Structural characterization of solid cellular polymers by X-ray tomography and light scattering

PROGRAMA DE DOCTORADO EN FÍSICA FACULTAD DE CIENCIAS DEPARTAMENTO DE FÍSICA DE LA MATERIA CONDENSADA, CRISTALOGRAFÍA Y MINERALOGÍA TESIS DOCTORAL: Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering Presentada por Saúl Pérez Tamarit para optar al grado de Doctor por la Universidad de Valladolid Dirigida por: Dr. Eusebio Solórzano Dr. Miguel Ángel Rodríguez Pérez Valladolid, Diciembre de 2018 Introducción en Castellano .................................................................... 15 Marco de la Tesis ......................................................................................................... 20 Objetivos ....................................................................................................................... 23 Desafíos ......................................................................................................................... 24 Principales Novedades ............................................................................................... 26 Estructura de la Tesis .................................................................................................. 27 Referencias .............................................................................................................. 35 Chapter 1 Introduction............................................................................................. 39 1.1 Framework of this Thesis .................................................................................... 44 1.2 Objectives ............................................................................................................... 47 1.3 Challenges .............................................................................................................. 48 1.4 Main Novelties ...................................................................................................... 50 1.5 Structure of this thesis .......................................................................................... 51 References ............................................................................................................... 59 Chapter 2 Basic Concepts on Cellular Materials .................................................... 63 2.1 Cellular Structure .................................................................................................. 65 2.1.1 μ-structure model ................................................................................................... 65 2.1.2 Microscopic descriptors .......................................................................................... 67 2.2 Foaming Dynamics ............................................................................................... 76 2.2.1 Cells formation ....................................................................................................... 76 2.2.2 Degeneration of the cellular structure ................................................................... 78 2.3 Materials ................................................................................................................. 80 2.3.1 Polyurethane (PU) and Reactive Foaming............................................................. 80 2.3.2 Polyethylene (PE), poly-methyl methacrylate (PMMA) and Gas Dissolution Foaming .......................................................................................................................... 83 2.3.3 Polystyrene (PS) and Extrusion Foaming ............................................................. 85 2.3.4 Nanosilica Aerosil R812 ........................................................................................ 87 References ............................................................................................................... 88 Introducción en Castellano 17 Los materiales celulares son estructuras bifásicas en las cuales una fase gaseosa que puede ser tanto continua como discontinua está dispersa en una fase continua de líquido o sólido [1]. Estos materiales han atraído mucha atención en los últimos tiempos debido a multitud de factores. La presencia de gas en el seno de la matriz sólida se traduce en una reducción de densidad en comparación a los materiales sólidos de partida [2]. Además, los materiales celulares extienden el rango de las propiedades físicas correspondientes de los materiales sólidos de partida (mostrado en la Figura 1) por lo tanto expandiendo también el rango de aplicaciones en las cuales pueden ser empleados. Figura 1. Propiedades físicas de los materiales celulares y de los sólidos de partida. Estos materiales muestran bajas propiedades de transferencia térmica, como puede ser la conductividad térmica, gran capacidad de absorción de energía así como excelentes rigidez y resistencia y además, dependiendo de su estructura celular, increíbles Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 18 propiedades de absorción acústica. De hecho, algunos materiales en la naturaleza presentan estructura celular interna y con propiedades increíbles como pueden ser el corcho, la madera, el coral o el hueso. Los materiales celulares creados por el hombre tienden a imitar aquellos de la naturaleza desarrollando procesos de producción que permitan controlar la estructura, fabricando así a medida materiales capaces de cumplir con requerimientos específicos. Por ello, los materiales celulares tienen un gran presente y un futuro prometedor en sectores industriales y tecnológicos tales como el aeronáutico, la automoción, la construcción, el confort, el empaquetado, las energías renovables, la biotecnología, el sector médico, etc. [3, 4] El tipo de material celular más representativo usa los polímeros o plásticos como material sólido de partida (llamados entonces polímeros celulares o espumas poliméricas). Para mostrar la importancia de estos materiales, se espera un consumo de polímeros celulares de 25.3 MT en 2019 [5], lo que representa casi el 10% en peso del consumo global de plásticos (y más del 50% del volumen total consumido) [6]. Entre todas las matrices poliméricas, el poliuretano (PU), el poliestireno (PS), el cloruro de polivinilo (PVC) y las poliolefinas (PO) son habitualmente consideradas en la producción de polímeros celulares aunque es importante incidir que el PU y el PS abarcan el 80% del consumo global de polímeros celulares [7] (como se muestra en la Figura 2). Figura 2. Importancia relativa de varios materiales empleados para fabricar polímeros celulares. Introducción en Castellano 19 Los materiales celulares basados en PU son principalmente usados como aislantes térmicos (tanto en edificación como en refrigeradores) y como relleno de confort en asientos. Por otra parte, las espumas de PS destacan en aplicaciones tanto de empaquetado (usando poliestireno expandido, EPS) como de aislamiento térmico (en este caso usando poliestireno extruido, XPS). Además de ello, los materiales celulares basados en PVC son básicos en aplicaciones estructurales y de perfilería. Finalmente, las espumas de poliolefinas tienen gran importancia en los mercados de empaquetado, aislamiento térmico y confort [8]. En las últimas décadas, se han llevado a cabo estudios teóricos y experimentales estudiando la tríada de relaciones proceso-estructura-propiedades en los materiales celulares para optimizar el rendimiento y extender aún más el rango de aplicación de estos materiales. Se ha avanzado enormemente en este campo gracias al desarrollo de técnicas de caracterización no destructivas (NDT, por sus siglas en inglés) que permiten caracterizar los materiales sin alterar su estructura. La mayoría de ellas se basan en la interacción radiación-materia (ya sea con radiación visible, infrarrojo, rayos-X, etc.) y en el análisis de la señal recibida para obtener características particulares de los materiales testeados. Teniendo en cuenta este concepto, esta tesis doctoral se ha enfocado en el uso de dos de estas técnicas, Tomografía de rayos-X y Light Scattering, para llevar a cabo una caracterización detallada de materiales celulares poliméricos. Este capítulo introductorio está dividido en cuatro secciones explicando la estructura de esta investigación. La primera sección muestra el marco científico en el cual la tesis se ha desarrollado. Después, se describen los objetivos principales, seguidos de los retos que ha habido que superar para completar la investigación. Finalmente, se describen brevemente los contenidos de cada capítulo para resumir al final tanto las publicaciones científicas como las comunicaciones en conferencias derivadas de esta tesis doctoral. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 20 Marco de la Tesis Esta tesis es parte de la investigación centrada en materiales celulares desarrollada en el Laboratorio de Materiales Celulares (CellMat) de la Universidad de Valladolid [9]. El director de este laboratorio es el Prof. Dr. Miguel Ángel Rodríguez Pérez, uno de los directores de esta tesis doctoral. El Prof. Dr. José Antonio de Saja, junto al Prof. Dr. Miguel Ángel Rodríguez Pérez fundaron el Laboratorio CellMat en 1999 después de la defensa de la tesis doctoral de Miguel Ángel Rodríguez Pérez, centrada en el estudio de propiedades térmicas y mecánicas de materiales celulares basados en poliolefinas [10]. En los primeros años, la investigación en CellMat se orientó hacia la caracterización de las propiedades físicas de materiales celulares de ese tipo, dando como resultado varias tesis doctorales y publicaciones científicas [11-22] y alcanzando gran comprensión sobre la relación entre la estructura y las propiedades físicas de polímeros celulares. Después de varios años, la investigación se extendió también a la producción de varios materiales para entender mejor la relación proceso-estructura [23-26]. Además de ello, una línea de investigación centrada en la producción y el estudio de espumas basadas en aluminio se inició estos años colateralmente [27-34]. Finalmente, en los últimos años se ha invertido gran esfuerzo en desarrollar técnicas no convencionales que proporcionan conocimiento adicional tanto de la estructura celular como de los procesos de espumado [35-43]. El principal promotor de algunas de estas técnicas fue el co-director de esta tesis doctoral, Dr. Eusebio Solórzano. Hoy en día, la investigación en CellMat se divide en cinco grandes líneas de investigación. Estas líneas son espumas de poliuretano [36, 42, 44-46], nanocompuestos celulares [35, 36, 44, 47-49], materiales celulares multifuncionales [5052], materiales celulares basados en bioplásticos [53-60] y polímeros nanocelulares [6167]. Todas ellas incluyen la producción, caracterización estructural y modelizado de las propiedades físico-químicas para cubrir aplicaciones específicas (Figura 3) dado que uno de los objetivos principales de este laboratorio es la transferencia de conocimiento desde la Universidad a la Industria. Introducción en Castellano 21 Figura 3. Tetraedro de los materiales correspondiente a la investigación en materiales celulares. La investigación llevada a cabo durante esta tesis doctoral trata de profundizar en el desarrollo y aplicación de técnicas de caracterización no convencionales centrándose en las NDT. Por una parte, la micro-Tomografía computarizada (μ-CT, por sus siglas en inglés) es una técnica de caracterización ampliamente utilizada dado que ofrece la posibilidad de obtener información del objeto escaneado en tres dimensiones [68-72]. La aplicación de esta técnica en el laboratorio CellMat comenzó con la investigación realizada por el Dr. Samuel Pardo Alonso, como parte de su tesis doctoral centrada en estudiar tanto los procesos de espumado como la estructura de los polímeros celulares usando técnicas de imagen por rayos-X (radioscopía y tomografía respectivamente) [36]. La investigación correspondiente a esta tesis doctoral ha permitido mejorar los resultados previos y desarrollar nuevos protocolos de análisis de imagen, proporcionando nuevos conocimientos en las relaciones proceso-estructurapropiedades en los materiales celulares. Adicionalmente, los resultados proporcionados por la Tomografía de rayos-X han servido como referencia para verificar la validez de la otra técnica principal desarrollada en esta tesis doctoral, el Light Scattering. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 22 Por otra parte, el desarrollo de una técnica de caracterización nueva que permita obtener resultados en 3D de una manera rápida, simple y sobre todo barata va a resultar siempre de gran interés para la comunidad científica. Teniendo en cuenta esta premisa, Light Scattering, usada ampliamente en el caso de materiales celulares en base acuosa [73], ha sido adaptada y aplicada en esta tesis doctoral en materiales celulares en base sólida obteniendo resultados prometedores. Finalmente, una vez que ambas técnicas se aplicaron en materiales celulares convencionales, ha sido posible aplicarlas a los novedosos y prometedores polímeros nanocelulares, una nueva clase de materiales celulares con propiedades mejoradas [74]. Introducción en Castellano 23 Objetivos Esta tesis tiene como objetivo establecer técnicas no destructivas para la caracterización detallada de una amplia gama de polímeros celulares. Para este fin, por una parte, la Tomografía de rayos-X fue seleccionada para obtener tanto la información básica sobre la fase gaseosa como la descripción detallada de características avanzadas correspondientes a la fase sólida de los materiales celulares, y estudiar su influencia en sus propiedades. Además de ello, su influencia en las propiedades térmicas y mecánicas de los materiales celulares ha sido analizada. Por otra parte, se ha desarrollado una nueva metodología para la caracterización rápida de parámetros básicos de la estructura celular como el tamaño de celda y la anisotropía, basándose en el Light Scattering. Estas técnicas han sido aplicadas y optimizadas para el caso de polímeros celulares convencionales (tamaño de celda entre 200 y 1000 μm) basados en PU, PS y PE y consecuentemente con diferente arquitectura celular. Adicionalmente, un objetivo adicional de esta tesis fue realizar experimentos tanto de Tomografía como de Light Scattering por primera vez en polímeros nanocelulares basados en polimetilmetacrilato (PMMA) con tamaños de celda en el rango de los nanómetros (30-1000 nm). Los objetivos de esta tesis doctoral pueden ser resumidos como sigue: Para completar dichos objetivos, varios desafíos que ha habido que superar durante esta tesis se describen a continuación. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 24 Desafíos Varios aspectos técnicos fueron propuestos para alcanzar los objetivos previamente comentados: o Diseñar, adaptar y optimizar el sistema de Tomografía de rayos-X del laboratorio CellMat para poder realizar experimentos con tamaño de pixel efectivo de 2.5 μm con contraste óptimo en polímeros celulares de baja densidad. o Diseñar y construir un sistema especifico para la realización de los experimentos de Light Scattering que permitiera poder testar materiales con características muy variadas (densidad y tamaño de celda). Además, se ha necesitado resolver multitud de aspectos metodológicos durante esta tesis doctoral: o Desarrollar nuevas metodologías de análisis de imagen para obtener una descripción detallada de la estructura celular de los polímeros celulares. Particularmente, nos hemos centrado en los parámetros correspondientes a la fase sólida, que no han sido aún estudiados en profundidad, tales como el reparto de material sólido entre las distintas partes de la estructura, el espesor de la fase sólida o la corrugación de la misma. o Desarrollar una metodología experimental novedosa para realizar y analizar los experimentos de Light Scattering de polímeros celulares sólidos. o Seleccionar una colección adecuada de polímeros celulares basados en PU, PE y PS que permitan verificar la validez de las técnicas y metodologías desarrolladas. Por ultimo pero no por ello menos importante, los principales temas a destacar desde el punto de vista científico son los siguientes: o Estudiar la morfología de la estructura de los polímeros celulares en 3D mediante Tomografía de rayos-X. Estos materiales están compuestos por elementos de bajo peso atómico, y además, con sólo 3-5% de volumen sólido. Por lo tanto, la absorción de rayos-X es muy baja, comprometiendo el contraste/calidad de los Introducción en Castellano 25 volúmenes reconstruidos. Una selección cuidadosa de los parámetros de experimento sirvió para optimizar el contraste en los experimentos realizados de Tomografía de rayos-X. o Determinar la influencia en las propiedades mecánicas y térmicas de los polímeros celulares de nuevos parámetros estructurales correspondientes a la fase sólida de estos materiales. o Desarrollar un modelo que permita describir el fenómeno de Light Scattering en los polímeros celulares sólidos. o Evaluar como las particularidades del proceso de espumado (como la presencia o ausencia de agentes nucleantes) pueden alterar la estructura de los materiales celulares mientras éstos espuman. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 32 S. Pérez-Tamarit, E. Solórzano, E. Laguna-Gutierrez, B. Notario, A. Hilger, I. Manke and M. A. Rodriguez-Perez Characterization of fillers dispersion in composites and nanocomposites by means of synchrotron X-ray microtomography (ORAL) XIV Reunión del Grupo Especializado de Polímeros (GEP 2016), Burgos (España) Septiembre 2016 S. Pérez-Tamarit, E. Solórzano, S. Pardo-Alonso, R. Mokso and M. A. Rodriguez-Perez Pore Nucleation and growth in cellular polymers analysed by time resolved synchrotron μ-CT (ORAL) III Conferencia Internacional en Tomografía de Materiales y Estructuras (ICTMS 2017), Lund (Suecia) Junio 2017 S. Pérez-Tamarit, E. Solórzano, E. Laguna-Gutierrez, B. Notario, A. Hilger, I. Manke and M. A. Rodriguez-Perez Novel quantification methods of fillers dispersion in polymer composites and nanocomposites based on high resolution synchrotron X-ray μ-CT (POSTER) III Conferencia Internacional en Tomografía de Materiales y Estructuras (ICTMS 2017), Lund (Suecia) Junio 2017 S. Pérez-Tamarit, E. Solórzano, A. Hilger, I. Manke and M. A. Rodriguez-Perez Multiscale analysis of cellular polymers (POSTER) VIII Conferencia en Tomografía Computarizada Industrial (iCT 2018), Wels (Austria) Febrero 2018 S. Pérez-Tamarit, E. Solórzano, A. Hilger, I. Manke and M. A. Rodriguez-Perez Determination