0.3213 0.788624 1271.6 0.7904 0.874714 1367.5 0.4114 0.800702 1283.5 0.8418 0.889103 1385.9 0.4526 0.806766 1289.7 0.8921 0.904666 1406.1 0.5072 0.815344 1298.6 0.9471 0.923650 1431.0 104 https://doi.org/10.1021/acs.jced.5b00802 DMF (1) + BA (2) ; T/K = 293.15 K 0.0599 0.747390 1277.7 0.5483 0.842154 1368.9 0.1056 0.755445 1285.0 0.6569 0.866102 1393.7 0.1591 0.765035 1293.8 0.6999 0.875844 1404.0 0.2505 0.782005 1309.6 0.7537 0.888314 1416.7 0.3017 0.791811 1318.9 0.8036 0.900101 1429.0 0.3583 0.802880 1329.6 0.8579 0.913315 1442.3 0.3992 0.811114 1337.8 0.9048 0.924751 1453.7 0.5059 0.833130 1359.6 0.9546 0.937212 1465.6 DMF (1) + BA (2) ; T/K = 298.15 K 0.0575 0.742224 1255.4 0.4381 0.814268 1324.9 0.1092 0.751333 1263.9 0.5028 0.827736 1338.6 0.1519 0.759015 1271.1 0.6005 0.848795 1360.6 0.2043 0.768674 1280.1 0.6934 0.869781 1382.5 0.2448 0.776215 1287.4 0.7572 0.884516 1398.0 0.3090 0.788510 1299.3 0.8056 0.895958 1410.0 0.3558 0.797705 1308.4 0.9076 0.920837 1435.1 0.3986 0.806285 1317.0 0.9553 0.932723 1446.6 DMF (1) + BA (2) ; T/K = 303.15 K 0.0505 0.736213 1233.0 0.5281 0.828281 1324.0 0.1477 0.753539 1249.4 0.6056 0.845104 1341.6 0.2019 0.763466 1259.0 0.6960 0.865473 1363.2 0.2410 0.770708 1266.0 0.7558 0.879286 1377.7 0.3024 0.782423 1277.5 0.8006 0.889962 1389.0 0.3558 0.792882 1287.8 0.8544 0.902880 1402.3 0.4358 0.808960 1304.1 0.8998 0.914033 1413.7 0.5114 0.824673 1320.3 0.9466 0.925732 1425.2 DMF (1) + HxA (2) ; T/K = 298.15 K 0.0506 0.765582 1307.1 0.6022 0.846551 1368.3 0.0992 0.771096 1310.8 0.7056 0.867688 1387.1 0.1725 0.779897 1316.7 0.7996 0.889217 1406.8 0.2548 0.790546 1324.2 0.8492 0.901602 1418.4 0.3476 0.803611 1333.7 0.8982 0.914549 1430.4 0.4461 0.818861 1345.5 0.9530 0.929990 1444.7 0.5500 0.836751 1360.1 a The standard uncertainties, u , are: ( ) 10.0008ux = ; ( ) 1up= kPa; ( ) 0.02uT = K. The combined expanded standard uncertainties (0.95 level of confidence) are: ( ) rc 0.0024U  = (relative value); ( ) c0.8Uc= m·s-1. 105 J. Chem. Eng. Data 61 (2016) 1468-1478 interactions. A similar trend is encountered in 1-alkanol + HxA, or + DPA systems [48, 49]. The more negative E m V value of the DMF + aniline mixture (–0.6931 cm3·mol-1) [20] compared to those of the systems with HxA or DPA suggests that the presence of an aromatic ring leads to stronger interactions between unlike molecules, which is in agreement with the largely negative E m H value of this system (see Introduction). Solutions including DPA or BA show negative values of ( ) =   E mpp A V T and  E p (Table S2). Thus, the use of E m V ( 1 x = 0.5) values obtained at different temperatures gives p A /cm3·mol-1·K-1 = − 1.8·10-3 (DPA); − 2·10-4 (BA). This means that the structure of the mixture is more difficult to be broken than that of the pure liquids, which may be considered as an evidence of the existence of interactions between unlike molecules. In fact, values of p A and  E p are positive at any composition for solutions where strong interactions between like molecules are present. This is the case, e.g, of the 2- ethoxyethanol + octane [50] or the pentan-1-ol + cyclohexane [51] systems ( p A /cm3·mol-1·K-1 = 7.6·10-3; 2.3·10-3, respectively). However, p A values are also negative for solutions characterized by relevant structural effects ( − 1.3·10-2 cm3·mol-1·K-1 for the hexane + hexadecane mixture [52]). Taking into account the different molar volumes of DPA (137.93 cm3·mol-1) and BA (99.88 cm3·mol-1), the more negative p A value of the DPA system may be related, at least partially, to structural effects. On the other hand, p A (DMF + aniline) [20] = − 2.9·10-3 cm3·mol-1·K-1, which is a more negative value than that of the DPA solution. This supports our previous statement, that DMF-amine interactions are stronger in the aniline system. The  E S values can be also interpreted in terms of structural and interactional effects [53]. Structural effects and interactions between unlike molecules lead to negative values of this magnitude (  E S /TPa-1= –142 (aniline + propanone) [54]). Positive values are encountered in solutions where interactions between like molecules are predominant (  E S /TPa-1 = 15.3 (2-ethoxyethanol + n-octane) [55]). For the systems under study,  E S /TPa-1 = − 47.8 (DPA); − 17.7 (DBA); − 41.9 (BA); − 13.3 (HxA), which is consistent with the trends mentioned above. In addition, the consistency between the signs of the E m V ,  E S and E c functions must be remarked, as E m V ,  E S are negative and E c is positive (Tables S1 and S3; Figures 1-6). The DBA mixture slightly separates from this trend and E m V is small and positive. However, we underline the strong asymmetry of the  E S curve, with a minimum in the region where E m V shows negative values (Figures 1 and 3). We have also determined the internal pressures, int P [56-59]:   =− int p T T Pp (10) and the excess internal pressures, =− E id int int int P P P , with  =− id id id int pT P T p [60]. The  T values of the mixtures were obtained from   =+ 2 m ,m p TS p TV C (11) 112 https://doi.org/10.1021/acs.jced.5b00802 assuming that E mp C = 0, and that  =id pp (equation (3)) when experimental data are not available. For pure compounds, we have int P /MPa = 455.7 (DMF); 303.9 (DPA); 306.7 (DBA); 339.2 (BA); 345 (HxA), and for the DMF mixtures, int P /MPa = 353.9 (DPA); 345.9 (DBA); 389.4 (BA); 382.2 (HxA). Because the main contributions to int P are related to dispersion forces and weak dipole-dipole interactions [58], these values suggest that dipolar interactions between unlike molecules are more relevant in systems including linear primary amines. On the other hand, E int P /MPa = 14.6 (DPA); 6.5 (DBA); 14.4 (BA); 5.9 (HxA). Large positive E int P values are encountered in systems characterized by strong interactions between unlike molecules. For example, E int P (aniline + propanone) = 61.4 MPa [54]. It is rather clear that the higher E int P value of the DPA system compared to that of the HxA mixture cannot be ascribed to stronger interactions between unlike molecules but to structural effects. On the other hand, int P values can be calculated using the equation [57]: =− ++ int E 1 f1 2 f2 m RT Pp x v x v V (12) In this expression, fi v denotes the molar free volume of component i, obtained from =+ f int, /( ) ii v RT p P [57]. Results on int P /MPa from equation (12) are: 380.7 (DPA), 365.7 (DBA), 389.4 (BA) and 394.1 (HxA). The differences with the experimental values (equation. (10)) are: 7.6%, 5.7%, 4.2% and 3.1%, respectively. This demonstrates that the van der Waals equation holds to a rather large extent for the investigated solutions, as equation (12) is derived from this equation of state [57]. The Rao’s constant [61], c R , (also termed molar sound velocity, =1/3 mc R V c ) is a quantity commonly used to investigate molecular interactions in liquid mixtures from ultrasonic measurements. In fact, if there is no association, or if the degree of association does not depend on concentration, c R changes linearly on the mole fractions of the components and one can write [62-64]: =+ 1 1 2 2c c c R x R x R Systems where complex formation is present show deviations from this behavior [64]. For the actual mixtures under study, c R varies linearly with 1 x (Figure 8), and this indicates that there is no complex formation [62, 63]. Finally, the D n values can be used for the determination of the molar refraction m R , a quantity closely related to the dispersion forces of the considered system, as D n at optical wavelengths is related to the mean electronic polarizability [65]. m R can be calculated using the Lorentz-Lorenz equation [65, 66]: − =+ 2 D mm 2 D 1 2 n RV n (13) We have m R (DMF)/cm3·mol-1 = 26.7 (DPA); 31.4 (DBA); 22.0 (BA); 26.7 (HxA). These results allow to state that: (i) as expected, dispersive interactions become more relevant when the amine size increases along a homologous series; (ii) dispersive interactions are more or less similar in DPA and HxA mixtures, which means that such solutions mainly differ in dipolar interactions. 113 J. Chem. Eng. Data 61 (2016) 1468-1478 6. Conclusions Data on  , c and D n for DMF + DPA, + DBA, + BA or + HxA mixtures at different temperatures have been reported, and the excess functions E m V ,  E S , E c ,  E p and E D n have been calculated. The data show the existence of interactions between unlike molecules and of structural effects in the investigated systems. E m V values of mixtures including linear secondary amines are lower than those of systems with linear primary amines, as for the latter solutions the contribution to E m V from the breaking of amine-amine interactions is larger. Mixtures with DPA or HxA differ essentially in dipolar interactions. Supporting information This material contains values of E m V and E D n at the working temperatures and values of  p ,  E p ,  E S , E c at 298.15 K. References [1] A.L. McClellan, Tables of Experimental Dipole Moments. Vols. 1,2,3, Rahara Enterprises, El Cerrito, US, 1974. [2] P. Venkatesu, Thermophysical contribution of N,N-dimethylformamide in the molecular interactions with other solvents. Fluid Phase Equilib. 298 (2010) 173-191. https://doi.org/10.1016/j.fluid.2010.07.010 [3] B. Blanco, M.T. Sanz, S. Beltrán, J.L. Cabezas, J. Coca, Vapor–liquid equilibria for the ternary system benzene+n-heptane+N,N-dimethylformamide at 101.33 kPa. Fluid Phase Equilib. 175 (2000) 117-124. https://doi.org/10.1016/S0378-3812(00)00438-6 [4] H.J. Noh, S.J. Park, S.J. In, Excess molar volumes and deviations of refractive indices at 298.15 K for binary and ternary mixtures with pyridine or aniline or quinoline. J. Ind. Eng. Chem. 16 (2010) 200-206. https://doi.org/10.1016/j.jiec.2010.01.038 [5] F. Inam, H. Yan, M.J. Reece, T. Peijs, Dimethylformamide: an effective dispersant for making ceramic–carbon nanotube composites. Nanotech. 19 (2008) 195710. https://doi.org/10.1088/0957-4484/19/19/195710 [6] T.T. Nguyen, S.U. Nguyen, D.T. Phuong, D.C. Nguyen, A.T. Mai, Dispersion of denatured carbon nanotubes by using a dimethylformamide solution. Adv. Nat. Sci.: Nanosci. Nanotech. 2 (2011) 035015. https://doi.org/10.1088/2043-6262/2/3/035015 [7] Y. Chen, B. Zhang, Z. Gao, C. Chen, S. Zhao, Y. Qin, Functionalization of multiwalled carbon nanotubes with uniform polyurea coatings by molecular layer deposition. Carbon 82 (2015) 470-478. https://doi.org/10.1016/j.carbon.2014.10.090 [8] E.S. Eberhardt, R.T. Raines, Amide-Amide and Amide-Water Hydrogen Bonds: Implications for Protein Folding and Stability. J. Am. Chem. Soc. 116 (1994) 2149-2150. https://doi.org/10.1021/ja00084a067 [9] G.-Z. Jia, K.-M. Huang, L.-J. Yang, X.-Q. Yang, Composition-Dependent Dielectric Properties of DMF-Water Mixtures by Molecular Dynamics Simulations. Int. J. Mol. Sci. 10 (2009) 1590-1600. https://doi.org/10.3390/ijms10041590 114 https://doi.org/10.1021/acs.jced.5b00802 [10] G.R. Desiraju, T. Steiner, The Weak Hydrogen Bond in Structural Chemistry and Biology. Oxford University Press, Oxford, UK, 1999. [11] W.L. Jorgensen, C.J. Swenson, Optimized intermolecular potential functions for amides and peptides. Structure and properties of liquid amides. J. Am. Chem. Soc. 107 (1985) 569-578. https://doi.org/10.1021/ja00289a008 [12] J.A. Gonzalez, J.C. Cobos, I. García de la Fuente, Thermodynamics of liquid mixtures containing a very strongly polar compound: Part 6. DISQUAC characterization of N,N- dialkylamides. Fluid Phase Equilib. 224 (2004) 169-183. https://doi.org/10.1016/j.fluid.2004.02.007 [13] J.S. Rowlinson, F.L. Swinton, Liquids and Liquid Mixtures. 3rd Edition, Butterworths, G. B., 1982. [14] J.A. González, I. García de la Fuente, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult's Law: Part 4. Application of the DISQUAC model to mixtures of 1-alkanols with primary or secondary linear amines. Comparison with Dortmund UNIFAC and ERAS results. Fluid Phase Equilib. 168 (2000) 31-58. https://doi.org/10.1016/S0378-3812(99)00326-X [15] U. Domańska, M. Marciniak, Volumetric and Solid + Liquid Equilibrium Data for Linear 1-Alkanol + Decylamine Mixtures. Analysis in Terms of ERAS, DISQUAC, and Modified UNIFAC†. Ind. Eng. Chem. Res. 43 (2004) 7647-7656. https://doi.org/10.1021/ie0401206 [16] F.F. Liew, T. Hasegawa, M. Fukuda, E. Nakata, T. Morii, Construction of dopamine sensors by using fluorescent ribonucleopeptide complexes. Bioorg. Med. Chem. 19 (2011) 4473-4481. https://doi.org/10.1016/j.bmc.2011.06.031 [17] J.M. Sonner, R.S. Cantor, Molecular Mechanisms of Drug Action: An Emerging View. Annu. Rev. Biophys. 42 (2013) 143-167. https://doi.org/10.1146/annurev-biophys- 083012-130341 [18] D.L. Nelson, M.M. Cox, Lehninger Principles of Biochemistry. 3rd ed., Worth Publishing, New York, 2000. [19] M. Götz, R. Reimert, S. Bajohr, H. Schnetzer, J. Wimberg, T.J.S. Schubert, Long-term thermal stability of selected ionic liquids in nitrogen and hydrogen atmosphere. Thermochim. Acta 600 (2015) 82-88. https://doi.org/10.1016/j.tca.2014.11.005 [20] P.S. Nikam, S.J. Kharat, Excess Molar Volumes and Deviations in Viscosity of Binary Mixtures of N,N-Dimethylformamide with Aniline and Benzonitrile at (298.15, 303.15, 308.15, and 313.15) K. J. Chem. Eng. Data 48 (2003) 972-976. https://doi.org/10.1021/je030101n [21] T.E. Vittal Prasad, A. Adi Sankara Reddy, S. Kailash, D.H.L. Prasad, Activity coefficients and excess Gibbs energy of binary mixtures of N,N-dimethyl formamide with selected compounds at 95.5 kPa. Fluid Phase Equilib. 273 (2008) 52-58. https://doi.org/10.1016/j.fluid.2008.07.018 [22] R.S. Ramadevi, P. Venkatesu, M.V. Prabhakara Rao, M.R. Krishna, Excess enthalpies of binary mixtures of N,N-dimethylformamide with substituted benzenes at 298.15 K. Fluid Phase Equilib. 114 (1996) 189-197. https://doi.org/10.1016/0378-3812(95)02816-1 [23] A.B. de Haan, J. Gmehling, Excess Enthalpies for Various Binary Mixtures with N- Methylacetamide or Acetic Anhydride. J. Chem. Eng. Data 41 (1996) 474-478. https://doi.org/10.1021/je950294h [24] M. Wieser, N. Holden, T.B. Coplen, J.K. Böhlke, M. Berglund, W.A. Brand, P. De Bièvre, G. M., R.D. Loss, J. Meija, T. Hirata, T. Prohaska, R. Schoenberg, G. O’Connor, 115 J. Chem. Eng. Data 61 (2016) 1468-1478 T. Walczyk, S. Yoneda, Z. X-K, Atomic weights of the elements 2011 (IUPAC Technical Report). Pure Appl. Chem. 85 (2013) 1047-1078. https://doi.org/10.1351/PAC-REP-13- 03-02 [25] J.A. González, I. Alonso, I. Mozo, I. García de la Fuente, J.C. Cobos, Thermodynamics of (ketone + amine) mixtures. Part VI. Volumetric and speed of sound data at (293.15, 298.15, and 303.15) K for (2-heptanone + dipropylamine, +dibutylamine, or +triethylamine) systems. J. Chem. Thermodyn. 43 (2011) 1506-1514. https://doi.org/10.1016/j.jct.2011.05.003 [26] D. Schneditz, T. Kenner, H. Heimel, H. Stabinger, A sound‐speed sensor for the measurement of total protein concentration in disposable, blood‐perfused tubes. J. Acoust. Soc. Am. 86 (1989) 2073-2080. https://doi.org/10.1121/1.398466 [27] E. Junquera, G. Tardajos, E. Aicart, Speeds of sound and isentropic compressibilities of (cyclohexane + benzene and (1-chlorobutane + n-hexane or n-heptane or n-octane or ndecane) at 298.15 K. J. Chem. Thermodyn. 20 (1988) 1461-1467. https://doi.org/10.1016/0021-9614(88)90041-9 [28] K. Tamura, K. Ohomuro, S. Murakami, Speeds of sound, isentropic and isothermal compressibilities, and isochoric heat capacities of {xc-C6H12+(1−x)C6H6}, x{CCl4+(1−x)C6H6}, and x{C7H16+(1−x)C6H6} at 298.15 K. J. Chem. Thermodyn. 15 (1983) 859-868. https://doi.org/10.1016/0021-9614(83)90092-7 [29] K. Tamura, S. Murakami, Speeds of sound, isentropic and isothermal compressibilities, and isochoric heat capacities of {xc-C6H12 + (1 − x)C6H6} from 293.15 to 303.15 K. J. Chem. Thermodyn. 16 (1984) 33-38. https://doi.org/10.1016/0021-9614(84)90072-7 [30] K.N. Marsh, Recommended reference materials for the realization of physicochemical properties. Blackwell Scientific Publications, Oxford, UK, 1987. [31] G.C. Benson, C.J. Halpin, A.J. Treszczanowicz, Excess volumes and isentropic compressibilities for (2-ethoxyethanol + n-heptane) at 298.15 K. J. Chem. Thermodyn. 13 (1981) 1175-1183. https://doi.org/10.1016/0021-9614(81)90017-3 [32] G. Douhéret, M.I. Davis, J.C.R. Reis, M.J. Blandamer, Isentropic Compressibilities— Experimental Origin and the Quest for their Rigorous Estimation in Thermodynamically Ideal Liquid Mixtures. ChemPhysChem 2 (2001) 148-161. https://doi.org/10.1002/1439- 7641(20010316)2:3<148::AID-CPHC148>3.0.CO;2-J [33] G. Douhéret, C. Moreau, A. Viallard, Excess thermodynamic quantities in binary systems of non electrolytes.: Different ways of calculating excess compressibilities. Fluid Phase Equilib. 22 (1985) 277-287. https://doi.org/10.1016/0378-3812(85)87027-8 [34] J.C.R. Reis, I.M.S. Lampreia, Â.F.S. Santos, M.L.C.J. Moita, G. Douhéret, Refractive Index of Liquid Mixtures: Theory and Experiment. ChemPhysChem 11 (2010) 3722-3733. https://doi.org/10.1002/cphc.201000566 [35] P.R. Bevington, Data Reduction and Error Analysis for the Physical Sciences. McGraw- Hill, New York, 1969. [36] J. Lobos, I. Mozo, M. Fernández Regúlez, J.A. González, I. García de la Fuente, J.C. Cobos, Thermodynamics of Mixtures Containing a Strongly Polar Compound. 8. Liquid−Liquid Equilibria for N,N-Dialkylamide + Selected N-Alkanes. J. Chem. Eng. Data 51 (2006) 623-627. https://doi.org/10.1021/je050428j [37] M. Rogalski, R. Stryjek, Mutual solubility of binary n-hexadecane and polar compound systems. Bull. Acad. Pol. Sci., Ser. Sci. Chim. 28 (1980) 139-147. [38] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids. McGraw- Hill, New York, US, 1987. 116 https://doi.org/10.1021/acs.jced.5b00802 [39] E. Matteoli, L. Lepori, A. Spanedda, Thermodynamic study of heptane + amine mixtures: I. Excess and solvation enthalpies at 298.15 K. Fluid Phase Equilib. 212 (2003) 41-52. https://doi.org/10.1016/S0378-3812(03)00260-7 [40] E. Matteoli, P. Gianni, L. Lepori, Thermodynamic study of heptane + secondary, tertiary and cyclic amines mixtures. Part IV. Excess and solvation enthalpies at 298.15 K. Fluid Phase Equilib. 306 (2011) 234-241. https://doi.org/10.1016/j.fluid.2011.04.013 [41] D. Patterson, Free Volume and Polymer Solubility. A Qualitative View. Macromolecules 2 (1969) 672-677. https://doi.org/10.1021/ma60012a021 [42] S.N. Bhattacharyya, M. Costas, D. Patterson, H.V. Tra, Thermodynamics of mixtures containing alkanes. Fluid Phase Equilib. 20 (1985) 27-45. https://doi.org/10.1016/0378- 3812(85)90019-6 [43] L. Lepori, P. Gianni, E. Matteoli, The Effect of the Molecular Size and Shape on the Volume Behavior of Binary Liquid Mixtures. Branched and Cyclic Alkanes in Heptane at 298.15 K. J. Solution Chem. 42 (2013) 1263-1304. https://doi.org/10.1007/s10953- 013-0023-9 [44] A.J. Treszczanowicz, G.C. Benson, Excess volumes for n-alkanols + n-alkanes II. Binary mixtures of n-pentanol, n-hexanol, n-octanol, and n-decanol + n-heptane. J. Chem. Thermodyn. 10 (1978) 967-974. https://doi.org/10.1016/0021-9614(78)90058-7 [45] L. Lepori, P. Gianni, A. Spanedda, E. Matteoli, Thermodynamic study of (heptane + amine) mixtures. II. Excess and partial molar volumes at 298.15 K. J. Chem. Thermodyn. 