of solid phase corrugation ratio of polymeric foams (POSTER) VIII Conferencia en Tomografía Computarizada Industrial (iCT 2018), Wels (Austria) Febrero 2018 S. Pérez-Tamarit, E. Solórzano and M. A. Rodriguez-Perez Characterization of the cellular architecture of solid polymeric foams by means of optical light transmission measurements (ORAL) XII Conferencia Europea en Espumas y Aplicaciones (EuFoam 2018), Lieja (Bélgica), Julio 2018 S. Pérez-Tamarit, P. Cimavilla, J. Martín-de León, V. Bernardo , E. Solórzano and M. A. Rodriguez-Perez X-ray tomographic homogeneity inspection in nanocellular polymers produced using different foaming conditions (POSTER) XII Conferencia Europea en Espumas y Aplicaciones (EuFoam 2018), Lieja (Bélgica), Julio 2018 P. Cimavilla, S. Pérez-Tamarit, M. Santiago-Calvo and M. A. Rodriguez-Perez In-situ physicochemical analysis of the foaming process of aerogel-rigid polyurethane composite foams (ORAL) XII Conferencia Europea en Espumas y Aplicaciones (EuFoam 2018), Lieja (Bélgica), Julio 2018 P. Cimavilla, S. Pérez-Tamarit, E. Solórzano, A. Hilger, I. Manke and M. A. Rodriguez-Perez Novel subresolution tomographic methods for quantifying fraction of mass in Plateau borders of solid polymeric foams (POSTER) XII Conferencia Europea en Espumas y Aplicaciones (EuFoam 2018), Lieja (Bélgica), Julio 2018 D. Batey, S. Cipiccia, X. Shi, S. Williams, K. Wanelik, A. Wilson, S. Pérez-Tamarit, P. Cimavilla, M. A. Rodríguez-Pérez and C. Rau Coherence Branch at I13, DLS: The Multiscale, Multimodal, Ptycho-tomographic End Station (ORAL) XIV Conferencia Internacional en Microscopía de rayos-X (XRM 2018), Saskatoon (Canadá), Agosto 2018 Introducción en Castellano 33 C. Rau, M. Storm, S. Marathe, A. J. Bodey, S. Cipiccia, D. Batey, X. Shi, M-C. Zdora, I. Zanette, S. Pérez-Tamarit, P. Cimavilla, M. A. Rodríguez-Pérez, F. Doring and C. David Multi-Scale Imaging at the Coherence and Imaging Beamline I13 at Diamond (ORAL) XIV Conferencia Internacional en Microscopía de rayos-X (XRM 2018), Saskatoon (Canadá), Agosto 2018 V. Bernardo, J. Martín-de León, F. Van Loock, N. A. Fleck, P. Cimavilla, S. Pérez-Tamarit and M. A. RodriguezPerez Nanocellular polymers based on PMMA/sepiolite nanocomposites: characterization of the mechanical behaviour (POSTER) V Materiales Cellulares (CellMat 2018), Bad Staffelstein (Alemania), Octubre 2018 Tabla 3 Proyectos de Investigación Desarrollo y fabricación en continuo de aislantes térmicos avanzados basados en polímeros nanocelulares Neadfoam: Aditivos innovadores para espumas con mejores prestaciones de aislamiento térmico y comportamiento frente al fuego Desarrollo de bandejas de espuma de poliestireno extruido con baja densidad y propiedades mejoradas Tabla 4 Estancias en otros centros de Investigación XXXIV Berlin School on Neutron Scattering Helmholtz Zentrum, Berlin (Alemania) 13-21 de Marzo de 2014 Synchrotron tomography of polymer foams: in the limits of resolution (Campaña de Experimentación) Sioncrotrón BESSY II, Berlín (Alemania) 5-8 de Junio de 2014 In-situ characterization of the foaming behaviour and exfoliation of nanoclays in nanocomposites using combined white-beam X-ray radioscopy & diffraction (Campaña de Experimentación) Sincrotrón BESSY II, Berlín (Germany) 7-10 de Mayo de 2015 In-situ study of nanoclay exfoliation of polymeric nanocomposites during foaming with azodicarbonamide (Campaña de Experimentación) Sincrotrón BESSY II, Berlín (Alemania) 3-9 de Octubre de 2016 Multiscale investigation of nanocellular polymers with synchrotron based tomography Sincrotrón Diamond Light Source, Oxford (Reino Unido) Septiembre-Diciembre de 2017 Estancia de Investigación de la Tesis Doctoral Multiscale investigation of nanocellular polymers with synchrotron based tomography (Campaña de Experimentación) Sincrotrón Diamond Light Source, Oxford (Reino Unido) 18-21 de Enero de 2018 Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 34 Otras Publicaciones Científicas E. Solórzano, E. Laguna-Gutierrez S. Pérez-Tamarit, A. Kaestner and M. A. Rodriguez-Perez Polymer foam evolution characterized by time-resolved neutron radiography Colloids and Surfaces A 473 (2015) 46-54 M. Santiago-Calvo, S. Pérez-Tamarit, J. Tirado-Mediavilla, F. Villafañe and M. A. Rodríguez-Pérez Infrared expandometry: A novel methodology to monitor the expansion kinetics of cellular materials produced with exothermic foaming mechanisms Polymer Testing 66 (2018) 383-393 D. Batey, S. Cipiccia, X. Shi, S. Williams, K. Wanelik, A. Wilson, S. Pérez-Tamarit, P. Cimavilla, M. A. Rodríguez-Pérez and C. Rau Coherence Branch at I13, DLS: The Multiscale, Multimodal, Ptycho-tomographic End Station Microscopy and Microanalysis 24 (2018) 40-41 C. Rau, M. Storm, S. Marathe, A. J. Bodey, S. Cipiccia, D. Batey, X. Shi, M-C. Zdora, I. Zanette, S. Pérez-Tamarit, P. Cimavilla, M. A. Rodríguez-Pérez, F. Doring and C. David Multi-Scale Imaging at the Coherence and Imaging Beamline I13 at Diamond Microscopy and Microanalysis 24 (2018) 254-255 V. Bernardo, M. Mugica, S. Perez-Tamarit, B. Notario, C. Jimenez and M. A. Rodriguez-Perez 1 Nanoclay Intercalation During Foaming of Polymeric Nanocomposites Studied in-Situ by Synchrotron X-Ray Diffraction Materials 11 (2018) 2459-2470 Introducción en Castellano 35 Referencias [1] L.J. Gibson, M.F. Ahsby, Cellular Solids: Structure and Properties, Pergamon Press, Oxford, England, 1988. [2] A. Cunningham, N.C. Hilyard, Low Density Cellular Plastics: Physical Basis of Behaviour, Ed. Chapman and Hall, London, 1994. [3] M.A. RodriguezPerez, J.I. Velasco, D. Arencón, O. Almanza, J.A. De Saja, Mechanical characterization of closed-cell polyolefin foams, Journal of Applied Polymer Science, 75 (2000) 156-166. [4] E. Solórzano, M.A. RodriguezPerez, Polymer Foams: Advanced Structural Materials in Transportation, in: D. Lehmhus, M. Busse, A. Herrmann, K. 