43 (2011) 805-813. https://doi.org/10.1016/j.jct.2010.12.025 [46] L. Lepori, P. Gianni, A. Spanedda, E. Matteoli, Thermodynamic study of (heptane + amine) mixtures. III: Excess and partial molar volumes in mixtures with secondary, tertiary, and cyclic amines at 298.15 K. J. Chem. Thermodyn. 43 (2011) 1453-1462. https://doi.org/10.1016/j.jct.2011.04.017 [47] T.M. Letcher, Thermodynamics of aliphatic amine mixtures I. The excess volumes of mixing for primary, secondary, and tertiary aliphatic amines with benzene and substituted benzene compounds. J. Chem. Thermodyn. 4 (1972) 159-173. https://doi.org/10.1016/S0021-9614(72)80021-1 [48] S. Villa, N. Riesco, I. Garcıa de la Fuente, J.A. González, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult’s law: Part 5. Excess molar volumes at 298.15 K for 1-alkanols+dipropylamine systems: characterization in terms of the ERAS model. Fluid Phase Equilib. 190 (2001) 113-125. https://doi.org/10.1016/S0378-3812(01)00595-7 [49] S. Villa, N. Riesco, I. Garcıa de la Fuente, J.A. González, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult’s law. Part 8. Excess molar volumes at 298.15 K for 1-alkanol + isomeric amine (C6H15N) systems: Characterization in terms of the ERAS model. Fluid Phase Equilib. 216 (2004) 123-133. https://doi.org/10.1016/j.fluid.2003.10.008 [50] H. Ohji, H. Ogawa, S. Murakami, K. Tamura, J.-P.E. Grolier, Excess volumes and excess thermal expansivities for binary mixtures of 2-ethoxyethanol with non-polar solvents at temperatures between 283.15 K and 328.15 K. Fluid Phase Equilib. 156 (1999) 101-114. https://doi.org/10.1016/S0378-3812(99)00035-7 [51] O. Hiroyuki, Excess volumes of (1-pentanol + cyclohexane or benzene) at temperatures between 283.15 K and 328.15 K. J. Chem. Thermodyn. 34 (2002) 849-859. https://doi.org/10.1006/jcht.2001.0940 117 J. Chem. Eng. Data 61 (2016) 1468-1478 [52] M.F. Bolotnikov, Y.A. Neruchev, Y.F. Melikhov, V.N. Verveyko, M.V. Verveyko, Temperature Dependence of the Speed of Sound, Densities, and Isentropic Compressibilities of Hexane + Hexadecane in the Range of (293.15 to 373.15) K. J. Chem. Eng. Data 50 (2005) 1095-1098. https://doi.org/10.1021/je050060q [53] L. Venkatramana, R.L. Gardas, K. Sivakumar, K. Dayananda Reddy, Thermodynamics of binary mixtures: The effect of substituents in aromatics on their excess properties with benzylalcohol. Fluid Phase Equilib. 367 (2014) 7-21. https://doi.org/10.1016/j.fluid.2014.01.019 [54] I. Alonso, V. Alonso, I. Mozo, I. García de la Fuente, J.A. González, J.C. Cobos, Thermodynamics of Ketone + Amine Mixtures. I. Volumetric and Speed of Sound Data at (293.15, 298.15, and 303.15) K for 2-Propanone + Aniline, + N-Methylaniline, or + Pyridine Systems. J. Chem. Eng. Data 55 (2010) 2505-2511. https://doi.org/10.1021/je900874z [55] K. Tamura, A. Osaki, S. Murakami, B. Laurent, J.-P.E. Grolier, Thermodynamic properties of binary mixtures {x(2-alkoxyethanol)+(1−x)n-octane}: densities at 298.15 and 303.15 K and speeds of sound at 298.15 K. Fluid Phase Equilib. 173 (2000) 285-296. https://doi.org/10.1016/S0378-3812(00)00434-9 [56] E.B. Bagley, T.P. Nelson, J.W. Barlow, S.A. Chen, Internal Pressure Measurements and Liquid-State Energies. Ind. Eng. Chem. Fundamen. 9 (1970) 93-97. https://doi.org/10.1021/i160033a015 [57] E.B. Bagley, T.P. Nelson, J.M. Scigliano, Internal pressures of liquids and their relation to the enthalpies and entropies of mixing in nonelectrolyte solutions. J. Phys. Chem. 77 (1973) 2794-2798. https://doi.org/10.1021/j100641a016 [58] M.R.J. Dack, Solvent structure. The use of internal pressure and cohesive energy density to examine contributions to solvent-solvent interactions. Aust. J. Chem. 28 (1975) 1643- 1648. https://doi.org/10.1071/CH9751643 [59] E. Zorebski, Internal pressure studies of alcohols on the basis of ultrasonic measurements. Mol. Quantum Acoust. 26 (2005) 317–326. [60] R. Dey, A.K. Singh, J.D. Pandey, A new theoretical approach for estimating excess internal pressure. J. Mol. Liq. 124 (2006) 121-123. https://doi.org/10.1016/j.molliq.2005.09.005 [61] O. Nomoto, Molecular Sound Velocity and Molecular Compressibility of Liquid Mixtures. J. Chem. Phys. 21 (1953) 950-951. https://doi.org/10.1063/1.1699084 [62] O. Nomoto, Deviation from Linearity of the Concentration Dependence of the Molecular Sound Velocity in Liquid Mixtures. J. Phys. Soc. Jpn. 13 (1958) 1524-1528. https://doi.org/10.1143/JPSJ.13.1524 [63] R. Abraham, M. Abdulkhadar, C.V. Asokan, Ultrasonic investigation of molecular interaction in binary mixtures of nitriles with methanol/toluene. J. Chem. Thermodyn. 32 (2000) 1-16. https://doi.org/10.1006/jcht.1999.0608 [64] S.L. Oswal, P. Oswal, J.P. Dave, Speed of sound and isentropic compressibility of binary mixtures containing alkyl acetate or ethyl alkanoate, or ethyl bromo-alkanoate with hexane. J. Mol. Liq. 94 (2001) 203-219. https://doi.org/10.1016/S0167-7322(01)00269-0 [65] A. Chelkowski, Dielectric Physics. Elsevier, Amsterdam, 1980. [66] P. Brocos, A. Piñeiro, R. Bravo, A. Amigo, Refractive indices, molar volumes and molar refractions of binary liquid mixtures: concepts and correlations. Phys. Chem. Chem. Phys. 5 (2003) 550-557. https://doi.org/10.1039/B208765K 118 https://doi.org/10.1021/acs.jced.5b00802 [67] D. Keshapolla, V. Singh, R.L. Gardas, Volumetric, acoustic and transport properties of binary mixtures of benzyldimethylammonium based ionic liquids with N,N- dimethylformamide at temperature from 293.15 to 328.15 K. J. Mol. Liq. 199 (2014) 330-338. https://doi.org/10.1016/j.molliq.2014.09.030 [68] I. Alonso, I. Mozo, I.G. de la fuente, J.A. González, J.C. Cobos, Thermodynamics of ketone + amine mixtures Part IV. Volumetric and speed of sound data at (293.15; 298.15 and 303.15 K) for 2-butanone +dipropylamine, +dibutylamine or +triethylamine systems. Thermochim. Acta 512 (2011) 86-92. https://doi.org/10.1016/j.tca.2010.09.004 [69] M. Domínguez, H. Artigas, P. Cea, M.C. López, J.S. Urieta, Speed of sound and isentropic compressibility of the ternary mixture (2-Butanol + n-Hexane + 1- Butylamine) and the constituent binary mixtures at 298.15 K and 313.15 K. J. Mol. Liq. 88 (2000) 243-258. https://doi.org/10.1016/S0167-7322(00)00143-4 [70] P. Góralski, M. Wasiak, A. Bald, Heat Capacities, Speeds of Sound, and Isothermal Compressibilities of Some n-Amines and Tri-n-amines at 298.15 K. J. Chem. Eng. Data 47 (2002) 83-86. https://doi.org/10.1021/je010206v [71] S.L. Oswal, P. Oswal, R.L. Gardas, S.G. Patel, R.G. Shinde, Acoustic, volumetric, compressibility and refractivity properties and reduction parameters for the ERAS and Flory models of some homologous series of amines from 298.15 to 328.15 K. Fluid Phase Equilib. 216 (2004) 33-45. https://doi.org/10.1016/j.fluid.2003.09.007 [72] Neeti, S.K. Jangra, J.S. Yadav, Dimple, V.K. Sharma, Thermodynamic investigations of ternary o-toluidine + tetrahydropyran + N,N-dimethylformamide mixture and its binaries at 298.15, 303.15 and 308.15 K. J. Mol. Liq. 163 (2011) 36-45. https://doi.org/10.1016/j.molliq.2011.07.008 [73] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic solvents: physical properties and methods of purification. Wiley, New York, 1986. [74] S. Miyanaga, K. Tamura, S. Murakami, Excess molar volumes, isentropic and isothermal compressibilities, and isochoric heat capacities of (acetonitrile + benzene), (benzene + dimethylformamide), and (acetonitrile + dimethylformamide) at the temperature 298.15 K. J. Chem. Thermodyn. 24 (1992) 1077-1086. https://doi.org/10.1016/S0021- 9614(05)80018-7 [75] M.S. AlTuwaim, K.H.A.E. Alkhaldi, A.S. Al-Jimaz, A.A. Mohammad, Comparative study of physico-chemical properties of binary mixtures of N,N-dimethylformamide with 1-alkanols at different temperatures. J. Chem. Thermodyn. 48 (2012) 39-47. https://doi.org/10.1016/j.jct.2011.12.002 [76] J.P.E. Grolier, G. Roux-Desgranges, M. Berkane, E. Jiménez, E. Wilhelm, Heat capacities and densities of mixtures of very polar substances 2. Mixtures containing N, N-dimethylformamide. J. Chem. Thermodyn. 25 (1993) 41-50. https://doi.org/10.1006/jcht.1993.1005 [77] J. Konicek, I. Wadso, Thermochemical Properties of Some Carboxylic Acids, Amines and N-Substituted Amides in Aqueous Solution. Acta Chem. Scand. 25 (1971) 1541-1551. https://doi.org/10.3891/acta.chem.scand.25-1541 [78] H. Iloukhani, Z. Rostami, Measurement of Some Thermodynamic and Acoustic Properties of Binary Solutions of N,N-Dimethylformamide with 1-Alkanols at 30°C and Comparison with Theories. J. Solution Chem. 32 (2003) 451-462. https://doi.org/10.1023/A:1024524928767 119 J. Chem. Eng. Data 61 (2016) 1468-1478 [79] C.M. Kinart, W.J. Kinart, D. Chȩcińska-Majak, Relative Permittivity, Viscosity, and Speed of Sound for 2-Methoxyethanol + Butylamine Mixtures. J. Chem. Eng. Data 48 (2003) 1037-1039. https://doi.org/10.1021/je030127e [80] T.M. Aminabhavi, V.B. Patil, Density, Viscosity, Refractive Index, and Speed of Sound in Binary Mixtures of Ethenylbenzene with N,N-Dimethylacetamide, Tetrahydrofuran, N,N-Dimethylformamide, 1,4-Dioxane, Dimethyl Sulfoxide, Chloroform, Bromoform, and 1-Chloronaphthalene in the Temperature Interval (298.15−308.15) K. J. Chem. Eng. Data 43 (1998) 497-503. https://doi.org/10.1021/je980031y 120 Supporting information for: Thermodynamics of amide + amine mixtures. 1. Volumetric, speed of sound and refractive index data for N,N-dimethylformamide + N-propylpropan-1-amine, + N-butylbutan-1-amine, + butan-1-amine, or + hexan-1- amine systems at several temperatures Fernando Hevia, Ana Cobos, Juan Antonio González*, Isaías García de la Fuente, Luis Felipe Sanz G.E.T.E.F., Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid, Paseo de Belén, 7, 47011 Valladolid, Spain *e-mail: [email protected]a.es; Tel: +34 983 423757 Reference of the article: F. Hevia, A. Cobos, J.A. González, I. García de la Fuente, L.F. Sanz. J. Chem. Eng. Data 61 (2016) 1468-1478. https://doi.org/10.1021/acs.jced.5b00802. 121 128 Thermodynamics of amide + amine mixtures. 2. Volumetric, speed of sound and refractive index data for N,N-dimethylacetamide + N-propylpropan-1-amine, + N-butylbutan-1-amine, + butan-1-amine, or + hexan-1- amine systems at several temperatures Fernando Hevia, Ana Cobos, Juan Antonio González*, Isaías García de la Fuente, Víctor Alonso G.E.T.E.F., Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid, Paseo de Belén, 7, 47011 Valladolid, Spain *e-mail: [email protected]a.es; Tel: +34 983 423757 Abstract Data on density,  , speed of sound, c , and refractive index, D n , of binary systems containing N,N- dimethylacetamide (DMA) + N-propylpropan-1-amine (DPA) or + butan-1-amine (BA) at 293.15 K, 298.15 K and 303.15 K, and + N-butylbutan-1-amine (DBA) or + hexan-1-amine (HxA) at 298.15 K are reported. A densimeter and sound analyzer Anton Paar DSA 5000 has been used for the measurement of  and c , whereas D n values have been obtained by means of a refractometer RFM970 from Bellingham+Stanley. Also, values of excess molar volumes, E m V , excess isentropic compressibilities, E S  , excess speeds of sound, E c , excess isobaric thermal expansion coefficients, E p  , and of excess refractive indices, E D n , have been determined from these data. The investigated systems are characterized by amideamine interactions and structural effects, as it is shown by their negative or low positive E m V values and by the results from the application of the Prigogine-Flory-Patterson (PFP) model. The breaking of amineamine interactions is more relevant in systems containing linear primary amines than in those with linear secondary amines, and the E m V values are lower for the latter systems. Molar refraction has been used to evaluate the dispersive interactions in the mixtures under study, yielding the result that DPA and HxA systems present similar dispersive interactions and mainly differ in their dipolar character. Steric hindrance of the amide group in DMA leads to weaker amide-amine interactions than in the corresponding N,N-dimethylformamide (DMF) + amine systems. Adapted by permission from Springer Nature: Springer, Journal of Solution Chemistry. F. Hevia, A. Cobos, J.A. González, I. García de la Fuente, V. Alonso, Thermodynamics of amide + amine mixtures. 2. Volumetric, speed of sound and refractive index data for N,N-dimethylacetamide + N-propylpropan-1- amine, + N-butylbutan-1-amine, + butan-1-amine, or + hexan-1-amine systems at several temperatures, J. Solution Chem. 46 (2017) 150-174. https://doi.org/10.1007/s10953-016-0560-0. Copyright Springer Science+Business Media New York (2016). 129 J. Solution Chem. 46 (2017) 150-174 1. Introduction N,N-dimethylformamide (DMF) and N,N-dimethylacetamide (DMA) are very polar compounds (their dipole moment is 3.7 D [1, 2]) widely used in the industry, since they are aprotic protophilic substances with excellent donor-acceptor properties and solubility. In addition, they are employed for the separation of aromatic compounds and petroleum hydrocarbons. Amides are very common in nature and are found in proteins, RNA, DNA, amino acids, hormones and vitamins. The knowledge of liquid mixtures containing the amide functional group is necessary for a deeper understanding of more complex molecules, as those of biological interest [3]. Moreover, amides deserve to be investigated, as in pure state they show a significant local order [4]. In the case of N,N-dialkylamides, due to the absence of hydrogen bonds, this has been attributed to the existence of strong dipolar interactions [5]. Linear primary and secondary amines can form hydrogen bonds, appearing self-associated complexes and even heterocomplexes in mixtures with other associated compounds [6-8]. The amine group is also present in compounds of great biological significance. The proteins usually bound to DNA polymers contain various amine groups [9]. Histamine and dopamine are amines with the role of neurotransmitters [8, 10], and the breaking of amino acids releases amines. On the other hand, the ions of many ionic liquids used in technical applications are related to amines [11]. In earlier works, we have studied the thermodynamic properties of mixtures containing ketones and amines [12-19]. It is interesting to examine the effect of replacing a ketone, a moderately polar compound, by a more polar one, such as an amide. In our previous study [20], we have reported data on density,  , speed of sound, c , and refractive index, D n of the binary systems DMF + N-propylpropan-1-amine (DPA) or + butan-1-amine (BA) at (293.15-303.15) K, and + N-butylbutan-1-amine (DBA) or + hexan-1-amine (HxA) at 298.15 K. Now, we continue this series of works by replacing DMF by DMA, and treating these systems by means of the Prigogine-Flory-Patterson (PFP) model [21]. A survey of literature data shows that there are no experimental data on the considered mixtures. Nevertheless, DMF, or DMA + aniline or pyridine mixtures have been investigated rather extensively, reporting calorimetric, volumetric, vapor-liquid equilibria, c , or D n data [22-27]. Interestingly, at equimolar composition and 298.15 K, the excess molar enthalpies ( E m H ) of the DMF or DMA + aniline systems are, respectively, –2946 J·mol-1 [25] and –352 J·mol-1 [27], which underlines the importance of interactions between unlike molecules in such systems. 2. Experimental 2.1. Materials Table 1 contains information about the source and the purity of the compounds, which have been used without further purification. Table 2 lists experimental values of  , c , D n , thermal expansion coefficient, p  , isentropic compressibility, S  , and isothermal compressibility, T  , for the pure compounds. Our values are in good agreement with the literature data. 130 https://doi.org/10.1007/s10953-016-0560-0 2.2. Apparatus and procedure Binary mixtures have been prepared by mass in small vessels of about 10 cm3, using an analytical balance HR-202 (weighing accuracy 0.01 mg), with all weighings corrected for buoyancy effects. The standard uncertainty in the final mole fraction is estimated to be 0.0001. Molar quantities were calculated using the relative atomic mass Table of 2015 issued by the Commission on Isotopic Abundances and Atomic Weights (IUPAC) [28]. Temperatures were measured using Pt-100 resistances, calibrated according to the ITS-90 scale of temperature, against the triple point of water and the melting point of Ga. The standard uncertainty of the equilibrium temperature measurements is 0.01 K and 0.02 K for  and D n measurements, respectively. Densities and speeds of sound have been measured using a vibrating-tube densimeter and sound analyzer DSA 5000 from Anton Paar, which is automatically thermostated within 0.01 K. The calibration of the device has been described in a previous work [14]. The repeatability of the  measurements is 0.005 kg·m-3, whereas their overall standard uncertainty is 1·10-2 kg·m-3. The determination of the speed of sound is based on the measurement of the time of propagation of short acoustic pulses, whose central frequency is 3 MHz [29], and which are transmitted repeatedly through the sample. The repeatability of these c measurements is 0.1 m·s-1 and their standard uncertainty is 0.2 m·s-1. The excess volume, E m V , and the excess speed of sound, E c , of the system cyclohexane + benzene have been measured at (293.15-303.15) K to check the experimental technique. The experimental results and published values [30-32] are in good agreement. The standard uncertainty of E m V is (0.010 E m,max V + 0.005 cm3·mol-1), where E m,max V stands for the maximum absolute experimental value of E m V respect to the composition. The standard uncertainty of E c is estimated to be 0.4 m·s-1. A refractometer RFM970 from Bellingham+Stanley has been used for the D n measurements. The technique is based on the optical detection of the critical angle at the wavelength of the sodium D line (589.3 nm). The temperature is controlled by means of Peltier modules and its stability is 0.02 K. The refractometer has been calibrated using 2,2,4-trimethylpentane and toluene at the working temperatures (293.15-303.15) K, as recommended by Marsh [33]. The repeatability of the measurements is 0.00004, and the standard uncertainty is 0.00008. Table 1. Sample description. Chemical CAS number Source Purification method Purity Analysis method N,N-dimethyacetamide (DMA) 127-19-5 Sigma-Aldrich none  0.995 GCa N-propylpropan-1-amine (DPA) 142-84-7 Aldrich none  0.99 GCa N-butylbutan-1-amine (DBA) 111-92-2 Aldrich none  0.995 GCa butan-1-amine (BA) 109-73-9 Sigma--Aldrich none  0.995 GCa hexan-1-amine (HxA) 111-26-2 Aldrich none  0.995 GCa a In mole fraction. b Gas Chromatography 131 J. Solution Chem. 46 (2017) 150-174 Table 2. Physical properties of pure compounds at temperature T and pressure p = 0.1 MPa. a Property T/K DMF DPA DBA BA HxA *  /g·cm-3 293.15 0.94087 0.940846 [63] 0.73778 0.7375 [1] 0.75970 0.759571 [17] 0.73705 0.73712 [64] 0.76439 0.7651 [65] 298.15 0.93630 0.936233 [63]] 0.73322 0.73321 [66] 0.75553 0.755457 [17] 0.73233 0.73233 [64] 0.76019 0.76013 [67] 303.15 0.93169 0.931618 [63] 0.72870 0.729087 [17] 0.75146 0.751329 [17] 0.72750 0.72751 [64] 0.75589 0.7562 [65] c*/m·s-1 293.15 1475.1 1208.7 1209 [17] 1261.1 1261.2 [17] 1268.1 1323.9 298.15 1455.7 1455.37 [68] 1458 [69] 1187.3 1198 [70] 1241.5 1248 [70] 1246.1 1247.8 [71] 1303.8 1304.7 [67] 303.15 1435.7 1441 [72] 1166.7 1174 [70] 1222.5 1227 [70] 1224.5 1227 [70] 1283.5 1285 [70] * p  /10-3K-1 298.15 0.980 0.960 [73] 1.239 1.29 [1] 1.090 1.12 [1] 1.304 1.314 [70] 1.119 1.13 [67] * S  /TPa-1 293.15 488.5 927.8 926.5 [70] 827.7 843.7 746.4 298.15 504.0 504.29 [68] 967.5 947 [70] 858.7 849 [70] 879.4 876.6 [71] 773.9 773 [67] 303.15 520.7 516 [72] 1008.2 992 [70] 890.4 883 [70] 916.7 912 [70] 803.1 800 [70] * T  /TPa-1 298.15 653.5 671 [74] 1217.3 1183 [70] 1059.4 1039 [70] 1148.7 1145 [70] 971.1 975 [67] *mp C /J·mol-1·K-1 298.15 178.2 [75] 252.84 [1] 302 [70] 188 [76] 252 [76] * D n 293.15 1.43814 1.4384 [1] 1.40398 1.4043 [1] 1.40059 298.15 1.43595 1.4363 [69] 1.40135 1.40132 [77] 1.41488 1.4152 [1] 1.39789 1.3987 [1] 1.41571 1.4160 [70] 303.15 1.43382 1.4342 [69] 1.39871 1.4022 [70] 1.39507 1.3978 [70] a *  , density; * c , speed of sound; * p  , isobaric thermal expansion coefficient; * S  , adiabatic compressibility; * T  , isothermal compressibility; *mp C , isobaric molar heat capacity; and * D n , refractive index. The standard uncertainties are: ( ) 0.01uT = K (for * D n values, ( ) 0.02uT = K); ( ) 1up= kPa; ( ) *0.2u c = m·s-1; ( ) *0.00005u  = gcm-3; ( ) *0.00008 D un = and (relative values) ( ) * r0.015 p u  = ; ( ) * r0.002 S u  = ; ( ) * r0.012 T u  = . 3. Equations The experimental values of  , molar volume, m V , p  , and S  , can be obtained by means of a densimeter and sound analyzer rather directly. The values of ( )( ) 1 pp T    =− have been calculated under the assumption that  depends linearly on T in the range of temperatures 132 https://doi.org/10.1007/s10953-016-0560-0 considered. Moreover, as long as it is possible to neglect the dispersion and absorption of the acoustic wave, S  can be determined using  and c values through the Newton-Laplace equation: 2 1 Sc  = (1) The values id F of a quantity, F , for an ideal mixture at the same temperature and pressure as the investigated solution are calculated from the relations: id * * 1 1 2 2 F x F x F=+ ( mm ,p F V C= ) (2) id * * 1 1 2 2 F F F  =+ ( , pT F  = ) (3) where * i F denotes the property for the pure component i , mp C is the molar heat capacity at constant pressure, T  is the isothermal compressibility and * id mm / iiix V V  = represents the ideal volume fraction. In the case of S  and c , the following expressions are used: id id 2 m id id id m () p ST p TV C   =− (4) 1/2 id id id 1 S c   =   (5) being ( ) id id 1 1 2 2 m /x M x M V  =+ the ideal density, and i M the molar mass of the pure component i . For the refractive index, D n , the ideal values are obtained from the equation [34]: ( ) ( ) id * * D D1 2 1/2 2 1D2 2 n n n   =+   (6) The excess properties, E F , are then obtained from the relation: E id F F F=− ( mD , , , , Sp F V c n  = ) (7) 4. Results Values of  , c , and E m V as functions of 1 x , the mole fraction of DMA, and at the considered temperatures are included in Table 3. For DBA or HxA mixtures, the measurements were made at 298.15 K only, due to: (i) their low E m ||V values; (ii) the weak temperature dependence of E m V encountered for the systems with BA or DPA. The corresponding results of E S  , E c , and E p  at 298.15 K are given in Table 4. The D n values and their corresponding excess functions, E D n , are collected in Table 5. Our experimental method is not accurate enough to determine E D n values for the systems containing DBA or HxA. Some of these results are represented in Figures 1-7. We have not found literature data for comparison. The data have been fitted by an unweighted linear least-squares regression to a Redlich- Kister equation [35]: 133 J. Solution Chem. 46 (2017) 150-174 Table 3. Densities,  , excess molar volumes, E m V , and speeds of sound, c, for N,N-dimethylacetamide (1) + amine (2) mixtures at temperature T and pressure p = 0.1 MPa. a 1 x  /g·cm-3 E m V /cm3·mol-1 c /m·s-1 1 x  /g·cm-3 E m V /cm3·mol-1 c /m·s-1 DMA (1) + DPA (2); T/K= 293.15 0.0000 0.73778 1208.7 0.4914 0.81947 –0.2137 1304.1 0.0621 0.74684 –0.0656 1218.8 0.5582 0.83282 –0.2096 1321.1 0.1201 0.75556 –0.1122 1228.6 0.6520 0.85273 –0.1936 1347.3 0.1432 0.75911 –0.1272 1232.6 0.7141 0.86668 –0.1719 1366.3 0.2142 0.77035 –0.1659 1245.4 0.7604 0.87751 –0.1495 1381.5 0.2434 0.77511 –0.1780 1250.8 0.8012 0.88743 –0.1312 1395.5 0.3154 0.78722 –0.1971 1264.9 0.8494 0.89962 –0.1098 1413.2 0.3398 0.79148 –0.2052 1269.9 0.9017 0.91334 –0.0754 1433.4 0.4140 0.80484 –0.2178 1286.0 0.9457 0.92538 –0.0441 1451.5 0.4668 0.81475 –0.2175 1298.2 1.0000 0.94087 1475.1 DMA (1) + DPA (2); T/K= 298.15 0.0000 0.73322 1187.3 0.5678 0.83024 –0.2214 1303.8 0.0668 0.74299 –0.0767 1198.4 0.5999 0.83691 –0.2120 1312.5 0.1010 0.74814 –0.1103 1204.2 0.6543 0.84864 –0.1998 1328.2 0.1466 0.75510 –0.1400 1212.2 0.7153 0.86240 –0.1823 1347.1 0.2032 0.76403 –0.1719 1222.5 0.7605 0.87301 –0.1619 1362.0 0.2606 0.77342 –0.1967 1233.5 0.8006 0.88277 –0.1440 1375.9 0.3112 0.78198 –0.2125 1243.6 0.8576 0.89720 –0.1137 1396.8 0.3584 0.79022 –0.2214 1253.4 0.8960 0.90729 –0.0875 1411.8 0.3933 0.79648 –0.2258 1261.1 0.9495 0.92191 –0.0469 1433.8 0.4622 0.80932 –0.2314 1277.0 1.0000 0.93630 1455.7 0.5019 0.81700 –0.2303 1286.7 DMA (1) + DPA (2); T/K= 303.15 0.0000 0.72870 1166.7 0.5632 0.82479 –0.2412 1282.9 0.0609 0.73755 –0.0658 1176.8 0.5926 0.83089 –0.2360 1290.9 0.1008 0.74351 –0.1011 1183.7 0.6511 0.84343 –0.2204 1307.7 0.1975 0.75853 –0.1674 1201.1 0.7089 0.85641 –0.2019 1325.4 0.2416 0.76569 –0.1905 1209.6 0.7618 0.86882 –0.1802 1342.8 0.2915 0.77407 –0.2173 1219.5 0.7881 0.87517 –0.1655 1351.9 0.3409 0.78258 –0.2288 1229.8 0.8571 0.89250 –0.1226 1376.9 0.3957 0.79240 –0.2427 1241.8 0.9026 0.90448 –0.0903 1394.6 0.4536 0.80316 –0.2476 1255.2 0.9464 0.91644 –0.0520 1412.6 0.4910 0.81033 –0.2451 1264.2 1.0000 0.93169 1435.7 DMA (1) + DBA (2); T/K= 298.15 0.0000 0.75553 1241.5 0.5040 0.81954 0.0540 1304.4 0.0556 0.76111 0.0057 1246.5 0.6059 0.83747 0.0568 1324.5 0.1101 0.76685 0.0150 1251.6 0.6466 0.84529 0.0572 1333.6 0.1416 0.77031 0.0202 1254.8 0.6971 0.85562 0.0542 1346.1 0.2017 0.77724 0.0263 1261.3 0.7538 0.86809 0.0502 1361.6 0.2645 0.78493 0.0327 1268.7 0.7900 0.87660 0.0437 1372.5 134 https://doi.org/10.1007/s10953-016-0560-0 0.3006 0.78956 0.0411 1273.2 0.8612 0.89469 0.0332 1396.6 0.3448 0.79551 0.0436 1279.2 0.8925 0.90328 0.0271 1408.3 0.3993 0.80324 0.0513 1287.1 0.9566 0.92228 0.0106 1435.3 0.4461 0.81028 0.0526 1294.4 1.0000 0.93629 1455.7 DMA (1) + BA (2); T/K= 293.15 0.0000 0.73705 1268.1 0.5968 0.85698 –0.1771 1383.5 0.0490 0.74668 –0.0355 1276.6 0.6577 0.86951 –0.1624 1396.8 0.1067 0.75803 –0.0680 1286.8 0.7542 0.88954 –0.1354 1418.5 0.1477 0.76612 –0.0867 1294.1 0.8499 0.90960 –0.1022 1440.4 0.2508 0.78662 –0.1253 1313.2 0.9063 0.92143 –0.0716 1453.5 0.3494 0.80649 –0.1611 1332.2 0.9420 0.92898 –0.0526 1461.8 0.4513 0.82709 –0.1687 1352.7 1.0000 0.94108 1475.2 0.5505 0.84739 –0.1736 1373.5 DMA (1) + BA (2); T/K= 298.15 0.0000 0.73233 1246.1 0.5646 0.84566 –0.1948 1356.4 0.0536 0.74283 –0.0378 1255.7 0.6946 0.87259 –0.1823 1385.3 0.1214 0.75625 –0.0862 1268.1 0.7540 0.88492 –0.1607 1398.7 0.1929 0.77041 –0.1198 1281.2 0.8534 0.90573 –0.1210 1421.8 0.2540 0.78258 –0.1418 1292.8 0.9055 0.91672 –0.0960 1434.2 0.3630 0.80457 –0.1808 1314.3 0.9446 0.92485 –0.0606 1443.0 0.4684 0.82594 –0.1925 1335.9 1.0000 0.93633 1455.6 0.5051 0.83343 –0.1938 1343.6 DMA (1) + BA (2); T/K= 303.15 0.0000 0.72750 1224.5 0.4971 0.82713 –0.2009 1321.7 0.0517 0.73770 –0.0456 1233.9 0.6574 0.86025 –0.1930 1356.9 0.1082 0.74889 –0.0875 1244.3 0.7957 0.88919 –0.1582 1388.8 0.1535 0.75783 –0.1083 1252.8 0.8498 0.90040 –0.1161 1401.1 0.2556 0.77826 –0.1617 1272.3 0.9090 0.91297 –0.0918 1415.1 0.2921 0.78562 –0.1783 1279.6 0.9404 0.91948 –0.0590 1422.3 0.3582 0.79885 –0.1832 1292.6 1.0000 0.93195 1436.1 0.4583 0.81922 –0.2014 1313.3 DMA (1) + HxA (2); T/K= 298.15 0.0000 0.76019 1303.8 0.6130 0.85274 0.0027 1374.5 0.0575 0.76737 0.0052 1308.5 0.6994 0.86931 –0.0020 1389.5 0.1197 0.77545 0.0052 1314.0 0.7620 0.88202 –0.0064 1401.2 0.1582 0.78060 0.0084 1317.5 0.8060 0.89133 –0.0094 1410.3 0.2079 0.78743 0.0114 1322.4 0.8544 0.90192 –0.0086 1420.5 0.2450 0.79271 0.0087 1326.1 0.8959 0.91134 –0.0090 1430.2 0.3068 0.80176 0.0082 1333.0 0.9467 0.92330 –0.0066 1442.2 0.4037 0.81674 0.0063 1344.4 1.0000 0.93637 1455.8 0.5122 0.83471 0.0068 1359.1 a The standard uncertainties are: ( ) 10.0001ux = ; ( ) 1up= kPa; ( ) 0.01uT = K. The standard uncertainties are: ( ) 0.00005u  = gcm-3; ( ) E m uV = (0.010 E m,max V + 0.005 cm3·mol-1); ( ) 0.2uc = m·s-1. 135 J. Solution Chem. 46 (2017) 150-174 Table 4. Excess functions, at temperature T = 298.15 K and pressure p = 0.1 MPa, for S  , adiabatic compressibility, c, speed of sound, and p  , isobaric thermal expansion coefficient, of N,N- dimethylacetamide (1) + amine (2) mixtures. a 1 x E S  /TPa-1 E c /m·s-1 E p  /10-6·K-1 b 1 x E S  /TPa-1 E c /m·s-1 E p  /10-6·K-1 b DMA (1) + DPA (2) 0.0668 –9.7 5.8 –1 0.5678 –45.0 38.3 –26 0.1010 –14.1 8.6 –2 0.5999 –44.6 39.1 –26 0.1466 –19.5 12.3 –4 0.6543 –43.4 39.9 –26 0.2032 –25.6 16.7 –7 0.7153 –40.5 39.7 –26 0.2606 –31.1 21.0 –10 0.7605 –37.3 38.3 –24 0.3112 –35.1 24.5 –14 0.8006 –33.6 36.1 –22 0.3584 –38.2 27.6 –16 0.8576 –26.7 30.7 –18 0.3933 –40.3 29.8 –19 0.8960 –20.9 25.4 –14 0.4622 –43.2 33.7 –22 0.9495 –11.2 14.7 –7 0.5019 –44.3 35.7 –24 DMA (1) + DBA (2) 0.0556 –2.3 1.7 0.5040 –16.7 15.2 0.1101 –4.3 3.3 0.6059 –18.1 17.5 0.1416 –5.5 4.3 0.6466 –18.2 18.1 0.2017 –7.8 6.2 0.6971 –18.1 18.8 0.2645 –10.1 8.1 0.7538 –17.2 18.7 0.3006 –11.2 9.2 0.7900 –16.2 18.3 0.3448 –12.7 10.6 0.8612 –13.1 15.9 0.3993 –14.3 12.3 0.8925 –11.0 13.9 0.4461 –15.4 13.6 0.9566 –5.4 7.4 DMA (1) + BA (2) 0.0536 –7.7 5.4 –11 0.5646 –35.9 35.0 –31 0.1214 –16.2 11.7 –20 0.6946 –31.3 33.6 –31 0.1929 –23.1 17.5 –25 0.7540 –27.4 30.8 –31 0.2540 –27.9 22.0 –27 0.8534 –18.8 22.9 –26 0.3630 –33.9 28.7 –29 0.9055 –13.2 16.8 –22 0.4684 –36.4 33.1 –30 0.9446 –8.1 10.6 –16 0.5051 –36.5 34.1 –30 DMA (1) + HxA (2) 0.0575 –1.8 1.6 0.6130 –12.2 13.3 0.1197 –3.8 3.4 0.6994 –11.7 13.5 0.1582 –4.9 4.3 0.7620 –10.6 12.6 0.2079 –6.3 5.7 0.8060 –9.7 11.9 0.2450 –7.1 6.6 0.8544 –7.9 10.0 0.3068 –8.8 8.3 0.8959 –6.4 8.3 0.4037 –10.5 10.3 0.9467 –3.5 4.8 0.5122 –11.9 12.3 a The standard uncertainties are: ( ) 10.0001ux = ; ( ) 1up= kPa; ( ) 0.01uT = K. The standard uncertainties are: ( ) E0.4uc = ; and (relative values) ( ) E r0.015 S u  = ; E r( ) 0.025 p u  = . b Density values at 293.15 K and 303.15 K at the mole fractions reported at 298.15 K were obtained from the corresponding Redlich-Kister adjustments for E m V . 136 https://doi.org/10.1007/s10953-016-0560-0 Table 5. Refractive indices, D n , and the corresponding excess values, E D n , of N,N-dimethylacetamide (1) + amine (2) mixtures at temperature T and pressure p = 0.1 MPa. a 1 x D n E D n /10-5 1 x D n E D n /10-5 DMA (1) + DPA (2); T/K = 293.15 0.0000 1.40398 0.5582 1.42085 104 0.0621 1.40569 23 0.6520 1.42418 102 0.1201 1.40731 42 0.7141 1.42649 97 0.1432 1.40797 49 0.7604 1.42826 90 0.2142 1.41003 69 0.8012 1.42986 82 0.3154 1.41303 87 0.8494 1.43179 69 0.3398 1.41376 89 0.9017 1.43396 52 0.4140 1.41609 99 0.9457 1.43581 32 0.4668 1.41780 103 1.0000 1.43814 0.4914 1.41860 104 DMA (1) + DPA (2); T/K = 298.15 0.0000 1.40135 0.4622 1.41524 110 0.0668 1.40324 28 0.5678 1.41882 111 0.1010 1.40422 41 0.6543 1.42192 107 0.1466 1.40554 56 0.7153 1.42421 101 0.2032 1.40720 72 0.7605 1.42597 94 0.2606 1.40892 86 0.8006 1.42755 85 0.3112 1.41045 95 0.8576 1.42988 70 0.3584 1.41191 101 0.9495 1.43376 31 0.3933 1.41302 106 1.0000 1.43595 DMA (1) + DPA (2); T/K = 303.15 0.0000 1.39871 0.5632 1.41619 105 0.0609 1.40041 21 0.5926 1.41723 104 0.1008 1.40155 35 0.6511 1.41934 97 0.1975 1.40440 65 0.7089 1.42153 91 0.2416 1.40577 79 0.7881 1.42468 79 0.2915 1.40727 87 0.8571 1.42755 63 0.3409 1.40885 99 0.9026 1.42948 46 0.3957 1.41059 104 0.9464 1.43142 29 0.4536 1.41246 106 1.0000 1.43382 0.4910 1.41370 106 DMA (1) + DBA (2); T/K = 298.15 0.0000 1.41495 0.5543 1.42341 0.0554 1.41559 0.6061 1.42456 0.1101 1.41627 0.6466 1.42545 0.1413 1.41667 0.6971 1.42667 0.2106 1.41761 0.7538 1.42813 0.2645 1.41838 0.7900 1.42907 0.3006 1.41893 0.8613 1.43120 0.3448 1.41961 0.8925 1.43216 0.3993 1.42053 0.9566 1.43436 0.4461 1.42137 1.0000 1.43592 0.5040 1.42243 137 J. Solution Chem. 46 (2017) 150-174 5.1. Theoretical results Table 7 lists the values of * m,i V and * i p used in this work. 12  values determined from E m V at 298.15 K and equimolar composition are given in Table 8, which also contains the different contributions to E m V calculated according to equations (10)-(12). A comparison between experimental and theoretical results is shown, for some selected mixtures, in Figures 8 and 9. Figure 8: Excess molar volumes, E m V , for DMA (1) + amine (2) systems at 0.1 MPa and 298.15 K. Full symbols, experimental values (this work): (), BA; (), DBA. Solid lines, Flory results. Dashed lines, contributions to E m V according to the Prigogine-Flory-Patterson model (“int”, interactional; “cur”, curvature; “P*”, p* effect): (– – –), BA; (– · · –), DBA. Figure 9: Excess molar volumes, E m V , for amide (1) + DPA (2) systems at 0.1 MPa and 298.15 K. Full symbols, experimental values: (), DMF [20]; (), DMA (this work). Solid lines, Flory results. Dashed lines, contributions to E m V according to the Prigogine-Flory-Patterson model (“int”, interactional; “cur”, curvature; “P*”, p* effect): (– – –), DMF; (– · · –), DMA. 6. Discussion In the present section, the values of the thermophysical properties and the excess functions are referred to T = 298.15 K and 10.5x= . DMA is a strongly polar compound (dipole moment /D  = 3.7 [1]). This is reflected in the fact that DMA + alkane mixtures present miscibility gaps up to quite high temperatures. For instance, the upper critical solution temperature of the heptane system is 309.8 K [40]. The amines considered in this work are linear, either primary or secondary. They are weakly self-associated and their dipole moments /D  are low: 1.3 (BA) [41], 1.3 (HxA) [2], 1.0 (DPA) 144 https://doi.org/10.1007/s10953-016-0560-0 [41], and 1.1 (DBA) [41]. The values of the excess molar enthalpy, E1 m/ J·molH− , for the heptane mixtures are: 1192 (BA) [42], 962 (HxA) [42], 424 (DPA) [43], and 317 (DBA) [43]. These values can be explained in terms of the breaking of amine-amine interactions upon mixing. We note that E m H values are lower for systems with secondary amines, as the amine group is more sterically hindered and self-association is lower in such amines. The corresponding values of E 3 1 m(heptane)/ cm ·molV− are: 0.7171 (BA) [44], 0.3450 (HxA) [44], 0.2752 (DPA) [45], and 0.0675 (DBA) [45]. It is well stated that positive E m V values arise from the disruption of interactions between like molecules, whereas negative ones appear when interactions between unlike molecules are created and/or when structural effects (differences in size and shape [46-48] or interstitial accommodation [49]) exist. The parallel change of E m H and E m V indicates that the disruption of amine-amine interactions upon mixing is the main contribution to E m V . Nevertheless, the low value of E m V in the DBA + heptane system and the negative one of the DBA + hexane system, –0.1854 cm3·mol-1 [50], allow to state that structural effects are present, since this is suggested to be the most relevant contribution when a positive E m H value is together with a negative E m V value [48]. For the DMA + amine mixtures, we have obtained here either negative or small and positive E 3 1 m/ cm ·molV− values (Figures 1, 2): –0.1940 (BA); –0.2275 (DPA), 0.0063 (HxA); 0.0553 (DBA), which point to the existence of interactions between unlike molecules and structural effects. On the other hand, along a given homologous series, E m V increases with the amine size (Figures 1, 2). This means that, other than the phenomena which decrease E m V (differences in size between components and lower positive contributions because of the disruption of amineamine interactions), the predominant effects are: i) the higher number of broken interactions between DMA molecules by longer amines; and ii) the lower number and weaker DMA-amine interactions created in systems involving larger amines, as then the amine group is more sterically hindered. The replacement of HxA by DPA leads to a lower E m V value, as in the case of the HxA or DPA + heptane mixtures (see above). Therefore, this trend can be explained by the decrease of the positive contribution to E m V related to the breaking of interactions between like molecules when a secondary amine is involved. Interestingly, the same behavior is encountered in 1-alkanol + HxA or + DPA systems [51, 52]. The small positive E m V values of the DBA solution over the whole concentration range underline the importance of the positive contribution to E m V from the breaking of DMA-DMA interactions by the large aliphatic surface of DBA. In fact, the corresponding E m V curve, skewed to higher 1 x values (Figure 1), reveals that DBA is a good breaker of the interactions between DMA molecules. The mentioned surface is smaller for HxA and then very small positive E m V values are encountered at lower DMA concentrations (Figure 2). Negative E m V values at the other side of the concentration range (Figure 2) suggest that interactions between unlike molecules are more favorable. This is consistent with the observed E m V minimum of the BA mixture at 1 x 0.56 (Figure 2). Interestingly, the symmetry of the E m V curve of the DPA system is opposite to that of the BA solution (Figure 1). This feature together with E m V (DMA + DPA) < E m V (DMA + BA) (Table 3) suggest that structural effects become relevant in the system with DPA. Calculations using the PFP model are in agreement with this statement (see below). 