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López-Gil, J.A. de Saja, Structureproperty relationships of medium-density polypropylene foams, Polymer International, 62 (2013) 1324-1333. [20] O. Almanza, L.O. Arcos y Rábago, M.A. RodriguezPerez, Structure-Property relationships in polyolefin foams, Journal of Macromolecular Science, Part B, 40 (2001) 603-613. [21] M.A. RodriguezPerez, S. Díez-Gutiérrez, J.A. De Saja, The recovery behaviour of crosslinked closed cell polyolefin foams, Polymer Engineering and Science, 38 (1998) 831-837. [22] M.A. Rodriguez-Perez, M. Álvarez-Láinez, J.A. de Saja, Microstructure and physical properties of open-cell polyolefin foams, Journal of Applied Polymer Science, 114 (2009) 11761186. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 36 [23] C. Saiz-Arroyo, Fabricación de materiales celulares mejorados basados en poliolefinas. Relación procesado-composición-estructura-propiedades, PhD Thesis, University of Valladolid, 2012. [24] O. Almanza, M.A. RodriguezPerez, J.A. De Saja, The microstructure of polyethylene foams produced by a nitrogen solution process, Polymer, 42 (2001) 7117-7126. [25] M.A. RodriguezPerez, O. Almanza, J.L. Ruiz-Herrero, J.A. De Saja, The effect of processing on the structure and properties of crosslinked closed cell polyethylene foams, Cellular Polymers, 27 (2008) 179-200. [26] M.A. RodriguezPerez, O. Almanza, J.A. De Saja, Anomalous thickness increase in crosslinked closed cell polyolefin foams during heat treatments, Journal of Applied Polymer Science, 73 (1998) 2825-2835. [27] J.A. Reglero Ruiz, Production and characterization of aluminium foams: Applications in the aeronaurical sector, PhD Thesis, University of Valladolid, 2007. [28] E. Solórzano, Aluminium foams: Foaming process, cellular structure and properties, PhD Thesis, University of Valladolid, 2008. [29] J. Lázaro Nebreda, Optimization of the cellular structure of aluminium foams, PhD Thesis, University of Valladolid, 2014. [30] E. Solórzano, M.A. Rodriguez-Perez, J.A. de Saja, Thermal Conductivity of Cellular Metals Measured by the Transient Plane Sour Method, Advanced Engineering Materials, 10 (2008) 371377. [31] E. Solórzano, M.A. Rodríguez-Perez, J.A. Reglero, J.A. de Saja, Mechanical Behaviour of Internal Reinforced Aluminium Foams, Advanced Engineering Materials, 9 (2007) 955-958. [32] J. Lázaro, E. Laguna-Gutiérrez, E. Solórzano, M.A. Rodríguez-Pérez, Effect of Microstructural Anisotropy of PM Precursors on the Characteristic Expansion of Aluminum Foams, Metallurgical and Materials Transactions B, 44 (2013) 984-991. [33] J. Lázaro, E. Solórzano, J.A. de Saja, M.A. Rodríguez-Pérez, Early anisotropic expansion of aluminium foam precursors, Journal of Materials Science, 48 (2013) 5036-5046. [34] J. Lázaro, E. Solórzano, M.A. Rodríguez Pérez, F. García-Moreno, Pore connectivity of aluminium foams: effect of production parameters, Journal of Materials Science, 50 (2015) 31493163. [35] E. Laguna Gutiérrez, Understanding the foamability of complex polymeric systems by using extensional rheology, PhD Thesis, University of Valladolid, 2016. [36] S. Pardo-Alonso, X-ray imaging applied to the characterization of polymer foams' cellular structure and its evolution, PhD Thesis, University of Valladolid, 2014. [37] E. Solórzano, S. PArdo-Alonso, J.A. de Saja, M.A. Rodriguez-Perez, X-ray radioscopy in-situ studies in thermoplastic polymer foams, Colloids and Surfaces A: Physicochemical and Engineering aspects, 438 (2013) 167-173. [38] E. Solórzano, S. Pardo-Alonso, J.A. de Saja, M.A. Rodríguez-Pérez, Study of aqueous foams evolution by means of X-ray radioscopy, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 438 (2013) 159-166. [39] S. Pardo-Alonso, E. Solórzano, S. Estravís, M.A. Rodriguez-Perez, J.A. de Saja, In situ evidence of the nanoparticle nucleating effect in polyurethane–nanoclay foamed systems, Soft Matter, 8 (2012) 11262. [40] M.M. Bernal, S. Pardo-Alonso, E. Solórzano, M.A. Lopez-Machado, R. Verdejo, M.A. RodriguezPerez, Effect of carbon nanofillers on flexible polyurethane foaming from a chemical and physical perspective, RSC Advances, 4 (2014). [41] E. Solórzano, J. Pinto, S. Pardo, F. Garcia-Moreno, M.A. Rodriguez-Perez, Application of a microfocus X-ray imaging apparatus to the study of cellular polymers, Polymer Testing, 32 (2013) 321-329. [42] M. Santiago-Calvo, S. Pérez-Tamarit, J. Tirado-Mediavilla, F. Villafañe, M.A. RodríguezPérez, Infrared expandometry: A novel methodology to monitor the expansion kinetics of Introducción en Castellano 37 cellular materials produced with exothermic foaming mechanisms, Polymer Testing, 66 (2018) 383-393. [43] E. Solórzano, M. Antunes, C. Saiz-Arroyo, M.A. Rodríguez-Pérez, J.I. Velasco, J.A. de Saja, Optical expandometry: A technique to analyze the expansion kinetics of chemically blown thermoplastic foams, Journal of Applied Polymer Science, 125 (2012) 1059-1067. [44] S. Estravís Sastre, Cellular nanocomposites based on rigid polyurethane and nanoclays: fabrication, characterization and modeling of the mechanical and thermal properties, PhD Thesis, University of Valladolid, 2014. [45] S. Estravís, J. Tirado-Mediavilla, M. Santiago-Calvo, J.L. Ruiz-Herrero, F. Villafañe, M.Á. Rodríguez-Pérez, Rigid polyurethane foams with infused nanoclays: Relationship between cellular structure and thermal conductivity, European Polymer Journal, 80 (2016) 1-15. [46] M. Santiago-Calvo, V. Blasco, C. Ruiz, R. París, F. Villafañe, M.Á. Rodríguez-Pérez, Synthesis, characterization and physical properties of rigid polyurethane foams prepared with poly(propylene oxide) polyols containing graphene oxide, European Polymer Journal, 97 (2017) 230-240. [47] J. Escudero Arconada, Polyolefin based cellular materials. Development of new production routes and optimization of barrier and mechanical properties by the addition of nanoclays, PhD Thesis, University of Valladolid, 2016. [48] S. Román Lorza, Production and characterization of flame retardant halogen-free polyolefin based cellular materials, PhD Thesis, University of Valladolid, 2010. [49] F. Silva-Bellucci, Preparation and characterization of multifunctional nanocomposites by adding paramagnetic ferroelectric nanoparticles to natural rubber films, PhD Thesis, University of Valladolid, Sao Paulo State University, 2013. [50] J. Lobos Martín, Improving the stiffness and strength of porous materials by enhancement of the matrix microstructure and cellular morphology, PhD Thesis, University