145 J. Solution Chem. 46 (2017) 150-174 The values of the derived properties E S  , E p  are negative, while those of E c are positive (Figures 3-6, Table 6). In any case, all of them are rather small in absolute value, indicating that the studied systems show a nearly ideal behavior with respect to these properties. Nevertheless, it should be mentioned that negative values of E S  , E p  and ( ) E mpp A V T=   (– 3·10-3 cm3·mol-1·K-1 (DPA); –2.8·10-3 cm3·mol-1·K-1 (BA)) are characteristic of systems where relevant interactions between unlike molecules and/or structural effects exist [19, 53]. On the other hand, the quantities E m V and E S  change in line along a homologous series, while E c shows an opposite variation. The same behavior is observed when replacing HxA by DPA. 6.1. Internal pressures The internal pressure [54-57], int P , is an adequate quantity to examine the intermolecular forces in liquids and liquid mixtures: int p T P T p   =− (17) Here, the T  values of the mixtures have been obtained from 2 m m () T p S p TV C   =+ (18) assuming E m0 p C= [58], and E0 p  = when experimental data are not available. For the pure compounds studied, * int / MPaP= 447.0 (DMA), 338.3 (BA), 343.5 (HxA), 303.4 (DPA), and 306.7 (DBA), whereas for the DMA mixtures int / MPaP= 386.8 (BA), 381.9 (HxA), 353.2 (DPA), and 348.2 (DBA). The most important contributions to int P arise from dispersion forces and weak dipole-dipole interactions [56], and therefore these results suggest that dipolar interactions are stronger in the systems with linear primary amines. We have also determined the excess internal pressures, E id int int int P P P=− , ( id i int idd/ p T P T p  =− [59]). Thus, E int(DMA)/ MPaP= 10.8 (BA), 5.3 (HxA), 11.7 (DPA), and 6.3 (DBA). Systems with strong interactions between unlike molecules show large E int P values. For example, E int P= 61.4 MPa for the aniline + 2-propanone system [19]. This is seen to be verified by the above results, although the fact that the value for the HxA mixture is lower than for the DPA system may be due, at least partially, to structural effects, as they are similar to the hexane + hexadecane mixture (6.5 MPa [1, 60]). This is also consistent with the observed trend for their E m V values [12-15, 17, 19]. The Van der Waals model allows to obtain the internal pressure from [55]: VDW int * * E fm,1 2 fm,21 m RT Pp x V x V V =− ++ (19) where ( ) ** fm, int, / ii V RT p P=+ is the free molar volume of the pure component i . The relative deviations of the results obtained from equation (19) and the experimental ones, 146 https://doi.org/10.1007/s10953-016-0560-0 ( ) VDW int int int /P P P− , for the DMA mixtures are 2.7% (BA), 1.6% (HxA), 5.8% (DPA), and 3.6% (DBA). One can conclude that the Van der Waals equation is useful for the int P calculation of the studied solutions. 6.2. Molar refractions The refractive index at optical wavelengths is closely related to dispersion forces, since the molar refraction (or molar refractivity), m R , defined by the Lorentz-Lorenz equation [61, 62]: mm 0 2 D 2 D 1 3 2 Ae nN RV n   − == + (20) (where A N and 0  stand for Avogadro’s constant and the vacuum permittivity, respectively) is proportional to the mean electronic contribution, e  , to the polarizability, [61]. The values of 31 m/ cm ·molR− for the investigated systems are 24.7 (BA), 28.2 (HxA), 29.0 (DPA), and 33.6 (DBA). Clearly, dispersive interactions are more important for larger amines in a homologous series. Moreover, it can be stated that these forces are quite similar for the HxA and DPA systems, and therefore the corresponding difference in their int P values is principally due to dipolar interactions. 6.3. Comparison with other systems For the considered amines, and also for aniline, mixtures with DMF are characterized by lower E 3 1 m/ cm ·molV− values: –0.2630 (BA), –0.0210 (HxA), –0.2893 (DPA), and 0.0178 (DBA) [20]; –0.6615 (aniline) [22], and –0.6092 cm3·mol-1 at 303.15 K for DMA + aniline [26]. This allows to conclude that amide-amine interactions are stronger in mixtures with DMF. Interestingly, deviations between experimental int P values and results from equation (12) are slightly larger for DMF systems: 7.6% (BA), 5.7% (HxA), 4.2% (DPA) and 3.1% (DBA) [20], which suggests that dipolar interactions are more relevant in such solutions. Finally, it is noteworthy that E m V values are much lower for the mixture including aniline; this reveals that interactions between unlike molecules are strengthened when aniline is involved. The same trend is encountered for 2-alkanone + DPA or + aniline systems [12-19]. It is here pertinent to examine the effect of replacing a N,N-dialkylamide (DMF or DMA) by a 2-alkanone of similar size (2-propanone or 2-butanone). E m V values of 2-propanone or 2- butanone + DPA, or + DBA mixtures are higher than those of the corresponding systems with DMF or DMA. For example, E 3 1 m(DPA)/ cm ·molV− = 0.243 (2-propanone) [12], 0.144 (2- butanone) [17] and E 3 1 m(DBA)/ cm ·molV− = 0.417 (2-propanone) [12]; 0.265 (2-butanone) [17]. In addition, the E m H values of these 2-alkanone mixtures are positive [16]. All this suggests that amide-amine interactions are stronger than alkanone-amine interactions in mixtures containing a linear secondary amine. Interestingly, aniline mixtures show a rather different behavior. For the 2-alkanone + aniline mixtures, we have E m H / J·mol-1 = –1236 (2-propanone); –1165 (2- butanone) [18] and E 3 1 m/ cm ·molV− = –1.183 (2-propanone) [19]; –1.246 (2-butanone) [13]. The lower E m V and the higher E m H values of the 2-propanone mixture compared to those of the DMF 147 J. Solution Chem. 46 (2017) 150-174 system indicate that interactions between unlike molecules are stronger in the latter solution and that structural effects are more relevant in the 2-propanone system. Surprisingly, DMA- aniline interactions seem to be weaker than (2-butanone)-aniline interactions (see the corresponding E m H values of these systems). This matter deserves a careful investigation, currently undertaken. 6.4. Prigogine-Flory-Patterson theory In the framework of this theory, calculations show that 12  increases when replacing DMF by DMA in systems with a given amine (component 2) (Table 8). In the original Flory model [37], 12  is proportional to * /s v   , being * s v the reduction volume of a segment and 11 22 12 2      = + − . The positive ij  magnitudes characterize the energy of interaction for a pair of neighboring sites. As 22  remains constant, the 12  value increase may be due to the predominance of the 12  decrease over that of 11  . The latter is linked to a weakening of the amide-amide interactions; the former merely reflects a weakening of the interactions between unlike molecules. Similar trends are also valid when BA is replaced by HxA in DMF solutions. Interestingly, the DMA + DPA or + DBA systems are characterized by the same 12  value (Table 8), which suggests that such mixtures essentially differ in size effects. Finally, an inspection of the different contributions to E m V listed in Table 8 shows that * E E E m,curvature m m, effect ( )/ p V V V+ is much higher (in absolute value) for systems with DPA. This indicates that structural effects are more important for such a type of solution. Regarding the composition dependence of E m V , the model describes fairly well this excess function for the systems DMF or DMA + BA, or + DPA (Figures 8,9) . Results for the mixtures with DBA or HxA are somewhat poorer as the representation of low E m V values is a very difficult task for any theoretical model. 7. Conclusions Binary systems of DMA + BA, + HxA, + DPA or + DBA have been studied at different temperatures, reporting values of  , c , D n and of the excess functions ( E m,V E, S  E,c E p  and E D n ) determined from these ones. Negative and low positive E m V values for the investigated mixtures point out to the existence of interactions between unlike molecules, as well as of structural effects. This is also supported by results from the PFP model. E m V values are higher in the case of systems with linear primary amines, as the breaking of amine-amine interactions is more relevant than when linear secondary amines are involved. Steric hindrance of the amide group appears to be relevant, since comparisons with results of systems including amines and DMF or DMA show that interactions between unlike molecules are stronger in the former systems. The main differences between mixtures containing DPA and HxA come essentially from dipolar interactions. Dispersive interactions increase with the amine size in systems with a given amide. 148 https://doi.org/10.1007/s10953-016-0560-0 Acknowledgements F. Hevia gratefully acknowledges the grant received from the program ‘Ayudas para la Formación de Profesorado Universitario (convocatoria 2014), de los subprogramas de Formación y de Movilidad incluidos en el Programa Estatal de Promoción del Talento y su Empleabilidad, en el marco del Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016, de la Secretaría de Estado de Educación, Formación Profesional y Universidades, Ministerio de Educación, Cultura y Deporte, Gobierno de España’. References [1] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic solvents: physical properties and methods of purification. Wiley, New York, 1986. [2] A.L. McClellan, Tables of Experimental Dipole Moments. Vols. 1,2,3, Rahara Enterprises, El Cerrito, US, 1974. [3] E.S. Eberhardt, R.T. Raines, Amide-Amide and Amide-Water Hydrogen Bonds: Implications for Protein Folding and Stability. J. Am. Chem. Soc. 116 (1994) 2149-2150. https://doi.org/10.1021/ja00084a067 [4] W.L. Jorgensen, C.J. Swenson, Optimized intermolecular potential functions for amides and peptides. Structure and properties of liquid amides. J. Am. Chem. Soc. 107 (1985) 569-578. https://doi.org/10.1021/ja00289a008 [5] J.A. Gonzalez, J.C. Cobos, I. García de la Fuente, Thermodynamics of liquid mixtures containing a very strongly polar compound: Part 6. DISQUAC characterization of N,N- dialkylamides. Fluid Phase Equilib. 224 (2004) 169-183. https://doi.org/10.1016/j.fluid.2004.02.007 [6] J.A. González, I. García de la Fuente, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult's Law: Part 4. Application of the DISQUAC model to mixtures of 1-alkanols with primary or secondary linear amines. Comparison with Dortmund UNIFAC and ERAS results. Fluid Phase Equilib. 168 (2000) 31-58. https://doi.org/10.1016/S0378-3812(99)00326-X [7] U. Domańska, M. Marciniak, Volumetric and Solid + Liquid Equilibrium Data for Linear 1-Alkanol + Decylamine Mixtures. Analysis in Terms of ERAS, DISQUAC, and Modified UNIFAC†. Ind. Eng. Chem. Res. 43 (2004) 7647-7656. https://doi.org/10.1021/ie0401206 [8] F.F. Liew, T. Hasegawa, M. Fukuda, E. Nakata, T. Morii, Construction of dopamine sensors by using fluorescent ribonucleopeptide complexes. Bioorg. Med. Chem. 19 (2011) 4473-4481. https://doi.org/10.1016/j.bmc.2011.06.031 [9] D.L. Nelson, M.M. Cox, Lehninger Principles of Biochemistry. 3rd ed., Worth Publishing, New York, 2000. [10] J.M. Sonner, R.S. Cantor, Molecular Mechanisms of Drug Action: An Emerging View. Annu. Rev. Biophys. 42 (2013) 143-167. https://doi.org/10.1146/annurev-biophys- 083012-130341 [11] M. Götz, R. Reimert, S. Bajohr, H. Schnetzer, J. Wimberg, T.J.S. Schubert, Long-term thermal stability of selected ionic liquids in nitrogen and hydrogen atmosphere. Thermochim. Acta 600 (2015) 82-88. https://doi.org/10.1016/j.tca.2014.11.005 [12] I. Alonso, V. Alonso, I. Mozo, I. García de la Fuente, J.A. González, J.C. Cobos, Thermodynamics of ketone + amine mixtures: Part II. Volumetric and speed of sound 149 J. Solution Chem. 46 (2017) 150-174 data at (293.15, 298.15 and 303.15) K for 2-propanone + dipropylamine, + dibutylamine or + triethylamine systems. J. Mol. Liq. 155 (2010) 109-114. https://doi.org/10.1016/j.molliq.2010.05.022 [13] I. Alonso, I. Mozo, I.G. de la Fuente, J.A. González, J.C. Cobos, Thermodynamics of Ketone + Amine Mixtures. Part III. Volumetric and Speed of Sound Data at (293.15, 298.15, and 303.15) K for 2-Butanone + Aniline, + N-Methylaniline, or + Pyridine Systems. J. Chem. Eng. Data 55 (2010) 5400-5405. https://doi.org/10.1021/je100472t [14] J.A. González, I. Alonso, I. Mozo, I. García de la Fuente, J.C. Cobos, Thermodynamics of (ketone + amine) mixtures. Part VI. Volumetric and speed of sound data at (293.15, 298.15, and 303.15) K for (2-heptanone + dipropylamine, +dibutylamine, or +triethylamine) systems. J. Chem. Thermodyn. 43 (2011) 1506-1514. https://doi.org/10.1016/j.jct.2011.05.003 [15] I. Alonso, I. Mozo, I.G. De La Fuente, J.A. González, J.C. Cobos, Thermodynamics of ketone + amine mixtures 7. Volumetric and speed of sound data at (293.15, 298.15 and 303.15) K for 2-pentanone + aniline, + N-methylaniline, or + pyridine systems. J. Mol. Liq. 160 (2011) 180-186. https://doi.org/10.1016/j.molliq.2011.03.015 [16] J.A. González, I. Alonso, I. García De La Fuente, J.C. Cobos, Thermodynamics of ketone + amine mixtures. Part IX. Excess molar enthalpies at 298.15 K for dipropylamine, or dibutylamine + 2-alkanone systems and modeling of linear or aromatic amine + 2-alkanone mixtures in terms of DISQUAC and ERAS. Fluid Phase Equilib. 343 (2013) 1-12. https://doi.org/10.1016/j.fluid.2013.01.011 [17] I. Alonso, I. Mozo, I.G. de la fuente, J.A. González, J.C. Cobos, Thermodynamics of ketone + amine mixtures Part IV. Volumetric and speed of sound data at (293.15; 298.15 and 303.15 K) for 2-butanone +dipropylamine, +dibutylamine or +triethylamine systems. Thermochim. Acta 512 (2011) 86-92. https://doi.org/10.1016/j.tca.2010.09.004 [18] I. Alonso, I. Mozo, I. García de la Fuente, J.A. González, J.C. Cobos, Thermodynamics of Ketone + Amine Mixtures. Part VIII. Molar Excess Enthalpies at 298.15 K for n- Alkanone + Aniline or + N-Methylaniline Systems. J. Chem. Eng. Data 56 (2011) 3236- 3241. https://doi.org/10.1021/je200333p [19] I. Alonso, V. Alonso, I. Mozo, I. García de la Fuente, J.A. González, J.C. Cobos, Thermodynamics of Ketone + Amine Mixtures. I. Volumetric and Speed of Sound Data at (293.15, 298.15, and 303.15) K for 2-Propanone + Aniline, + N-Methylaniline, or + Pyridine Systems. J. Chem. Eng. Data 55 (2010) 2505-2511. https://doi.org/10.1021/je900874z [20] F. Hevia, A. Cobos, J.A. González, I. García de la Fuente, L.F. Sanz, Thermodynamics of Amide + Amine Mixtures. 1. Volumetric, Speed of Sound, and Refractive Index Data for N,N-Dimethylformamide + N-Propylpropan-1-amine, + N-Butylbutan-1-amine, + Butan-1-amine, or + Hexan-1-amine Systems at Several Temperatures. J. Chem. Eng. Data 61 (2016) 1468-1478. https://doi.org/10.1021/acs.jced.5b00802 [21] H. Van Tra, D. Patterson, Volumes of mixing and the P * effect: Part I. Hexane isomers with normal and branched hexadecane. J. Solution Chem. 11 (1982) 793-805. https://doi.org/10.1007/BF00650519 [22] H.J. Noh, S.J. Park, S.J. In, Excess molar volumes and deviations of refractive indices at 298.15 K for binary and ternary mixtures with pyridine or aniline or quinoline. J. Ind. Eng. Chem. 16 (2010) 200-206. https://doi.org/10.1016/j.jiec.2010.01.038 [23] P.S. Nikam, S.J. Kharat, Excess Molar Volumes and Deviations in Viscosity of Binary Mixtures of N,N-Dimethylformamide with Aniline and Benzonitrile at (298.15, 303.15, 150 https://doi.org/10.1007/s10953-016-0560-0 308.15, and 313.15) K. J. Chem. Eng. Data 48 (2003) 972-976. https://doi.org/10.1021/je030101n [24] T.E. Vittal Prasad, A. Adi Sankara Reddy, S. Kailash, D.H.L. Prasad, Activity coefficients and excess Gibbs energy of binary mixtures of N,N-dimethyl formamide with selected compounds at 95.5 kPa. Fluid Phase Equilib. 273 (2008) 52-58. https://doi.org/10.1016/j.fluid.2008.07.018 [25] R.S. Ramadevi, P. Venkatesu, M.V. Prabhakara Rao, M.R. Krishna, Excess enthalpies of binary mixtures of N,N-dimethylformamide with substituted benzenes at 298.15 K. Fluid Phase Equilib. 114 (1996) 189-197. https://doi.org/10.1016/0378-3812(95)02816-1 [26] G. Chandrasekhar, P. Venkatesu, M.V. Prabhakara Rao, Excess Volumes and Ultrasonic Studies of n,n-Dimethyl Acetamide with Substituted Benzenes at 303.15 k. Phys. Chem. Liq. 40 (2002) 181-189. https://doi.org/10.1080/00319100208086661 [27] G. Chandra Sekhar, M.V. Prabhakara Rao, D.H.L. Prasad, Y.V.L. Ravi Kumar, Excess molar enthalpies of N,N-dimethylacetamide with substituted benzenes at 298.15 K. Thermochim. Acta 402 (2003) 99-103. https://doi.org/10.1016/S0040-6031(02)00542-7 [28] CIAAW, Atomic weights of the elements 2015. ciaaw.org/atomic-weights.htm (accessed 2015) [29] D. Schneditz, T. Kenner, H. Heimel, H. Stabinger, A sound‐speed sensor for the measurement of total protein concentration in disposable, blood‐perfused tubes. J. Acoust. Soc. Am. 86 (1989) 2073-2080. https://doi.org/10.1121/1.398466 [30] E. Junquera, G. Tardajos, E. Aicart, Speeds of sound and isentropic compressibilities of (cyclohexane + benzene and (1-chlorobutane + n-hexane or n-heptane or n-octane or ndecane) at 298.15 K. J. Chem. Thermodyn. 20 (1988) 1461-1467. https://doi.org/10.1016/0021-9614(88)90041-9 [31] K. Tamura, K. Ohomuro, S. Murakami, Speeds of sound, isentropic and isothermal compressibilities, and isochoric heat capacities of {xc-C6H12+(1−x)C6H6}, x{CCl4+(1−x)C6H6}, and x{C7H16+(1−x)C6H6} at 298.15 K. J. Chem. Thermodyn. 15 (1983) 859-868. https://doi.org/10.1016/0021-9614(83)90092-7 [32] K. Tamura, S. Murakami, Speeds of sound, isentropic and isothermal compressibilities, and isochoric heat capacities of {xc-C6H12 + (1 − x)C6H6} from 293.15 to 303.15 K. J. Chem. Thermodyn. 16 (1984) 33-38. https://doi.org/10.1016/0021-9614(84)90072-7 [33] K.N. Marsh, Recommended reference materials for the realization of physicochemical properties. Blackwell Scientific Publications, Oxford, UK, 1987. [34] J.C.R. Reis, I.M.S. Lampreia, Â.F.S. Santos, M.L.C.J. Moita, G. Douhéret, Refractive Index of Liquid Mixtures: Theory and Experiment. ChemPhysChem 11 (2010) 3722-3733. https://doi.org/10.1002/cphc.201000566 [35] O. Redlich, A.T. Kister, Algebraic Representation of Thermodynamic Properties and the Classification of Solutions. Ind. & Eng. Chem. 40 (1948) 345-348. https://doi.org/10.1021/ie50458a036 [36] P.R. Bevington, D.K. Robinson, Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill, New York, 2000. [37] P.J. Flory, Statistical Thermodynamics of Liquid Mixtures. J. Am. Chem. Soc. 87 (1965) 1833-1838. https://doi.org/10.1021/ja01087a002 [38] R. Bravo, M. Pintos, A. Amigo, Dependence upon temperature of the excess molar volumes of tetrahydropyran + n-alkane mixtures. Can. J. Chem. 73 (1995) 375-379. https://doi.org/10.1139/v95-049 151 J. Solution Chem. 46 (2017) 150-174 [39] J.A. González, N. Riesco, I. Mozo, I. García De La Fuente, J.C. Cobos, Thermodynamics of Mixtures Containing Alkoxyethanols. XXI. Application of the Flory Theory to the Study of Orientational Effects in Systems with Dibutyl Ether or 1-Butanol. Ind. Eng. Chem. Res. 46 (2007) 1350-1359. https://doi.org/10.1021/ie0609012 [40] X. An, H. Zhao, F. Jiang, W. Shen, The (liquid + liquid) critical phenomena of (a polar liquid + an n-alkane) V. Coexistence curves of (N,N-dimethylacetamide + heptane). J. Chem. Thermodyn. 28 (1996) 1221-1232. https://doi.org/10.1006/jcht.1996.0109 [41] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids. McGraw- Hill, New York, US, 1987. [42] E. Matteoli, L. Lepori, A. Spanedda, Thermodynamic study of heptane + amine mixtures: I. Excess and solvation enthalpies at 298.15 K. Fluid Phase Equilib. 212 (2003) 41-52. https://doi.org/10.1016/S0378-3812(03)00260-7 [43] E. Matteoli, P. Gianni, L. Lepori, Thermodynamic study of heptane + secondary, tertiary and cyclic amines mixtures. Part IV. Excess and solvation enthalpies at 298.15 K. Fluid Phase Equilib. 306 (2011) 234-241. https://doi.org/10.1016/j.fluid.2011.04.013 [44] L. Lepori, P. Gianni, A. Spanedda, E. Matteoli, Thermodynamic study of (heptane + amine) mixtures. II. Excess and partial molar volumes at 298.15 K. J. Chem. Thermodyn. 43 (2011) 805-813. https://doi.org/10.1016/j.jct.2010.12.025 [45] L. Lepori, P. Gianni, A. Spanedda, E. Matteoli, Thermodynamic study of (heptane + amine) mixtures. III: Excess and partial molar volumes in mixtures with secondary, tertiary, and cyclic amines at 298.15 K. J. Chem. Thermodyn. 43 (2011) 1453-1462. https://doi.org/10.1016/j.jct.2011.04.017 [46] D. Patterson, Free Volume and Polymer Solubility. A Qualitative View. Macromolecules 2 (1969) 672-677. https://doi.org/10.1021/ma60012a021 [47] S.N. Bhattacharyya, M. Costas, D. Patterson, H.V. Tra, Thermodynamics of mixtures containing alkanes. Fluid Phase Equilib. 20 (1985) 27-45. https://doi.org/10.1016/0378- 3812(85)90019-6 [48] L. Lepori, P. Gianni, E. Matteoli, The Effect of the Molecular Size and Shape on the Volume Behavior of Binary Liquid Mixtures. Branched and Cyclic Alkanes in Heptane at 298.15 K. J. Solution Chem. 42 (2013) 1263-1304. https://doi.org/10.1007/s10953- 013-0023-9 [49] A.J. Treszczanowicz, G.C. Benson, Excess volumes for n-alkanols + n-alkanes II. Binary mixtures of n-pentanol, n-hexanol, n-octanol, and n-decanol + n-heptane. J. Chem. Thermodyn. 10 (1978) 967-974. https://doi.org/10.1016/0021-9614(78)90058-7 [50] T.M. Letcher, Thermodynamics of aliphatic amine mixtures I. The excess volumes of mixing for primary, secondary, and tertiary aliphatic amines with benzene and substituted benzene compounds. J. Chem. Thermodyn. 4 (1972) 159-173. https://doi.org/10.1016/S0021-9614(72)80021-1 [51] S. Villa, N. Riesco, I. Garcıa de la Fuente, J.A. González, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult’s law: Part 5. Excess molar volumes at 298.15 K for 1-alkanols+dipropylamine systems: characterization in terms of the ERAS model. Fluid Phase Equilib. 190 (2001) 113-125. https://doi.org/10.1016/S0378-3812(01)00595-7 [52] S. Villa, N. Riesco, I. Garcıa de la Fuente, J.A. González, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult’s law. Part 8. Excess molar volumes at 298.15 K for 1-alkanol + isomeric amine (C6H15N) systems: 152 https://doi.org/10.1007/s10953-016-0560-0 Characterization in terms of the ERAS model. Fluid Phase Equilib. 216 (2004) 123-133. https://doi.org/10.1016/j.fluid.2003.10.008 [53] L. Venkatramana, R.L. Gardas, K. Sivakumar, K. Dayananda Reddy, Thermodynamics of binary mixtures: The effect of substituents in aromatics on their excess properties with benzylalcohol. Fluid Phase Equilib. 367 (2014) 7-21. https://doi.org/10.1016/j.fluid.2014.01.019 [54] E.B. Bagley, T.P. Nelson, J.W. Barlow, S.A. Chen, Internal Pressure Measurements and Liquid-State Energies. Ind. Eng. Chem. Fundamen. 9 (1970) 93-97. https://doi.org/10.1021/i160033a015 [55] E.B. Bagley, T.P. Nelson, J.M. Scigliano, Internal pressures of liquids and their relation to the enthalpies and entropies of mixing in nonelectrolyte solutions. J. Phys. Chem. 77 (1973) 2794-2798. https://doi.org/10.1021/j100641a016 [56] M.R.J. Dack, Solvent structure. The use of internal pressure and cohesive energy density to examine contributions to solvent-solvent interactions. Aust. J. Chem. 28 (1975) 1643- 1648. https://doi.org/10.1071/CH9751643 [57] E. Zorebski, Internal pressure studies of alcohols on the basis of ultrasonic measurements. Mol. Quantum Acoust. 26 (2005) 317–326. [58] W. Marczak, K. Kielek, Internal Pressure in Binary Mixtures of Methylpyridine Isomers with H2O and D2O. Int. J. Thermophys. 31 (2009) 85-96. https://doi.org/10.1007/s10765-009-0615-1 [59] R. Dey, A.K. Singh, J.D. Pandey, A new theoretical approach for estimating excess internal pressure. J. Mol. Liq. 124 (2006) 121-123. https://doi.org/10.1016/j.molliq.2005.09.005 [60] M.F. Bolotnikov, Y.A. Neruchev, Y.F. Melikhov, V.N. Verveyko, M.V. Verveyko, Temperature Dependence of the Speed of Sound, Densities, and Isentropic Compressibilities of Hexane + Hexadecane in the Range of (293.15 to 373.15) K. J. Chem. Eng. Data 50 (2005) 1095-1098. https://doi.org/10.1021/je050060q [61] A. Chelkowski, Dielectric Physics. Elsevier, Amsterdam, 1980. [62] P. Brocos, A. Piñeiro, R. Bravo, A. Amigo, Refractive indices, molar volumes and molar refractions of binary liquid mixtures: concepts and correlations. Phys. Chem. Chem. Phys. 5 (2003) 550-557. https://doi.org/10.1039/B208765K [63] J. Krakowiak, H. Koziel, W. Grzybkowski, Apparent molar volumes of divalent transition metal perchlorates and chlorides in N,N-dimethylacetamide. J. Mol. Liq. 118 (2005) 57-65. https://doi.org/10.1016/j.molliq.2004.07.013 [64] S.S. Bittencourt, R.B. Torres, Volumetric properties of binary mixtures of (acetonitrile + amines) at several temperatures with application of the ERAS model. J. Chem. Thermodyn. 93 (2016) 222-241. https://doi.org/10.1016/j.jct.2015.09.002 [65] Y. Miyake, A. Baylaucq, F. Plantier, D. Bessières, H. Ushiki, C. Boned, High-pressure (up to 140 MPa) density and derivative properties of some (pentyl-, hexyl-, and heptyl-) amines between (293.15 and 353.15) K. J. Chem. Thermodyn. 40 (2008) 836-845. https://doi.org/10.1016/j.jct.2008.01.006 [66] F. Sarmiento, M.I. Paz Andrade, J. Fernandez, R. Bravo, M. Pintos, Excess enthalpies of 1-heptanol + n-alkane and di-n-propylamine + normal alcohol mixtures at 298.15 K. J. Chem. Eng. Data 30 (1985) 321-323. https://doi.org/10.1021/je00041a025 [67] P. Góralski, M. Wasiak, A. Bald, Heat Capacities, Speeds of Sound, and Isothermal Compressibilities of Some n-Amines and Tri-n-amines at 298.15 K. J. Chem. Eng. Data 47 (2002) 83-86. https://doi.org/10.1021/je010206v 153 CHAPTER 5 256 For a fixed amine, the replacement of DMF by DMA leads to decreased E m H values (Figure 5.1). The difference in size between both amides suggests that the contribution from the disruption of amine-amine interactions should be higher for DMA mixtures. However, the amide group is less sterically hindered in DMF, and we recognize that, in pure state, DMF-DMF interactions are stronger than those between DMA molecules. In fact (see above), UCST(DMF + heptane) > UCST(DMA + heptane). This is also supported by calculations on entropy changes under the action of an electrostatic field and by the application of the Kirkwood- Fröhlich model [46]. Therefore, we can conclude that the breaking of DMF-DMF interactions contributes more positively to E m H than the disruption of DMA-DMA interactions, and that the formation of interactions between unlike molecules should contribute more negatively to E m H in the case of DMF systems. The mentioned trend suggests that the variation of the contribution of amide-amide interactions is predominant over the other two. The same phenomenon is encountered in 2-alkanone + amine mixtures when the chain length of the 2-alkanone is increased (Figure 5.3) [67]. Interestingly, the replacement of HxA by DPA in systems involving a given amide leads to slightly higher E m H values (Figure 5.1). This can be explained taking into account that, since the amine group is less sterically hindered in HxA, a higher number of interactions between unlike molecules is formed in solutions with this amine and that such interactions are also stronger. It should be noted that the opposite trend is encountered for HxA or DPA + heptane mixtures, and that the difference E m H (HxA)– E m H (DPA) for these systems is remarkably higher than that for the corresponding amide solutions: 438 (heptane); –90 (DMF) and –85 (DMA) (all values in J·mol-1). This underlines the relevance of amide-amine interactions in the studied solutions. The difference between amide + HxA or + DPA solutions is rather low in terms of E m H values, but it increases when considering E m,V U , reinforcing our statement (Appendix A). Eventually, let us mention the large and negative value of the E m H of the system N-methylacetamide + HxA (–1000 Jmol-1, T = 363.15 K) [17], for which the contribution from the formation of amideamine interactions is dominant by far. The excess molar volumes, E m V , of the considered mixtures are either negative or small and positive [43, 44] (Figure 5.2 and Figure 5.4), and can be ascribed to important contributions from amide-amine interactions and structural effects. The latter are clearly seen because the corresponding E m H values are positive, showing in this aspect a similar behavior to amine + nalkane systems (see above). It is also to be noted that E m H and E m V change in line, which reveals that the interactional contribution to E m V is relevant. For a fixed amide, the increase of the amine size along a homologous series leads to increased E m V values. This means that the contributions that increase E m V (larger number of DMF-DMF interactions broken by the longer amines and the weakening of the amide-amine interactions related to the fact that the amine group is more sterically hindered in such amines) are predominant over those decreasing E m V (structural effects, lower positive contribution from the disruption of the amine-amine interactions). The replacement of a linear primary amine (HxA) by a linear secondary amine (DPA) leads to lower E m V values (Figure 5.2). It is remarkable that the same behavior is encountered for HxA or DPA + heptane DISCUSSION OF THE RESULTS 257 mixtures (see above). Therefore, the observed variation in DMF solutions can be ascribed to a lower positive contribution to E m V from the breaking of the amine-amine interactions. A similar trend is encountered in 1-alkanol + HxA, or + DPA systems (Figure 5.4) [21, 26]. Finally, the replacement of DMF by DMA for a fixed amine leads to a higher E m V , due to the stronger amide-amine interactions in mixtures with DMF (Figure 5.2). Mixtures of DMF or DMA with aniline contrast drastically with those of linear primary or secondary amines. The dipole moment of aniline (1.51 D [49]) is higher than that of linear primary and secondary amines, and proximity effects between the phenyl ring and the amine group lead to strong dipolar interactions between aniline molecules. As a consequence, aniline + n-alkane mixtures are characterized by relatively high UCST (see introduction). When aniline molecules are mixed with DMF or DMA molecules, very strong interactions between unlike molecules are created, and we have E m H /Jmol-1 = − 2946 (DMF + aniline) [14]; − 352 (DMA + aniline) [16] (Figure 5.3). Similarly, large differences are also encountered between values of the excess relative permittivity for the DMF + linear primary or secondary amine or + aniline mixtures [45, 46] (see below). It must be observed that E m H values are very different for DMF and DMA + aniline systems, newly remarking that interactions between unlike molecules are much more relevant in DMF systems. The rather large and negative E 3 1 m/ cm ·molV− results for the mentioned aniline solutions (–0.6615 (DMF + aniline) [11] and –0.6092 (DMA + aniline, T = 303.15 K) [15]) (Figure 5.3) are in agreement with the E m H values and underline the importance of the interactional contribution to E m V . The same trends are encountered for 2- alkanone + DPA or + aniline systems [67-74] (Figure 5.3 and Figure 5.4). It is here pertinent to examine the effect of replacing the N,N-dialkylamide (DMF or DMA) by a 2-alkanone of similar size (propanone or butanone). For a fixed linear secondary amine (DPA or DBA), E m H values of DMF or DMA systems are higher than those of propanone or butanone solutions respectively (Figure 5.3), pointing out a contribution from the breaking of amide-amide interactions that is larger than the contribution from alkanone-alkanone interactions. In contrast, E m V values of propanone or butanone + DPA, or + DBA (Figure 5.4) mixtures are higher than those of the corresponding systems with DMF or DMA, thus suggesting that structural effects in E m V are more relevant in N,N-dialkylamide mixtures. The behavior of these two types of mixtures is parallel when: (i) for a given amine (DPA or DBA), we increase the size of the amide or alkanone (lower E m H and E m V values are obtained); and (ii) for a fixed amide (DMF or DMA) or alkanone (propanone or butanone), DPA is replaced by DBA (it gives higher E m H and E m V values). Both effects can be explained in similar terms (see above). Interestingly, aniline mixtures show a rather different behavior (Figure 5.3 and Figure 5.4). The lower E m V and the higher E m H values of the propanone mixture compared to those of the DMF system indicate that interactions between unlike molecules are stronger in the latter solution and that structural effects are more relevant in the propanone system. Surprisingly, DMA-aniline interactions seem to be weaker than butanone-aniline interactions (see the corresponding E m H values of these systems). This matter deserves a careful investigation. The results are very different when replacing the N,N-dialkylamide (strongly polar compound) by a 1-alkanol (self-associated compound) of similar size (1-propanol or 1-butanol) CHAPTER 5 258 (Figure 5.3 and Figure 5.4). Both E m H and E m V of 1-alkanol + HxA, DPA or DBA mixtures are large and negative. This can be explained by the (1-alkanol)-amine cross-association, which is stronger than the self-association of the 1-alkanol (see introduction). Replacing the aliphatic amine by aniline in the case of 1-alkanol mixtures has the opposite effect to N,N-dialkylamide or 2-alkanone systems. In fact, E m H turn positive or small and negative, and E m V values become much higher. Their E m V are still negative, though, due to strong structural effects. Actually, the differences EE m m,V HU− are significant not only for (1-alkanol) + aniline systems but also for (1- alkanol) + aliphatic amine solutions [21]. 5.2.2. ERAS model results Both excess functions, E m H and E m V , are reasonably well represented by the model (Figure 5.5 to Figure 5.8, Appendix A). Larger differences for E m V results are encountered for mixtures characterized by low E m V values, as then the overall result is obtained from the difference of two large magnitudes of different sign: the positive physical contribution and the negative chemical contribution. ERAS parameters of amide + amine mixtures (Table A.4, [46]) are represented from Figure 5.9 to Figure 5.12, together with the corresponding parameters of 1-alkanol + HxA, + DPA and + TEA solutions [21, 26]. The low * AB h and AB K and values for N,N-dialkylamide + linear primary or secondary amine systems (2 to 9 kJ·mol-1 and 1 to 1.3 respectively) indicate that solvation effects are not relevant and that the enthalpy of the H bonds between unlike molecules is weak. The large AB X values reveal that the physical contribution is important, particularly with regards to E m H . These ERAS parameters largely differ from those determined for 1-alkanol + linear primary or secondary amine systems, which are characterized by strong solvation effects and, in consequence, by large AB K and * AB h values and low AB X values. For N,N-dialkylamide + linear primary or secondary amine systems, we note that ERAS results on E m H are, as an average, better for DMA systems (Table A.5). This suggests that, in such a case, physical interactions are more properly described by the model, that is, dipolar interactions are more relevant in DMF mixtures, particularly in the BA solution. 5.2.3. Excess relative permittivities It is known that the disruption of interactions between like molecules, in the present case amide-amide and amine-amine interactions, contributes negatively to E r  . The creation of new interactions between unlike molecules along this process leads to the formation of multimers whose molecular structure is determinant to provide a more or less effective impact on the macroscopic response to an electric field [36]. If the mentioned multimers are linear chains, the contribution to E r  is positive. In contrast, if cyclic species are created, the contribution to E r  is negative. n-Alkylamine + dodecane systems at 293.15 K show negative E r  values that increase with the chain length of the amine [75] (Figure 5.13). The negative contribution from the rupture of amine-amine interactions diminishes when increasing the chain length of the amine, as the DISCUSSION OF THE RESULTS 259 amine group is then more sterically hindered, in such a way that the effective polarity of longer amines becomes weaker. The E r  values of N,N-dialkylamide (DMF or DMA) + linear amine (BA, HxA, DPA or DBA) are large and negative (Figure 5.13), revealing that the negative contributions from the breaking of interactions between molecules of the same species are dominant. They are much lower than those of n-alkylamine + dodecane mixtures, suggesting that amide-amide interactions are dominant. On the other hand, one can expect that interactions between unlike molecules contribute positively to E r  . In fact, the E r  value of the DMF + heptane mixture at 10.0171  = and 293.15 K is lower (–0.24, calculated from data of the literature [76]) than the values of the corresponding systems with amines at the same conditions: –0.129 (DPA), –0.146 (DBA), –0.104 (BA), and –0.137 (HxA) [75]. We note that, for a fixed amide, E r  (DBA) < E r  (DPA) and E r  (HxA) < E r  (BA). This can be explained as follows: (i) longer amines are better breakers of the amide-amide interactions due to their large aliphatic surface; (ii) the formation of interactions between unlike molecules becomes easier when shorter amines are involved, as the amine group is then less sterically hindered. This also explains why E r  (HxA) > E r  (DPA) in mixtures with a given amide. Comparison between E r  values of mixtures with a given linear amine shows that E r  (DMF) > E r  (DMA). In addition, E r  curves of the DMA systems are more skewed towards larger 1  values (Table 7 of reference [46]). This suggests that linear amines can disrupt more easily DMA-DMA interactions and that the creation of amide-amine interactions is favored when DMF molecules participate. Finally, we must remark that the replacement of HxA by aniline in DMF solutions has a large impact on the E r  values of these mixtures, which show opposite signs. Therefore, the aromaticity effect leads here to an increase of the number of effective dipole moments in the aniline system. The fact that E r  is positive for the DMF + aniline mixture clearly indicates that E r  is now mainly determined by the positive contribution related to the aniline-DMF interactions created upon mixing. Other systems like methanol + DMF ( E r  = 2.57 [77]); + DMA (0.52 [78]); + pyridine (2.85 [77]), or + cyclohexylamine (1.13 [30]) also show positive E r  values. 