of Valladolid, 2013. [51] M. Dumon, J.A. Reglero Ruiz, J. Pinto, M.A. RodriguezPerez, M.A. Tallon, J.M. Pedros, M. Cloutet, P. Viot, Block copolymer-assisted microcellular supercritical CO2 foaming of Polymers and Blends, Cellular Polymers, 31 (2012) 207-221. [52] J.A. Reglero Ruiz, C. Saiz-Arroyo, M. Dumon, M.A. Rodriguez-Perez, L. Gonzalez, Production, cellular structure and thermal conductivity of microcellular (methyl methacrylate)- (butyl acrylate)-(methyl methacrylate) triblock copolymers, Polymer International, 60 (2011) 146-152. [53] D. Velasco Nieto, Development of cellular biomaterials based on EVA, PLA and PHB, production and characterization, PhD Thesis, University of Valladolid, 2017. [54] A. López Gil, Development of environmentally friendly cellular polymers for packing and structural applications. Study of the relationship cellular structure-mechanical properties, PhD Thesis, University of Valladolid, 2016. [55] H. Ventura Casellas, Development of new lightweight green composites reinforced with nonwoven structures of flax fibers, PhD Thesis, Polytechnic University of Catalonioa and University of Valladolid, 2017. [56] L. Oliveira-Salmazo, Foaming kinetics and cellular structure control of materials based on natural rubber and polyolefins, PhD Thesis, University of Valladolid and Sao Paulo State University, 2015. [57] M.A. Rodriguez-Perez, R.D. Simoes, S. Roman-Lorza, M. Alvarez-Lainez, C. MontoyaMesa, C.J.L. Constantino, J.A. de Saja, Foaming of EVA/starch blends: Characterization of the structure, physical properties, and biodegradability, Polymer Engineering & Science, 52 (2012) 62-70. [58] M.A. Rodriguez-Perez, R.D. Simoes, C.J.L. Constantino, J.A. de Saja, Structure and physical properties of EVA/starch precursor materials for foaming applications, Journal of Applied Polymer Science, 121 (2011) 2324-2330. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 38 [59] A. Lopez-Gil, F. Silva-Bellucci, D. Velasco, M. Ardanuy, M.A. Rodriguez-Perez, Cellular structure and mechanical properties of starch-based foamed blocks reinforced with natural fibers and produced by microwave heating, Industrial Crops and Products, 66 (2015) 194-205. [60] L. Oliveira-Salmazo, A. Lopez-Gil, F. Silva-Bellucci, A.E. Job, M.A. Rodriguez-Perez, Natural rubber foams with anisotropic cellular structures: Mechanical properties and modeling, Industrial Crops and Products, 80 (2016) 26-35. [61] J. Pinto, Fabrication and characterization of nanocellular polymeric materials from nanostructured polymers, PhD Thesis, University of Valladolid and University of Bordeaux, 2014. [62] B. Notario Collado, Fabrication and characterization of the physical properties of nanocellular polymers: The transition from the micro to the nanoscale, PhD Thesis, University of Valladolid, 2016. [63] B. Notario, J. Pinto, E. Solorzano, J.A. de Saja, M. Dumon, M.A. Rodríguez-Pérez, Experimental validation of the Knudsen effect in nanocellular polymeric foams, Polymer, 56 (2015) 57-67. [64] B. Notario, J. Pinto, M.A. Rodríguez-Pérez, Towards a new generation of polymeric foams: PMMA nanocellular foams with enhanced physical properties, Polymer, 63 (2015) 116-126. [65] V. Bernardo, J. Martín-de León, E. Laguna-Gutiérrez, M.Á. Rodríguez-Pérez, PMMAsepiolite nanocomposites as new promising materials for the production of nanocellular polymers, European Polymer Journal, 96 (2017) 10-26. [66] J. Pinto, B. Notario, R. Verdejo, M. Dumon, S. Costeux, M.A. Rodriguez-Perez, Molecular confinement of solid and gaseous phases of self-standing bulk nanoporous polymers inducing enhanced and unexpected physical properties, Polymer, 113 (2017) 27-33. [67] J. Martín-de León, V. Bernardo, M. Rodríguez-Pérez, Low Density Nanocellular Polymers Based on PMMA Produced by Gas Dissolution Foaming: Fabrication and Cellular Structure Characterization, Polymers, 8 (2016) 265. [68] S. Pardo-Alonso, E. Solórzano, L. Brabant, P. Vanderniepen, M. Dierick, L. Van Hoorebeke, M.A. RodriguezPerez, 3D Analysis of the progressive modification of the cellular architecture in polyurethane nanocomposite foams via X-ray microtomography, European Polymer Journal, 49 (2013) 999-1006. [69] M.D. Montminy, A.R. Tannenbaum, C.W. Macosko, The 3D structure of real polymer foams, Journal of colloid and interface science, 280 (2004) 202-211. [70] Y. Ma, R. Pyrz, M.A. Rodriguez-Perez, J. Escudero, J.C. Rauhe, X. Su, X-ray microtomographic study of nanoclay-polypropylene foams, Cellular Polymers, 30 (2011) 95-110. [71] J. Lambert, I. Cantat, R. Delannay, A. Renault, F. Graner, J.A. Glazier, I. Veretennikov, P. Cloetens, Extraction of relevant physical parameters from 3D images of foams obtained by Xray tomography, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 263 (2005) 295-302. [72] A. Elmoutaouakkil, G. Fuchs, P. Bergounhon, F. Peyrin, Three-dimensional quantitative analysis of polymer foams from synchrotron radiation x-ray microtomography, Journal of Physics D: Applied Physics, 36 (2003) A37-A43. [73] I. Cantat, S. Cohen-Addad, F. Elias, F. Graner, R. Höhler, O. Pitois, F. Rouyer, A. SaintJalmes, Foams Structure and Dynamics, Oxford University Press2013. [74] B. Notario, J. Pinto, M.A. Rodriguez-Perez, Nanoporous polymeric materials: A new class of materials with enhanced properties, Progress in Materials Science, 78-79 (2016) 93-139. Chapter 1 Introduction 1. Introduction 41 Cellular materials are biphasic structures in which a continuous or discontinuous gas phase is dispersed in a continuous liquid or solid phase [1]. These materials have focused a lot of attention in recent decades due to several interesting factors. The presence of the gas phase within the structure provides density reduction in comparison to the solids [2]. In addition, cellular materials extend the range of physical properties of the respective solid precursors (as shown in Figure 1-1) thus expanding the application capabilities of these materials. Figure 1-1. Comparative properties of solid and cellular materials. They exhibit extremely low thermal transport properties, as for instance a low thermal conductivity, high energy absorption capability as well as excellent stiffness and