5.2.4. Kirkwood-Fröhlich model results From r  and D n (refractive index) data, we can calculate the Kirkwood correlation factor ( K g ) in the framework of a one-fluid model (see section 4.3.6). However, K g values of pure N,N- dialkylamides and linear amines are very similar. For such systems, the shape of the K g curves is very sensitive to the  values of the pure compounds. Since the uncertainty in the dipole moments of linear amines is not low enough to ensure a unique shape of the curves, it is better to evaluate the Balankina relative excess Kirkwood correlation factors of the mixtures, E K,rel g , defined by [79]: id ,iid EK K m K,re d2 r r r r r r id ,id lid id ,id 2 r r r r r id Km r )(2 ) ( 2) 1 )(2 ) ) ( (( 2 g g V ggV                   − − + + = = − − + + (5.1) CHAPTER 5 260 where id K g is obtained substituting ideal values in the definition of K g . The quantity E K,rel g does not depend on the dipole moments of the pure compounds and is a useful tool to probe into the structure of the mixtures, as it gives a measure of the balance of structure creation and destruction during the mixing process in comparison to the ideal mixture. The E K,rel g curves are very skewed to low 1  values [46], which means that according to the model the change in the relative orientation of neighboring permanent dipoles is not the only responsible for the shape of E r  curves of such systems. However, their contribution is relevant, as the curves are negative and the relative variation of the minimum of the E K,rel g curves (Figure 5.14) is parallel to the E r  change (Figure 5.13). This is consistent with the conclusions extracted from the analysis of E r  . It is interesting to see the effect of replacing the N,N-dialkylamide by a 1-alkanol of similar size. The dielectric and refractive properties of such systems were measured experimentally, and are interpreted in the following section. 5.3. Discussion of 1-alkanol + amine liquid mixtures Along the discussion, nOH will denote the 1-alkanol with n carbon atoms. 5.3.1. Excess relative permittivities 1-Alkanols are self-associated compounds with moderate dipole moments [80]: 1.666 (1OH), 1.650 (2OH), 1.627 (3OH), 1.612 (4OH), 1.597 (5OH), 1.586 (6OH), 1.581 (7OH), 1.568 (8OH), 1.566 (9OH), 1.564 (10OH). Accordingly, nOH + heptane mixtures show large and negative values of E r  (Figure 5.15), which can be ascribed to the rupture of the 1-alkanol self-association. For the system 1OH + heptane, a partial immiscibility region appears [81]. The comparison of these results with nOH + HxA (for n ≥ 3), + DPA (for n ≥ 3) or + TEA (for n ≥ 4), which show higher E r  values (Figure 5.15), reveals that (1-alkanol)-amine interactions contribute positively to E r  in these type of mixtures. The positive values for the 1OH systems confirm this statement. An important result is that E r  (3OH + TEA) < E r  (3OH + heptane). This suggests that TEA is an effective breaker of the alkanol self-association, and that the interactions between unlike molecules do not sufficiently compensate the large negative contribution to E r  from the disruption of 3OH-3OH interactions. For systems with heptane or a given amine (HxA, DPA or TEA) and increasing n, E r  decreases to a minimum (n = 7 for the available data in heptane mixtures, n = 5 for HxA and DPA, and n = 4 for TEA) and then increases again. A similar trend is encountered for systems with cyclohexylamine (c-HxA) (Figure 5.16). For heptane systems, it has been explained in terms of the lower and weaker self-association of longer 1-alkanols [36]. For amine systems, this statement is still valid, but interactions between unlike molecules must also be considered. Studies on 1-alkanol + amine mixtures using the ERAS model show that solvation effects between unlike molecules decrease when the 1-alkanol size is increased [21, 26, 27]. This means that, along the mixing process, the polarization changes to a lower extent when longer 1- alkanols are involved, since these alcohols are less self-associated and the corresponding solvation effects are also less important. It is to be noted that E r  changes more sharply when DISCUSSION OF THE RESULTS 261 increasing n for mixtures with shorter 1-alkanols than for systems involving longer 1-alkanols and that the same occurs for the excess molar volumes and for the excess molar enthalpies [26]. For a given 1-alkanol, E r  varies in the following manner: TEA < HxA < DPA. The fact that E r  (HxA) < E r  (DPA) suggests that in DPA solutions multimers with parallel alignment of the molecular dipoles are favored and cyclic multimers are disfavored when compared to HxA mixtures. Furthermore, at 10.47  = , the 4OH + N-ethylethan-1-amine mixture [76] shows an even higher value (–0.13), which can be explained by the formation of more and stronger H bonds between unlike molecules, because the amine group is less sterically hindered in this amine. E r  (TEA) is lower due to the effectivity of this amine in breaking the self-association of the 1-alkanol (see above). For a better understanding of systems containing TEA, we start examining 1-alkanol + linear primary or secondary amine systems. A literature survey shows that E r  (3OH + DPA) = –0.246 [82] > E r  (3OH + HxA) = –0.96 [47] > E r  (3OH + propan-1-amine) = –1.99 [83] and that E r  (4OH + DPA) = –0.715 [82] > E r  (4OH + HxA) = –1.424 [47] > E r  (4OH + butan-1-amine) = –2.87 [83]. Since solvation effects are expected to be more relevant in systems involving amines where the amine group is less sterically hindered (propan-1-amine, butan-1-amine), one can conclude that characteristic mixtures where larger solvation effects are present show more negative E r  values. The same trend is observed when comparing, at 303.15 K, E r  results for 3OH + primary aromatic amine, aniline, (–2.07) [84] or + secondary aromatic amine, N- methylaniline, (–1.27) [85]. This behavior can be explained taking into account that larger solvation effects imply a decreased number of interactions between like molecules and, therefore, a more negative contribution to E r  from the disruption of interactions between like molecules, particularly between alkanol molecules. In the case of amine mixtures, cyclic species may be more probable in mixtures containing amines with the functional group less sterically hindered. We must now remark that systems with TEA deviate from this picture. This can be ascribed to the globular shape of TEA molecules, which makes them better breakers of the 1-alkanol selfassociation (see above). In fact, the volume fraction at which minimum E r  values are measured changes in the sequence DPA < HxA < TEA for mixtures with shorter 1-alkanols. Thus, 1  (4OH) = 0.3183 (DPA; E r  = –0.896) [82] < 0.4138 (HxA; E r  = –1.428) [47] < 0.4969 (TEA; E r  = –1.964). For 7OH, the alcohol self-association becomes less relevant, and the minimum E r  values are encountered at similar volume fractions for HxA or TEA mixtures, although these concentrations are still higher than for the DPA solution, e.g. 1  (7OH) = 0.5003 (DPA; E r  = –0.793) [82] < 0.5982 (TEA; E r  = –1.455). The fact that the E r  curves of HxA systems are skewed to higher 1  values than those of mixtures with DPA supports our previous statement about that higher solvation effects lead to a more important breaking of the alcohol network upon mixing. We complete the present analysis as follows. (i) According to the ERAS model, the equilibrium constants, AB K , change in the order HxA > DPA > TEA in systems with a given 1-alkanol [21, 26, 37]. For example, AB K (1OH) = 2500 (HxA) > 2450 (DPA) > 620 (TEA). That is, solvation effects are less important in mixtures with TEA, in agreement with the fact that the amine group becomes more sterically hindered in the same sequence [86]. (ii) The CC(0)S function is a quantity which allows to study the fluctuations in the number of CHAPTER 5 262 molecules of a binary mixture regardless of the components, the fluctuations in the mole fraction and the cross fluctuations. It is defined by [87, 88]: 12 CC(0) xx SD = (5.2) where, denoting by m G the molar Gibbs energy of mixing: 2 2 E 1 2 1 2 m 22 1, m 1, 1 T p T p x x G x x G DRT RT xx      = = +               (5.3) For ideal mixtures, E,id m G = 0 (excess Gibbs energy of the ideal mixture); Did = 1 and CC(0)S = x1x2. From stability conditions, CC(0)S > 0. If a system is close to phase separation, CC(0)S must be large and positive (  , if the mixture presents a miscibility gap). In the case of compound formation between components, CC(0)S must be very low (0, in the limit). Therefore, SCC(0) > x1x2 (D < 1) indicates that the dominant trend in the system is homocoordination (separation of the components), and the mixture is then less stable than the ideal. If 0 < SCC(0) < x1x2 = SCC(0)id, (D > 1), the fluctuations in the system have been removed, and the dominant trend in the solution is heterocoordination (compound formation). In such a case, the system is more stable than ideal. We have shortly applied this formalism to methanol + HxA, or + DPA, or + TEA systems at 298.15 K, calculating E m G by means of the DISQUAC [89] model with interaction parameters for the OH/amine contacts previously determined [22, 37]. At equimolar composition, we have obtained: SCC(0) = 0.165 (HxA) < 0.201 (DPA) < 0.341 (TEA). This means that heterocoordination is dominant in the systems with HxA or DPA, while homocoordination is prevalent in the TEA mixture. It is in full agreement with the variation of the AB K constants given above, and with available E m G data for methanol + amine mixtures. Thus, E m G (methanol)/J·mol-1= –799 (BA, 348.15 K) [90], 284 (TEA, 303.15 K) [91]. Cyclohexylamine (c-HxA, * r  = 4.53 [36]) is a cyclic primary amine with a slightly higher permittivity than HxA ( * r  = 3.904 [47]). Cyclization of the amine leads to increased values compared to those of systems with HxA [30, 36] (Figure 5.16); i.e., multimers formed by unlike molecules contribute more positively to E r  in cyclohexylamine solutions. The effect of aromaticity is more dramatic than that of cyclization. In fact, aniline ( * r  = 7.004 [92]) shows a greater value of the relative permittivity, underlining the importance of aniline-aniline interactions and the polarizability of the aromatic ring. The values of the corresponding excess property are of course negative [92] (Figure 5.16). In addition, they are lower than those of the mixtures with HxA or c-HxA. This may be explained taking into account that the breaking of the dipolar interactions between aniline molecules contributes more negatively to E r  . It may be pertinent to compare the dielectric behavior of mixtures formed by 1-alkanol and DPA or di-n-propylether (DPE), as both solvents have similar size and structure (Figure 5.17). It is well known that the thermodynamic properties of the DPE systems are mainly characterized by the 1-alkanol self-association [93]. Thus, the E m H values are moderately positive ( E m H /J·mol-1 = 740 for the 3OH system [94]); remain nearly constant for mixtures involving the longer 1-alkanols, and the corresponding E m H curves are shifted towards low mole fractions of the 1-alkanol [93]. In contrast, as it has been previously mentioned, solvation, i.e. strong E r  DISCUSSION OF THE RESULTS 263 interactions between unlike molecules, is the main feature of 1-alkanol + DPA mixtures [22]. This is clearly demonstrated by the large and negative E m H values of these systems (Figure 5.3). For DPE mixtures, the dependence of E r  with the alcohol size is similar to that encountered for the amine systems examined (Figure 5.17): –1.03 (2OH) < –1.24 (4OH) < –1.60 (6OH) > –0.80 (10OH) [95]. On the other hand, for mixtures with a given 1-alkanol, as a general trend it is observed that E r  changes in the order: heptane < DPE < DPA (see above, Figure 5.17). This reveals that interactions between unlike molecules contribute more positively to the polarization of the mixture in the case of DPA systems. 5.3.2. Temperature dependence of the permittivity Firstly, we note that, for pure compounds, * r () p T   values are negative (see below and Figure 5.18), which is the typical behavior of normal liquids. In the case of 1-alkanols, this quantity increases with n, because then the alcohol self-association decreases and a lower number of interactions between alcohol molecules are broken when the temperature is increased. The higher * r () p T   values of HxA (–0.0098 K-1), DPA (–0.012 K-1) or TEA (–0.004 K-1) can be explained similarly. Pure TEA shows a very low absolute value of * r () p T   , since TEA is not self-associated and has a low * r  value (= 2.419). Thus, the increase of thermal agitation hardly modifies the liquid structure. Values of r () p T   of 1-alkanol + HxA, DPA or TEA systems are higher than for pure alkanols (Figure 5.18), which underlines the existence of (1-alkanol)-amine interactions. This can be explained as follows. (i) The contribution to r () p T   related to the breaking of amineamine interactions when T is increased is very low, especially for TEA (see above); (ii) The enthalpy of hydrogen bonds between 1-alkanol molecules is larger than that corresponding to 1- alkanol-amine interactions (see introduction). Therefore, one can expect that the number of (1- alkanol)-TEA interactions broken when the temperature is increased is lower than the number of disrupted (1-alkanol)-(1-alkanol) interactions. This leads to a lower r  decrease when T is increased in comparison to that produced in pure 1-alkanols. The variation of r ( )p T   with n can be explained in similar terms, i.e., in terms of the lower self-association of longer 1-alkanols and of the less important solvation effects involved. For mixtures with a given 1-alkanol, r ( )p T   changes in the order TEA > HxA > DPA (Figure 5.18). The r  values vary in the opposite sequence; for example, for 1OH mixtures we have r  = 17.597 (TEA) < 19.739 (HxA) < 20.256 (DPA). That is, the structure of mixtures characterized by a higher dielectric polarization is more sensitive to temperature changes. In addition, * r () p T   of pure amines varies in the same order as r ( )p T   . We remark that the replacement of DPA by HxA in systems with a given 1-alkanol leads to less negative r () p T   values, newly suggesting that cyclic multimers formed by unlike molecules exist in 1-alkanol + HxA systems, as the disruption of such multimers for increased temperature values should contribute positively to the polarization of the mixture. CHAPTER 5 264 Finally, we note that E r () p T   can show negative or positive values (Figure 5.19). Lower results are encountered for mixtures for which the effects from 1-alkanol self-association and solvation between unlike molecules are more relevant, leading to a network that is more difficult to break with the increase of temperature when compared with the ideal mixture. Thus, for a fixed amine (HxA, DPA or TEA) it increases with n, whereas for a given 1-alkanol it varies as HxA < DPA < TEA. 5.3.3. Kirkwood-Fröhlich model results We compare the K g curves obtained from 1OH or 7OH + isomeric amine in Figure 5.20. Except for values of 1  very close to zero, where the structure of the mixture is basically that of the pure amine, it is found that K g (DPA) > K g (TEA) > K g (HxA). DPA mixtures show higher values of K g than HxA systems, which would mean that parallel alignment of the dipoles is more favored in DPA mixtures, supporting our previous statement inferred from the analysis of E r  and r () p T   . The K g results for the 1OH + DPA mixture deserve a comment. We note that K g rapidly increases with 1  , and that it is nearly constant from 1  = 0.5 and very close to the value of the neat alcohol. This might occur because the contribution to the mixture polarization arising from interactions between alcohol molecules also increases rapidly with 1  in such a way that interactions between unlike molecules contribute to K g to a lower extent. It is remarkable that K g changes more smoothly with 1  for the 1OH + HxA system, in agreement with our analysis of E r  results. It is quite clear that 1-alkanol + TEA mixtures show an intermediate behavior, which could be due to the existence of a higher proportion of shorter linear-like multimers of 1-alkanol molecules which are less present in the systems with HxA. In order to examine these results with more detail, we provide some K g values for 1-alkanol + amine mixtures: K g (3OH) = 2.72 (DPA) > 2.32 (HxA) > 1.87 (propan-1-amine), and K g (4OH) = 2.60 (DPA) > 2.16 (HxA) > 1.72 (BA). In addition, K g (3OH, 303.15 K) = 1.54 (aniline) < 1.71 (N-methylaniline). This points out that parallel alignment of molecular dipoles has a lower weight in those systems characterized by larger solvation effects and, according to our previous description of E r  , these cooperative effects will lead to a lower polarization of the mixture. This underlines the lower contribution to the structure of the mixture from alkanolalkanol interactions in systems with larger solvation effects, and suggests the presence of cyclic species in such systems. We have also evaluated the excess Kirkwood correlation factors (Figure 5.21), K E id KK g g g=− , where id K g is calculated as already explained. Positive values are encountered for 1OH + HxA or + DPA mixtures, which can be justified by the strong solvation effects present in these solutions. The minima of the E K g curves occurs at lower 1  than in the E r  curves. Moreover, for a fixed amine, in general it does not change with n in the same order as E r  . Thus, according to the Kirkwood-Fröhlich model, the destruction of the correlations of the dipoles is not the only responsible for the E r  minima, but there are other effects involved. The trend of E K g (TEA) is slightly deviated from the parallel behavior of E K g (HxA) and E K g (DPA), and this reflects the stronger structural effects already mentioned in the former mixtures. DISCUSSION OF THE RESULTS 265 We now examine the effect of cyclization and aromaticity in 1-alkanol + primary amine systems (Figure 5.22). For c-HxA systems, E K g values are higher, indicating that in these mixtures the balance of destruction and creation of correlations is more inclined to the latter than in the case 1-alkanol + HxA. Aniline systems are quite interesting, as E K g (HxA) < E K g (aniline) for the 1-pentanol mixtures. This phenomenon may be related to the higher importance of the rupture of interactions between like molecules in 1-alkanol + aniline solutions, as showed by E r  values and also by E m H . It is interesting to compare these K g results with those for nOH + strongly polar compounds (work included in reference [96]), such as nitromethane (NM), ethanenitrile (EtN), dimethyl sulfoxide (DMSO), sulfolane (SULF), nitrobenzene (NTBz) or benzonitrile (BzCN). In fact, the K g of these mixtures are slightly higher than 1 or very close to 1. For example, K g (3OH) = 1.04 (NM, T = 293.15 K [76, 97]), 1.13 (EtN [98, 99]), 1.55 (DMSO [100, 101]). 1.20 (NTBz, T = 293.15 K [102, 103]), 1.13 (BzCN, T = 303.15 K [104, 105]); and K g (1OH + SULF [106, 107]) = 1.33. When n increases along a homologous series, the 1K()g  have progressively a wider region where K g values remain close to 1 (see, for example, ethanenitrile systems, Figure 5.23). For low 1  , interactions between unlike molecules do not contribute to K g as much as in nOH + amine mixtures (Figure 5.20 and Figure 5.23). CHAPTER 5 272 Figure 5.13: E r  at 1  = 0.5, T = 298.15 K and p = 0.1 MPa of N,N-dialkylamide + amine [45, 46] or primary amine + dodecane ([75], [76]) liquid mixtures as functions of n, the number of C atoms of the amine. Solid lines, primary amines (-NH2); dashed lines, secondary amines (-NH-). Symbols: (●), dodecane; (), DMF; (▲), DMA. Figure 5.14: Minimum (primary or secondary amine) or maximum (aniline) of E K,rel g (equation (5.1)) at T = 298.15 K and p = 0.1 MPa of N,N-dialkylamide + amine [45, 46] liquid mixtures as functions of n, the number of C atoms of the amine. Solid lines, primary amines (-NH2); dashed lines, secondary amines (-NH-). Full symbols: (), DMF; (▲), DMA. Hollow symbols: (), DMF + aniline. DISCUSSION OF THE RESULTS 273 Figure 5.15: E r  at 1  = 0.5, T = 298.15 K and p = 0.1 MPa of 1-alkanol + amine or + heptane liquid mixtures as functions of n, the number of C atoms of the 1-alkanol. Full symbols: (●), HxA [47]; (▲), DPA [82]; (), TEA (Appendix B); (◆), heptane [114, 115]. Figure 5.16: E r  at 1  = 0.5, T = 298.15 K and p = 0.1 MPa of 1-alkanol + primary amine liquid mixtures as functions of n, the number of C atoms of the 1-alkanol. Symbols: (●), HxA [47]; (), c-HxA [30, 36]; (▲), aniline [92]. CHAPTER 5 274 Figure 5.17: E r  at 1  = 0.5, T = 298.15 K and p = 0.1 MPa of 1-alkanol + DPA, + DPE or + heptane liquid mixtures as functions of n, the number of C atoms of the 1-alkanol. Symbols: (▲), DPA [82]; (●), DPE [95]; (◆), heptane [114, 115]. Figure 5.18: r () p T   at T = 298.15 K and p = 0.1 MPa of pure 1-alkanols and of 1-alkanol(nOH) + amine liquid mixtures at 1  = 0.5 as functions of n, the number of C atoms of the 1-alkanol. Full symbols: (●), HxA [47]; (▲), DPA [82]; (), TEA (Appendix B); (◆), pure 1-alkanols ([47, 82], Appendix B). DISCUSSION OF THE RESULTS 275 Figure 5.19: E r () p T   at 1  = 0.5, T = 298.15 K and p = 0.1 MPa of 1-alkanol + amine liquid mixtures as functions of n, the number of C atoms of the 1-alkanol. Full symbols: (●), HxA [47]; (▲), DPA [82]; (), TEA (Appendix B). Figure 5.20: K g at T = 298.15 K and p = 0.1 MPa of 1OH or 7OH + amine liquid mixtures as functions of 1  . Solid lines, HxA [47]; dashed lines, DPA [82]; dashed-dotted lines, TEA (Appendix B). CHAPTER 5 276 Figure 5.21: E K g at 1  = 0.5, T = 298.15 K and p = 0.1 MPa of 1-alkanol + amine liquid mixtures as functions of n, the number of C atoms of the 1-alkanol. Full symbols: (●), HxA [47]; (▲), DPA [82]; (), TEA (Appendix B). Figure 5.22: E K g at 1  = 0.5, T = 298.15 K and p = 0.1 MPa of 1-alkanol + primary amine liquid mixtures as functions of n, the number of C atoms of the 1-alkanol. Symbols: (●), HxA [47]; (), c-HxA [30, 36]; (▲), aniline [92]. DISCUSSION OF THE RESULTS 277 Figure 5.23: K g at T = 298.15 K and p = 0.1 MPa of 1-alkanol(nOH) + EtN [98, 99] or + HxA [47] liquid mixtures as functions of 1  . 5.4. References [1] E.S. Eberhardt, R.T. Raines, Amide-Amide and Amide-Water Hydrogen Bonds: Implications for Protein Folding and Stability. J. Am. Chem. Soc. 116 (1994) 2149-2150. https://doi.org/10.1021/ja00084a067 [2] T.W. Whitfield, G.J. Martyna, S. Allison, S.P. Bates, H. Vass, J. Crain, Structure and Hydrogen Bonding in Neat N-Methylacetamide: Classical Molecular Dynamics and Raman Spectroscopy Studies of a Liquid of Peptidic Fragments. J. Phys. Chem. B 110 (2006) 3624-3637. https://doi.org/10.1021/jp053140+ [3] J.A. Gonzalez, J.C. Cobos, I. García de la Fuente, Thermodynamics of liquid mixtures containing a very strongly polar compound: Part 6. DISQUAC characterization of N,N- dialkylamides. Fluid Phase Equilib. 224 (2004) 169-183. https://doi.org/10.1016/j.fluid.2004.02.007 [4] J. Barthel, R. Buchner, B. Wurm, The dynamics of liquid formamide, N- methylformamide, N,N-dimethylformamide, and N,N-dimethylacetamide. A dielectric relaxation study. J. Mol. Liq. 98 (2002) 51-69. https://doi.org/10.1016/S0167- 7322(01)00309-9 [5] W.L. Jorgensen, C.J. Swenson, Optimized intermolecular potential functions for amides and peptides. Structure and properties of liquid amides. J. Am. Chem. Soc. 107 (1985) 569-578. https://doi.org/10.1021/ja00289a008 [6] F.F. Liew, T. Hasegawa, M. Fukuda, E. Nakata, T. Morii, Construction of dopamine sensors by using fluorescent ribonucleopeptide complexes. Bioorg. Med. Chem. 19 (2011) 4473-4481. https://doi.org/10.1016/j.bmc.2011.06.031 CHAPTER 5 278 [7] J.M. Sonner, R.S. Cantor, Molecular Mechanisms of Drug Action: An Emerging View. Annu. Rev. Biophys. 42 (2013) 143-167. https://doi.org/10.1146/annurev-biophys- 083012-130341 [8] D.L. Nelson, M.M. Cox, Lehninger Principles of Biochemistry. 3rd ed., Worth Publishing, New York, 2000. [9] Y. Coulier, A. Lowe, P.R. Tremaine, J.Y. Coxam, K. Ballerat-Busserolles, Absorption of CO2 in aqueous solutions of 2-methylpiperidine: Heats of solution and modeling. Int. J. Greenh. Gas Control 47 (2016) 322-329. https://doi.org/10.1016/j.ijggc.2016.02.009 [10] M. Götz, R. Reimert, S. Bajohr, H. Schnetzer, J. Wimberg, T.J.S. Schubert, Long-term thermal stability of selected ionic liquids in nitrogen and hydrogen atmosphere. Thermochim. Acta 600 (2015) 82-88. https://doi.org/10.1016/j.tca.2014.11.005 [11] H.J. Noh, S.J. Park, S.J. In, Excess molar volumes and deviations of refractive indices at 298.15 K for binary and ternary mixtures with pyridine or aniline or quinoline. J. Ind. Eng. Chem. 16 (2010) 200-206. https://doi.org/10.1016/j.jiec.2010.01.038 [12] P.S. Nikam, S.J. Kharat, Excess Molar Volumes and Deviations in Viscosity of Binary Mixtures of N,N-Dimethylformamide with Aniline and Benzonitrile at (298.15, 303.15, 308.15, and 313.15) K. J. Chem. Eng. Data 48 (2003) 972-976. https://doi.org/10.1021/je030101n [13] T.E. Vittal Prasad, A. Adi Sankara Reddy, S. Kailash, D.H.L. Prasad, Activity coefficients and excess Gibbs energy of binary mixtures of N,N-dimethyl formamide with selected compounds at 95.5 kPa. Fluid Phase Equilib. 273 (2008) 52-58. https://doi.org/10.1016/j.fluid.2008.07.018 [14] R.S. Ramadevi, P. Venkatesu, M.V. Prabhakara Rao, M.R. Krishna, Excess enthalpies of binary mixtures of N,N-dimethylformamide with substituted benzenes at 298.15 K. Fluid Phase Equilib. 114 (1996) 189-197. https://doi.org/10.1016/0378-3812(95)02816-1 [15] G. Chandrasekhar, P. Venkatesu, M.V. Prabhakara Rao, Excess Volumes and Ultrasonic Studies of n,n-Dimethyl Acetamide with Substituted Benzenes at 303.15 k. Phys. Chem. Liq. 40 (2002) 181-189. https://doi.org/10.1080/00319100208086661 [16] G. Chandra Sekhar, M.V. Prabhakara Rao, D.H.L. Prasad, Y.V.L. Ravi Kumar, Excess molar enthalpies of N,N-dimethylacetamide with substituted benzenes at 298.15 K. Thermochim. Acta 402 (2003) 99-103. https://doi.org/10.1016/S0040-6031(02)00542-7 [17] A.B. de Haan, J. Gmehling, Excess Enthalpies for Various Binary Mixtures with N- Methylacetamide or Acetic Anhydride. J. Chem. Eng. Data 41 (1996) 474-478. https://doi.org/10.1021/je950294h [18] A. Heintz, P.K. Naicker, S.P. Verevkin, R. Pfestorf, Thermodynamics of alkanol + amine mixtures. Experimental results and ERAS model calculations of the heat of mixing. Ber. Bunsenges. Phys. Chem. 102 (1998) 953-959. https://doi.org/10.1002/bbpc.19981020707 [19] K. Nakanishi, H. Touhara, N. Watanabe, Studies on Associated Solutions. II. Heat of Mixing of Methanol with Aliphatic Amines. Bull. Chem. Soc. Jpn. 43 (1970) 2671-2676. https://doi.org/10.1246/bcsj.43.2671 [20] A. Heintz, A New Theoretical Approach for Predicting Excess Properties of Alkanol/Alkane Mixtures. Ber. Bunsenges. Phys. Chem. 89 (1985) 172-181. https://doi.org/10.1002/bbpc.19850890217 [21] S. Villa, N. Riesco, I. Garcıa de la Fuente, J.A. González, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult’s law. Part 8. Excess molar volumes at 298.15 K for 1-alkanol + isomeric amine (C6H15N) systems: DISCUSSION OF THE RESULTS 279 Characterization in terms of the ERAS model. Fluid Phase Equilib. 216 (2004) 123-133. https://doi.org/10.1016/j.fluid.2003.10.008 [22] J.A. González, I. García de la Fuente, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult's Law: Part 4. Application of the DISQUAC model to mixtures of 1-alkanols with primary or secondary linear amines. Comparison with Dortmund UNIFAC and ERAS results. Fluid Phase Equilib. 168 (2000) 31-58. https://doi.org/10.1016/S0378-3812(99)00326-X [23] R. Srivastava, B.D. Smith, Total-pressure vapor-liquid equilibrium data for binary systems of diethylamine with acetone, acetonitrile, and methanol. J. Chem. Eng. Data 30 (1985) 308-313. https://doi.org/10.1021/je00041a022 [24] L. Wang, G.C. Benson, B.C.Y. Lu, Excess enthalpies of 1-propanol + n-hexane + ndecane or n-dodecane at 298.15 K. J. Chem. Eng. Data 37 (1992) 403-406. https://doi.org/10.1021/je00008a007 [25] S.-c. Hwang, R.L. Robinson, Vapor-liquid equilibria at 25 ºC for nine alcoholhydrocarbon binary systems. J. Chem. Eng. Data 22 (1977) 319-325. https://doi.org/10.1021/je60074a025 [26] S. Villa, N. Riesco, I. Garcıa de la Fuente, J.A. González, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult’s law: Part 5. Excess molar volumes at 298.15 K for 1-alkanols+dipropylamine systems: characterization in terms of the ERAS model. Fluid Phase Equilib. 190 (2001) 113-125. https://doi.org/10.1016/S0378-3812(01)00595-7 [27] S. Villa, N. Riesco, I. Garcıa de la fuente, J.A. González, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult’s law: Part 6. Excess molar volumes at 298.15 K for 1-alkanols + dibutylamine systems. Characterization in terms of the ERAS model. Fluid Phase Equilib. 198 (2002) 313-329. https://doi.org/10.1016/S0378-3812(01)00808-1 [28] L.F. Sanz, J.A. González, I. García De La Fuente, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult's law. XI. Densities, viscosities and refractives indices at (293.15–303.15) K for cyclohexylamine + 1-propanol, or +1- butanol systems. J. Mol. Liq. 172 (2012) 26-33. https://doi.org/10.1016/j.molliq.2012.05.003 [29] L.F. Sanz, J.A. González, I. García de la Fuente, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult’s law. XII. Densities, viscosities and refractive indices at T = (293.15 to 303.15) K for (1-heptanol, or 1-decanol + cyclohexylamine) systems. Application of the ERAS model to (1-alkanol + cyclohexylamine) mixtures. J. Chem. Thermodyn. 80 (2015) 161-171. https://doi.org/10.1016/j.jct.2014.09.005 [30] L.F. Sanz, J.A. González, I.G. De La Fuente, J.C. Cobos, Thermodynamics of mixtures with strong negative deviations from raoult’s law. XIV. density, permittivity, refractive index and viscosity data for the methanol + cyclohexylamine mixture at (293.15–303.15) K. Thermochim. Acta 631 (2016) 18-27. https://doi.org/10.1016/j.tca.2016.03.002 [31] U. Domańska, M. Głoskowska, Experimental Solid + Liquid Equilibria and Excess Molar Volume of Alkanol + Octylamine Mixtures. Analysis in Terms of ERAS, DISQUAC, and Modified UNIFAC. J. Chem. Eng. Data 49 (2004) 101-108. https://doi.org/10.1021/je0301895 CHAPTER 5 280 [32] K. Nakanishi, H. Touhara, Excess molar enthalpies of (methanol + aniline), (methanol + N-methylaniline), and (methanol + N,N-dimethylaniline). J. Chem. Thermodyn. 18 (1986) 657-660. https://doi.org/10.1016/0021-9614(86)90067-4 [33] I. Nagata, Excess enthalpies of (aniline + butan-1-ol) and of (aniline + butan-1-ol + benzene) at the temperature 298.15 K. J. Chem. Thermodyn. 25 (1993) 1281-1285. https://doi.org/10.1006/jcht.1993.1127 [34] H. Matsuda, K. Ochi, K. Kojima, Determination and Correlation of LLE and SLE Data for the Methanol + Cyclohexane, Aniline + Heptane, and Phenol + Hexane System. J. Chem. Eng. Data 48 (2003) 184-189. https://doi.org/10.1021/je020156+ [35] S. Villa, R. Garriga, P. Pérez, M. Gracia, J.A. González, I.G. de la Fuente, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult's law: Part 9. Vapor–liquid equilibria for the system 1-propanol + di-n-propylamine at six temperatures between 293.15 and 318.15 K. Fluid Phase Equilib. 231 (2005) 211-220. https://doi.org/10.1016/j.fluid.2005.01.013 [36] J.A. González, L.F. Sanz, I. García de la Fuente, J.C. Cobos, Thermodynamics of mixtures with strong negative deviations from Raoult’s law. XIII. Relative permittivities for (1-alkanol + cyclohexylamine) systems, and dielectric study of (1-alkanol + polar) compound (amine, amide or ether) mixtures. J. Chem. Thermodyn. 91 (2015) 267-278. https://doi.org/10.1016/j.jct.2015.07.032 [37] J.A. González, I.G. de la Fuente, J.C. Cobos, Thermodynamics of mixtures with strongly negative deviations from Raoult's law. Part 3. Application of the DISQUAC model to mixtures of triethylamine with alkanols. Comparison with Dortmund UNIFAC and ERAS results. Can. J. Chem. 78 (2000) 1272-1284. https://doi.org/10.1139/v00-114 [38] J.A. González, I. Mozo, I. García de la Fuente, J.C. Cobos, Thermodynamics of organic mixtures containing amines. IV. Systems with aniline. Can. J. Chem. 83 (2005) 1812- 1825. https://doi.org/10.1139/v05-190 [39] J.A. González, I. Mozo, I.G.d.l. Fuente, J.C. Cobos, Thermodynamics of organic mixtures containing amines: V. Systems with pyridines. Thermochim. Acta 441 (2006) 53-68. https://doi.org/10.1016/j.tca.2005.11.027 [40] J.A. González, I. Mozo, I.G. de la Fuente, J.C. Cobos, N. Riesco, Thermodynamics of mixtures containing amines: VII. Systems containing dimethyl or trimethylpyridines. Thermochim. Acta 467 (2008) 30-43. https://doi.org/10.1016/j.tca.2007.10.011 [41] J.A. González, I.G. de la Fuente, I. Mozo, J.C. Cobos, N. Riesco, Thermodynamics of Organic Mixtures Containing Amines. VII. Study of Systems Containing Pyridines in Terms of the Kirkwood−Buff Formalism. Ind. Eng. Chem. Res. 47 (2008) 1729-1737. https://doi.org/10.1021/ie071226e [42] J.A. González, J.C. Cobos, I. García de la Fuente, I. Mozo, Thermodynamics of mixtures containing amines. IX. Application of the concentration–concentration structure factor to the study of binary mixtures containing pyridines. Thermochim. Acta 494 (2009) 54- 64. https://doi.org/10.1016/j.tca.2009.04.017 [43] F. Hevia, A. Cobos, J.A. González, I. García de la Fuente, L.F. Sanz, Thermodynamics of Amide + Amine Mixtures. 1. Volumetric, Speed of Sound, and Refractive Index Data for N,N-Dimethylformamide + N-Propylpropan-1-amine, + N-Butylbutan-1-amine, + Butan-1-amine, or + Hexan-1-amine Systems at Several Temperatures. J. Chem. Eng. Data 61 (2016) 1468-1478. https://doi.org/10.1021/acs.jced.5b00802 [44] F. Hevia, A. Cobos, J.A. González, I.G. de la Fuente, V. Alonso, Thermodynamics of Amide + Amine Mixtures. 2. Volumetric, Speed of Sound and Refractive Index Data for DISCUSSION OF THE RESULTS 281 N,N-Dimethylacetamide + N-Propylpropan-1-Amine, + N-Butylbutan-1-Amine, + Butan-1-Amine, or + Hexan-1-Amine Systems at Several Temperatures. J. Solution Chem. 46 (2017) 150-174. https://doi.org/10.1007/s10953-016-0560-0 [45] F. Hevia, J.A. González, I. García de la Fuente, L.F. Sanz, J.C. Cobos, Thermodynamics of amide + amine mixtures. 3. Relative permittivities of N,N-dimethylformamide + N- propylpropan-1-amine, + N-butylbutan-1-amine, + butan-1-amine, or + hexan-1-amine systems at several temperatures. J. Mol. Liq. 238 (2017) 440-446. https://doi.org/10.1016/j.molliq.2017.05.025 [46] F. Hevia, J.A. González, A. Cobos, I. García de la Fuente, L.F. Sanz, Thermodynamics of amide + amine mixtures. 4. Relative permittivities of N,N-dimethylacetamide + N- propylpropan-1-amine, + N-butylbutan-1-amine, + butan-1-amine, or + hexan-1-amine systems and of N,N-dimethylformamide + aniline mixture at several temperatures. Characterization of amine + amide systems using ERAS. J. Chem. Thermodyn. 118 (2018) 175-187. https://doi.org/10.1016/j.jct.2017.11.011 [47] F. Hevia, J.A. González, A. Cobos, I. García de la Fuente, C. Alonso-Tristán, Thermodynamics of mixtures with strongly negative deviations from Raoult's law. XV. Permittivities and refractive indices for 1-alkanol + n-hexylamine systems at (293.15– 303.15) K. Application of the Kirkwood-Fröhlich model. Fluid Phase Equilib. 468 (2018) 18-28. https://doi.org/10.1016/j.fluid.2018.04.007 [48] A.L. McClellan, Tables of Experimental Dipole Moments. Vols. 1,2,3, Rahara Enterprises, El Cerrito, US, 1974. [49] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic solvents: physical properties and methods of purification. Wiley, New York, 1986. [50] J. Lobos, I. Mozo, M. Fernández Regúlez, J.A. González, I. García de la Fuente, J.C. Cobos, Thermodynamics of Mixtures Containing a Strongly Polar Compound. 8. Liquid−Liquid Equilibria for N,N-Dialkylamide + Selected N-Alkanes. J. Chem. Eng. Data 51 (2006) 623-627. https://doi.org/10.1021/je050428j [51] M. Rogalski, R. Stryjek, Mutual solubility of binary n-hexadecane and polar compound systems. Bull. Acad. Pol. Sci., Ser. Sci. Chim. 28 (1980) 139-147. [52] X. An, H. Zhao, F. Jiang, W. Shen, The (liquid + liquid) critical phenomena of (a polar liquid + an n-alkane) V. Coexistence curves of (N,N-dimethylacetamide + heptane). J. Chem. Thermodyn. 28 (1996) 1221-1232. https://doi.org/10.1006/jcht.1996.0109 [53] H. Funke, M. Wetzel, A. Heintz, New applications of the ERAS model. Thermodynamics of amine + alkane and alcohol + amine mixtures. Pure Appl. Chem. 61 (1989) 1429- 1439. https://doi.org/10.1351/pac198961081429 [54] S. Villa, J.A. González, I.G. De La Fuente, N. Riesco, J.C. Cobos, Thermodynamics of Organic Mixtures Containing Amines. II. Excess Molar Volumes at 25°C for Methylbutylamine + Alkane Systems and Eras Characterization of Linear Secondary Amine + Alkane Mixtures. J. Solution Chem. 31 (2002) 1019-1038. https://doi.org/10.1023/A:1021881627444 [55] J.A. González, L.F. Sanz, I. García De La Fuente, J.C. Cobos, Thermodynamics of mixtures containing amines: XIII. Application of the ERAS model to cyclic amine + alkane mixtures. Thermochim. Acta 573 (2013) 229-236. https://doi.org/10.1016/j.tca.2013.09.033 [56] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids. McGraw- Hill, New York, US, 1987. CHAPTER 6 288 • In HxA mixtures, cyclic multimers are favored and linear multimers disfavored when compared with DPA systems. • As a general trend in mixtures with primary or secondary amines, higher solvation effects appear together with lower E r  and K g values. • 1-alkanol + TEA mixtures behave in a different way from systems with primary or secondary amines, due to structural effects and to the effectiveness of TEA to break the 1- alkanol self-association. • Solvation determines to a great extent the structure of the HxA, DPA, TEA or c-HxA mixtures. For methanol mixtures, K1 ()g  curves increase sharply for low 1  values and remain practically constant in the high 1  region. • Cyclization (c-HxA) of a primary amine (HxA) leads to increased E r  values. The effect of aromaticity (aniline) of the primary amine leads to decreased E r  , due to the rupture of strong aniline-aniline interactions. c) Orientational effects in alkanone, alkanal or dialkyl carbonate + alkane mixtures and in alkanone + alkanone or + dialkyl carbonate systems • In systems containing ketones with the same number of C atoms and a given alkane, dipolar interactions become weaker in the sequence: aromatic > cyclic > linear. • For a given alkane, they are also weaker in the order: dialkyl carbonate > linear alkanone > linear alkanal. The size and shape of the OCOO group has a large impact on the thermodynamic properties. • According to the Flory model, in alkanone, alkanal or linear organic carbonate + alkane mixtures, orientational (i.e. non-random) effects are similar for linear, cyclic or aromatic polar compounds. They are also similar in alkanone or alkanal + alkane mixtures. In contrast, orientational effects become weaker in dialkyl carbonate + alkane mixtures. • Mixtures of two alkanones show a behavior close to random mixing, and so do systems of long 2-alkanones or cyclohexanone and a dialkyl carbonate. • Larger orientational effects are encountered in solutions of carbonates and short 2-alkanones. d) Orientational effects in mixtures of organic carbonates and alkanes or 1-alkanols • The considered mixtures are characterized by dipolar interactions and by interactions between like molecules. • In systems with a given solvent, dipolar interactions become weaker in the sequence: propylene carbonate (PC) > dimethyl carbonate (DMC)> diethyl carbonate (DEC). • (1-alkanol)-carbonate interactions are stronger in solutions with DMC, and become weaker when the alcohol size increases in systems with a given carbonate. • Results from the Flory model show that orientational effects decrease in the order: DEC > PC > DMC. They are particularly important for mixtures with methanol or ethanol. • In systems with DMC, orientational effects are weaker in 1-alkanol mixtures than in those containing alkanes. A similar trend appears in DEC systems for 1-alkanols longer than ethanol. Part IV Appendices 291 Equation Section (Next) Appendix A. Excess molar enthalpies of amide + amine mixtures and ERAS model results Although at the time of writing this manuscript the experimental data and the results of the application of the model to amide + amine mixtures have not yet been published, they have been sent for publication. We will provide this part of the work in the form of the submitted manuscript. Thermodynamics of amide + amine mixtures. 5. Excess molar enthalpies of N,N- dimethylformamide or N,N-dimethylacetamide + N-propylpropan-1-amine, + N- butylbutan-1-amine, + butan-1-amine, or + hexan-1-amine systems at 298.15 K. Application of the ERAS model Fernando Hevia(1), Karine Ballerat-Busserolles(2), Yohann Coulier(2), Jean-Yves Coxam(2), Juan Antonio González(1), Isaías García de la Fuente(1), José Carlos Cobos(1) (1) G.E.T.E.F., Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid, Paseo de Belén, 7, 47011 Valladolid, Spain. (2) Institut de Chimie de Clermont Ferrand, University Clermont Auvergne, CNRS UMR 6296, SIGMA Clermont, F-63000 Clermont-Ferrand, France. Abstract Excess molar enthalpies, E m H , over the whole composition range have been determined for the liquid mixtures N,N-dimethylformamide (DMF) or N,N-dimethylacetamide (DMA) + butan-1-amine (BA), or + hexan-1-amine (HxA), or + N-propylpropan-1-amine (DPA), or N-butylbutan-1-amine (DBA) at 298.15 K and at 0.1 MPa using a BT2.15 calorimeter from Setaram adapted to work in dynamic mode at constant temperature and pressure. All the E m H values are positive, indicating that interactions between like molecules are predominant. The replacement of DMF by DMA in systems with a given amine leads to lower E m H results, which have been ascribed to stronger amide-amide interactions in DMF mixtures. The replacement of HxA by DPA in systems with a given amide leads to slightly higher E m H values, as interactions between unlike molecules are weaker for the latter. Structural effects in the investigated solutions are also present, since the corresponding excess molar volumes ( E m V ), previously determined, are negative or slightly positive. The systems have been characterized in terms of the ERAS model reporting the interaction parameters. The model correctly describes both E m H and E m V . The application of the model suggests that, in the systems under study, solvation effects are of minor importance and that physical interactions are dominant. APPENDIX A 292 A.1. Introduction It is well-known that a suitable approach for the investigation of the highly complex chemical environment of proteins is to study small organic molecules whose functional groups are similar to those present in the biomolecule [1]. The systematic physical and chemical characterization of such molecules and of their mixtures in terms of thermodynamic, transport and dielectric properties is necessary in this framework. The study of amide + amine systems is relevant, as it allows to gain insight into the behavior of the amide group when it is surrounded by different environments. In fact, the hydrogen-bonded structures where the amide group is involved can show very different biological activities depending on the mentioned environments [2]. On the other hand, the strong polarity of amides, which in the case of tertiary amides leads to the creation of a certain local order [3, 4], together with their high solvating capability and liquid state range –due to their ability to form hydrogen bonds– [5], makes them a very important kind of organic solvents. Similarly, amines are also an important class of substances since many biological relevant molecules contain the amine group [6-8]. In addition, the low vapor pressure of amines makes them useful in green chemistry. Thus, mixtures containing amines are being investigated to be used in CO2 capture [9] and, interestingly, many of the ions of the technically important ionic liquids are related to amine groups [10]. In previous works, we have measured densities, speeds of sound and refractive indices of N,N- dimethylformamide (DMF) [11], or N,N-dimethylacetamide (DMA) [12] + N-propylpropan-1- amine (DPA) or + butan-1-amine (BA) at (293.15-303.15) K, and + N-butylbutan-1-amine (DBA) or + hexan-1-amine (HxA) at 298.15 K. In addition, we have reported low-frequency permittivity measurements of the mentioned systems and of the DMF + aniline mixture at (293.15-303.15) K [13, 14]. This database has been interpreted in terms of solute-solvent interactions and structural effects. We have also applied the ERAS [15] and the Kirkwood- Fröhlich models [16-19] to the study of amine + amide mixtures. The latter is useful for the calculation of the Balankina relative excess Kirkwood correlation factors [20], which provide information on the dipole correlations present in the considered systems. Calorimetric data are essential for the study of the type and strength of interactions present in liquid mixtures. As the data available in the literature on excess molar enthalpies, E m H , for amine + amide mixtures is scarce [21-23], we continue this series of works reporting E m H values for DMF or DMA + DPA, or + DBA, or + BA or + HxA systems at 298.15 K. Finally, the systems are characterized in terms of the ERAS model, revisiting the previously reported parameters which were determined using volumetric data only [14]. A.2. Experimental A.2.1. Materials Information about the purity and source of the pure compounds used along the experiments is collected in Table A.1. They were used without further purification. It also shows their densities (  ) at 0.1 MPa and at 298.15 K. These results agree well with literature data. A.2.2. Apparatus and procedure Molar quantities were calculated using the relative atomic mass Table of 2015 issued by the Commission on Isotopic Abundances and Atomic Weights (IUPAC) [24]. EXCESS MOLAR ENTHALPIES OF AMIDE + AMINE MIXTURES AND ERAS RESULTS 293 Table A.1. Description, source and purity of the pure liquids and their density,  , at temperature T = 298.15 K and pressure p = 0.1 MPa. b Chemical name CAS number Source Puritya  / g·cm-3 Exp. Lit. N,N-dimethylformamide (DMF) 68-12-2 Sigma-Aldrich 0.9996 0.94378 0.944163 [25] N,N-dimethylacetamide (DMA) 127-19-5 Honeywell >0.999 0.93614 0.936233 [26] N-propylpropan-1-amine (DPA) 142-84-7 Aldrich 0.999 0.73337 0.73321 [27] N-butylbutan-1-amine (DBA) 111-92-2 Aldrich 0.997 0.75570 0.755457 [28] butan-1-amine (BA) 109-73-9 Sigma-Aldrich 0.9978 0.73218 0.73233 [29] hexan-1-amine (HxA) 111-26-2 Aldrich 0.999 0.76016 0.76013 [30] a In mole fraction. By gas chromatography. Provided by the supplier. b The standard uncertainties are: ( ) uT = 0.01 K, ( ) up = 1 kPa. The relative standard uncertainty is: ( ) r u  = 0.0012. Figure A.1: Schematic view of the experimental setup used to determine excess molar enthalpies. APPENDIX A 294 Densities were obtained using a vibrating-tube densimeter DMA HPM from Anton Paar. The temperature regulation of the densimetric block is insured by the use of a thermostatic bath from Julabo. The standard uncertainty in the temperature is 0.01 K. Experiments were performed at atmospheric pressure, in a static mode. The calibration was carried out using pure octane, dodecane and tridistilled water, and comparing with literature values. The excess molar enthalpies were determined from heat of mixing measurements performed with a BT2.15 calorimeter from Setaram adapted to work in dynamic mode at constant temperature and pressure. The arrangement is depicted in Figure A.1. The fluids flow in stainless steel tubes with an external diameter of 1.6 mm and an internal diameter of 1.0 mm and mix in a custom-made cell. They are injected into the system by means of two syringe pumps model Teledyne ISCO 260 D, which are controlled by a Teledyne ISCO D-Series Pump Controller. Mixtures of different concentrations are obtained varying the volumetric flow rates given by the pumps. These flow rates can be chosen from 1 μL·min-1 to 25 mL·min-1 with a relative standard uncertainty of 0.5%. The capacity of the pumps is 266.05 mL, and they can be regulated up to a pressure of 52 MPa with a 2% relative standard uncertainty. To ensure the stability of the molar flow rates, the fluids are kept inside the pumps at a constant temperature of 298.15 K by means of a thermostatic bath Fisher Scientific Polystat 36, with a stability of 0.03 K. The relative standard uncertainty in the mole fraction is estimated to be 0.004. The pressure in the system is maintained constant with the help of a pressure regulator located at the end of the flow line, and the pressure relative to the atmospheric pressure is determined by a Keller transducer with a relative standard uncertainty of 0.25% of full scale (40 MPa). For the measurements in this work, the pressure regulator was open to the atmospheric pressure. The temperature of the calorimetric block is regulated by heating a cold can by means of a Setaram G11 Universal Controller. The temperature of the can is maintained constant using a circulating fluid at 10 K below the expected temperature of the experiment, using an external ultra-cryostat Julabo FL1201. The temperature of the block is then regulated using the G11 Universal Controller with a stability of 0.01 K. The temperature of the injected fluids is adjusted to the working temperature with the help of an external precooler and an internal preheater. The external precooler is situated on top of the calorimetric block and is connected in series to the cooler can of the calorimeter and to the ultra-cryostatic bath. The internal preheater is inside the calorimetric block; it supplies the necessary power to reach the exact temperature of the experiment using a heating cartridge, and its temperature is controlled by means of a platinum resistance connected to a Fluke Hart Scientific 2200 PID controller with a stability of 0.01 K. The heat flow is detected by a thermopile, generating an electromotive force (EMF) that is collected by a 6 ½ digit multimeter from Keysight model 34401A and sent to a computer through a GPIB connection. The thermopile EMF, S , is converted into the mixing enthalpy through the steady-state relation: ( ) EBL m12 SS HK n n − =+ (A.1) where K is a temperature-dependent calibration constant, i n is the molar flow rate of component i and BL S is the baseline signal, recorded when only one of the fluids is flowing. The constant K is obtained by measuring the E m H of the system ethanol + water and comparing the results with reference values from Ott et al. [31, 32]. Taking into account uncertainties on fluid flow rates, thermopile calibration K, and calorimetric signal noises, the estimated maximum relative standard uncertainty on E m H for the set of experimental points in this work is 0.03. EXCESS MOLAR ENTHALPIES OF AMIDE + AMINE MIXTURES AND ERAS RESULTS 295 A.3. Results Data on E m H are listed in Table A.2. They were fitted to a Redlich-Kister equation [33] by an unweighted linear least-squares regression. The Redlich-Kister equation for the excess property E F is given by: ( ) ( ) E11 1 01 1 2 1 i i k i F x x A x − = = − −  (A.2) The number, k , of necessary coefficients for this regression has been determined, for each system, by applying an F-test of additional term [34] at 99.5% confidence level. The standard deviations, ( ) E F  , are defined by: ( ) ( ) EE cal, exp, 1/2 2 E 1 1jj N j F Nk FF  =  =−  −    (A.3) where the index j takes one value for each of the N data points E exp,j F , and E cal,j F is the corresponding value of the excess property calculated from equation (A.2). Excess molar energies of constant volume, E m,V U , are given by [35]: E E E m, m m p VT U H T V   =− (A.4) where p  is the isobaric thermal expansion coefficient, T  is the coefficient of isothermal compressibility and E m V is the excess molar volume. The E m,V U curves of amide + amine systems were obtained at 1 x = 0.05 using smoothed values of E m H and of volumetric properties previously measured [11, 12]. Let us denote by m,i V , ,pi  and ,m,pi C the molar volume, isobaric thermal expansion coefficient and molar isobaric heat capacity of component i respectively, and by m, 1 m,1 2 m,2 () i ii xV x V x V  =+ the volume fraction of component i. In the application of equation (A.4), p  was assumed ideal ( id 1 ,1 2 ,2p p p      =+ ) for HxA and DBA mixtures; the error in using this assumption is negligible due to the smallness of E m V for these systems and, actually, the difference EE m, mV UH− is not relevant. T  was obtained from the equation: 2 m ,m p TS p T C V   =+ (A.5) with the molar isobaric heat capacity of the mixture, ,mp C , taken as ideal ( 1 ,m,1 id ,m,2,m 2ppp C x C x C=+ ). The E m,V U curves have also been adjusted to Redlich-Kister polynomials using the same procedure given above. Table A.3 includes the parameters i A obtained for E F (= E m H , E m,V U ), together with the standard deviations ( ) E F  . Values of E m H at temperature 298.15 K are plotted in Figure A.2 Figure A.3, and their corresponding Redlich-Kister regressions in Figures A.S1 and A.S2. The corresponding E m,V U curves are depicted in Figures A.S3 and A.S4. APPENDIX A 296 Table A.2. Excess molar enthalpies, E m H , of amide (1) + amine (2) liquid mixtures as functions of the mole fraction of the amide, 1 x , at temperature T = 298.15 K and pressure p = 0.1 MPa. a x1 E m H / J·mol-1 x1 E m H / J·mol-1 x1 E m H / J·mol-1 x1 E m H / J·mol-1 DMF (1) + DPA (2) 0.0358 88 0.3016 595 0.5505 753 0.7983 542 0.1002 241 0.3483 657 0.6012 743 0.8485 441 0.1512 351 0.4005 695 0.6587 708 0.8991 318 0.1984 446 0.4495 737 0.6997 673 0.9504 170 0.2504 529 0.5005 748 0.7518 613 DMF (1) + DBA (2) 0.0491 188 0.3006 877 0.5505 1118 0.7994 815 0.1014 386 0.3510 956 0.5990 1098 0.8503 669 0.1488 543 0.4021 1032 0.6500 1060 0.9000 488 0.2006 680 0.4497 1082 0.6997 1001 0.9501 270 0.2482 782 0.4982 1113 0.7506 921 DMF (1) + BA (2) 0.0510 89 0.2498 320 0.5008 384 0.7559 245 0.1009 166 0.3007 352 0.5463 374 0.8005 208 0.1496 226 0.3496 373 0.6008 355 0.8495 158 0.1703 247 0.4008 391 0.6463 326 0.9003 106 0.2005 279 0.4508 393 0.7011 289 0.9519 55 DMF (1) + HxA (2) 0.0514 118 0.3006 533 0.5505 659 0.8005 441 0.1007 219 0.3519 586 0.5982 648 0.8506 354 0.1516 318 0.4007 619 0.6507 615 0.8995 246 0.2009 394 0.4518 648 0.7002 569 0.9502 129 0.2522 461 0.5003 661 0.7503 510 DMA (1) + DPA (2) 0.0597 98 0.3009 399 0.5497 519 0.8009 385 0.0996 166 0.3462 435 0.5972 509 0.8504 318 0.1496 235 0.4062 477 0.6495 493 0.8989 239 0.2011 300 0.4491 495 0.6975 473 0.9368 156 0.2497 358 0.5035 514 0.7478 437 0.9507 126 DMA (1) + DBA (2) 0.0499 150 0.3002 673 0.5507 832 0.8004 618 0.0976 276 0.3526 732 0.6007 825 0.8512 508 0.1510 405 0.3983 774 0.6477 803 0.9019 371 0.1969 503 0.4472 807 0.6968 756 0.9507 203 0.2472 590 0.5007 833 0.7481 698 EXCESS MOLAR ENTHALPIES OF AMIDE + AMINE MIXTURES AND ERAS RESULTS 297 DMA (1) + BA (2) 0.0498 48 0.3004 189 0.5509 201 0.9002 64 0.0992 89 0.3493 202 0.6005 195 0.9594 27 0.1518 123 0.4015 207 0.7008 160 0.1985 152 0.4508 209 0.7995 120 0.2512 165 0.5005 208 0.8502 94 DMA (1) + HxA (2) 0.0509 71 0.3018 338 0.5493 424 0.7996 296 0.1005 141 0.3484 369 0.6002 416 0.8513 238 0.1507 196 0.3980 402 0.6492 401 0.9008 171 0.1994 244 0.4502 419 0.7001 375 0.9503 91 0.2488 295 0.5006 423 0.7491 341 a The standard uncertainties are: ( ) uT = 0.01 K, ( ) up = 1 kPa. The relative standard uncertainty is: ( ) 1r ux = 0.004. The relative combined expanded uncertainty (0.95 level of confidence) is ( ) E rc m 0.06UH = . Table A.3. Coefficients Ai and standard deviations, ( ) E F  (equation (A.3)), for the representation of E F at temperature T = 298.15 K and pressure p = 0.1 MPa for amide + amine liquid mixtures by equation (A.2). Property E F System 0 A 1 A 2 A 3 A ( ) E F  E m H / J·mol-1 DMF + DPA 2999 476 178 4 DMF + DBA 4410 731 634 7 DMF + BA 1545 –374 –75 1.9 DMF + HxA 2639 238 –93 4 DMA + DPA 2038 444 274 4 DMA + DBA 3314 476 544 255 2 DMA + BA 834 –158 3 DMA + HxA 1699 234 3 E m,V U / J·mol-1 DMF + DPA 3408 657 338 0.7 DMF + DBA 4385.4 841 758 0.5 DMF + BA 1954.3 –193 45 0.4 DMF + HxA 2669.7 376 0.7 DMA + DPA 2359.7 457 368 0.4 DMA + DBA 3237.3 436 532 250 0.3 DMA + BA 1131 –59 93 0.3 DMA + HxA 1690 269 31 0.6 APPENDIX A 304 represented with a rather good degree of approximation. The results from the model suggest that physical interactions are important when calculating the excess functions of the mixtures under study. A.7. Supplementary material Table A.S1. ERAS parametersa for pure liquids at temperature 298.15 K and pressure 0.1 MPa. Compound m,i V /cm3·mol-1 i K i h  /kJ·mol-1 i v  /cm3·mol-1 m,i V /cm3 ·mol-1 i p /J·cm-3 BAb 99.89 0.96 –13.2 –2.8 77.59 565.7 HxAb 133.11 0.78 –13.2 –2.8 106.87 495.0 DPAc 138.07 0.55 –7.5 –2.8 106.50 526.0 DBAc 171.03 0.16 –4.5 –2.8 135.86 466.2 DMFd 77.44 0 0 0 62.07 714.1 DMAd 93.04 0 0 0 75.56 649.5 a m,i V , molar volume; i K , equilibrium constant; m,i V and i p , reduction parameters for volume and pressure, respectively; i h  , hydrogen-bonding enthalpy; i v  , self-association volume; b Ref. [51]; c Ref. [52]; d [53]. Figure A.S1: Excess molar enthalpies, E m H , of DMF (1) + amine (2), or BA (1) + heptane (2) liquid mixtures at 0.1 MPa and 298.15 K. Full symbols, DMF (1) + amine (2) experimental values (this work): (), BA; (), HxA; (▲), DPA; (♦), DBA. Solid lines, calculations with equation (A.2) using the coefficients from Table A.3. Dashed line, BA (1) + heptane (2) [62]. Figure A.S2: Excess molar enthalpies, E m H , of DMA (1) + amine (2), or + cyclohexane (2) liquid mixtures at 0.1 MPa and 298.15 K. Full symbols, DMA (1) + amine (2) experimental values (this work): (), BA; (), HxA; (▲), DPA; (♦), DBA. Solid lines, calculations with equation (A.2) using the coefficients from Table A.3. Dashed line, DMA (1) + cyclohexane (2) [71]. [Document text truncated for crawler view.]