strength and depending on their cellular structure excellent acoustic absorption properties. In fact, some materials in nature present an internal cellular structure with impressive properties such as cork, wood, coral or bone. The man-made cellular Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scat tering 48 1.3 Challenges Various technical aspects were proposed with the aim of achieving the objectives previously described: o To design, adapt and optimize the tomography system at CellMat Laboratory to obtain tomographic reconstructions with up to 2.5 μm effective pixel size with optimum contrast for low density cellular polymers. o To design and build a specific system for the characterization of cellular polymers of a wide range of characteristics (density, cell size) by means of Light Scattering. Furthermore, during this PhD thesis it has been necessary to overcome several methodological aspects: o To develop novel methodologies based on image analysis to obtain a detailed description of the cellular structure of cellular polymers. In particular, we have focused our attention on non well-studied parameters of the solid phase of these materials such as the repartition of material throughout the solid skeleton, the solid material thickness distribution and the quantification of the corrugation of the structure. o To develop a novel experimental methodology to perform and analyse the Light Scattering experiments in solid cellular polymers. o To select a suitable collection of conventional cellular polymers based on PU, PE and PS that allow verifying the reliability of the developed techniques and methodologies. Last but not least, from a scientific perspective, the main topics to highlight are: o To study the morphology of cellular polymers structure in 3D by means of X-ray μ-CT. These materials are low X-ray absorbing materials with only 2-5% of solid volume in the material. Therefore, the X-ray absorption is reduced to the minimum compromising the contrast in the final reconstructed volumes. A careful 1. Introduction 49 selection of the experiment parameters has served for the contrast optimization on the X-ray tomography performed experiments. o To determine the influence of novel structural descriptors of the solid phase on mechanical and thermal properties of cellular polymers. o To develop a model to describe Light Scattering in solid cellular polymers including the key characteristics of cellular polymers. o To evaluate how the particularities of the foaming process such as the presence/absence of external nucleating agents may alter the structure of the cellular materials while foaming. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scat tering 50 1.4 Main Novelties The main novelties of this thesis over current scientific literature could be summarized as follows: o The establishment of novel image analysis protocols for the quantification of features corresponding to the solid phase of cellular materials by means of X-ray tomography reaching a global description of the biphasic structure of cellular materials. o The study of the influence of solid phase corrugation in both collapse stress and thermal expansion coefficient of flexible cellular polymers. o The visualization and quantification of cell nucleation and growth in cellular polymers in 3D by using real time synchrotron X-ray Tomography. o The development of both a novel methodology and theoretical model to enable the characterization of solid cellular polymers by means of Light Scattering methodologies with great results concerning the measurement of cell size and anisotropy. o The 3D structure visualization of non-conventional/nanocellular polymers for the first time by using synchrotron based X-ray nanotomography techniques. o The application of Light Scattering technique to nanocellular polymers establishing the first evidence about the possibility of manufacturing nanocellular polymers transparent to visible light. 1. Introduction 51 1.5 Structure of this thesis This thesis is written in the format of a compendium of publications. The presented experimental results are supported by 10 scientific articles, 4 of them already published and the rest pending of publication (table 1-1). Communications in national and international conferences (table 1-2) and research projects developed during the time of this investigation (table 1-3) are also addressed. Additional activities developed during this investigation such as other scientific publications or stays at foreign research facilities are summarized (table 1-4). The structure of this thesis is developed over eight chapters and one annex. After the two first introductory chapters, the following five are divided in three blocks (X-ray Tomography, Light Scattering and application of both techniques on nonconventional ocellular polymers) with pyramidal structure (Figure 1-4). Finally, the conclusions of the investigation are presented as the eighth and last chapter of this thesis. Figure 1-4. Schematic view of the structure of this thesis. Moreover, this thesis fulfils the necessary requirements to be accredited with the International Mention. Chapter 1 introduces the main insights about this investigation as well as the scientific framework and the main objectives and milestones. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scat tering 52 Chapter 2 deals with a revision of the main concepts related to the structure of cellular materials introducing a new multicomponent model of the cellular structure, including the definition of several new advanced descriptors. In addition, basic ideas about the involved mechanisms (cell generation and degeneration processes) occurring during foaming are addressed. Chapter 3 provides a general overview of the basic concepts of X-ray imaging focused on the case of X-ray μ-CT. The different steps and key factors to obtain optimized tomographic results are presented. Furthermore, a brief description of the different Xray facilities in which the experimental work of this thesis has been carried out is included as well as the employed image analysis softwares and processing protocols. Chapter 4 presents the main results of this thesis concerning X-ray μ-CT. Firstly, a detailed tomographic characterization of two sets of cellular polymers combining two sets of tomographies with different spatial resolutions is presented (one paper). After that, the thermo-mechanical properties of one of the precedents cellular polymers collection have been suitably modelled including the effect of the corrugation in the structure (one paper). Finally, the foaming process of two PU systems is studied by means of time–resolved X-ray μ-CT (one paper). Chapter 5 includes the development of Light Scattering theory for the study of cellular materials, discussing the basis of the existing theories of scattering (Rayleigh, Mie) and the deduction/approach to aqueous system solution. Finally, the practical aspects of implementation that have been overcome for the final application in solid cellular polymers are addressed. Chapter 6 represents then the experimental process followed in this investigation to reach the final result about the Light Scattering as an effective tool for the characterization of solid cellular polymers. To this end, firstly the Light Scattering equation is solved numerically due to its own particularities (one paper) to reach finally the modification of the model that allows the characterization of solid cellular polymers (one paper). Finally, the results concerning the cellular anisotropy measurements by this technique are addressed (one paper). 1. Introduction 53 Chapter 7 summarizes the first results concerning both X-ray nano-Tomography (nCT) novel techniques (one paper) and Light Scattering application in nonconventional/nanocellular polymers (one paper). Finally, chapter 8 summarizes the most remarkable conclusions of this investigation and it proposes topics for further work. There is also one annex including other practical uses of X-ray imaging techniques (two papers). Figure 1-5 shows the summary of the chapters and scientific publications contributing to this investigation. Figure 1-5. Summary of the chapters and scientific publications contributing to this thesis. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scat tering 54 Table 1-1 No. Scientific Publications Ch. 1 S. Pérez-Tamarit, E. Solórzano, A. Hilger, I. Manke and M. A. Rodriguez-Perez 4 Multi-scale tomographic analysis of polymeric foams: A detailed structural analysis European Polymer Journal 109 (2018) 169-178 2 S. Pérez-Tamarit, E. Solórzano, A. Hilger, I. Manke and M. A. Rodriguez-Perez 4 Effect of solid phase corrugation on the thermo-mechanical properties of low density flexible cellular polymers Materials and Design 161 (2019) 106-113 3 S. Pérez-Tamarit, E. Solórzano, R. Mokso and M. A. Rodríguez-Pérez 4 In-situ understanding of pore nucleation and growth in polyurethane foams by using real-time synchrotron X-ray tomography Physical Review Letters (submitted) 4 S. Pérez-Tamarit, E. Solórzano and M. A. Rodriguez-Perez 6 Efficient prediction of cell size in solid polymeric foams by numerically solving the diffusion approximation of light scattering equation Colloid and Surfaces A 534 (2017) 130-137 5 S. Pérez-Tamarit, E. Solórzano and M. A. Rodriguez-Perez 6 Semi-empirical modified light scattering model for cell size characterization of solid cellular polymers Colloid and Surfaces A (submitted) 6 S. Pérez-Tamarit, E. Solórzano and M. A. Rodriguez-Perez 6 Light transmission as a novel tool for the characterization of cell anisotropy in cellular polymers Materials Letters (submitted) 7 S. Pérez-Tamarit, P. Cimavilla, J. Martín-de León, V. Bernardo, E. Solórzano, D. Batey, C. Rau and M. A. Rodriguez-Perez 7 First 3D inspection of non-conventional cellular polymers by means of X-ray ptycho-tomography Macromolecular Communications (submitted) 8 S. Pérez-Tamarit, B. Notario, E. Solórzano and M. A. Rodriguez-Perez 7 Light transmission in nanocellular polymers: Are semi-transparent cellular polymers possible? Materials Letters 210 (2018) 39-41 9 S.Pérez-Tamarit, E.Solórzano, A.Kaestner and M.A. Rodriguez-Perez Annex Fast Fourier Transform procedures applied to X-ray transmission images Microscopy and Microanalysis (submitted) 10 S. Pérez-Tamarit, E. Solórzano, E. Laguna-Gutierrez, A. Hilger, I. Manke and M. A. Rodriguez-Perez Annex Novel quantification methods of fillers dispersion in polymer composites based on high resolution synchrotron X-ray μ-CT Polymer (submitted) 1. Introduction 55 Table 1-2 Scientific Communications in Conferences S. Pérez Tamarit, B.Notario, E.Solórzano, M.A. Rodriguez-Perez Cell size determination by means of light scattering methodologies in micro and nanoporous foams (ORAL) VII European School on Molecular Nanoscience (ESMolNa 2014), Valencia (Spain), October 2014 S. Pérez-Tamarit, E. Solórzano, M. A. Rodriguez-Perez, A. Salonen and W. Drenkham Modified light scattering models in solid polymeric foams (ORAL) X European Conference on Foams and Applications (EuFoam 2014), Thessaloniki (Greece), July 2014 S. Pérez-Tamarit, E. Solórzano, A. Kaestner and M. A. Rodriguez-Perez Cell size determination by means of FFT in X-ray transmission images (POSTER) X European Conference on Foams and Applications (EuFoam 2014), Thessaloniki (Greece), July 2014 E. Solórzano, E. Laguna-Gutierrez S. Pérez-Tamarit, A. Kaestner, J. Pinto and M. A. Rodriguez-Perez Polymer foam evolution characterized by time-resolved neutron radiography (ORAL) X European Conference on Foams and Applications (EuFoam 2014), Thessaloniki (Greece), July 2014 S. Pérez-Tamarit, E. Solórzano, A. Hilger, I. Manke and M. A. Rodriguez-Perez Solid-phase structural characterization in polymeric foams: Synchrotron micro-CT in the limits of resolution (ORAL) II International Conference on Tomography of Materials and Structures (ICTMS 2015), Quebec city (Canada) July 2015 J. Martín-de León, V. Bernardo, S. Pérez-Tamarit, E. Solórzano and M. A. Rodriguez-Perez Nanocellular foams fabrication methods by gas dissolution process (POSTER) IX International Conference on Porous Metals and Metallic Foams (Metfoam 2015), Barcelona (Spain), September 2015 V. Bernardo, J. Martín-de León, S. Pérez-Tamarit, E. Solórzano and M. A. Rodriguez-Perez Cellular structure, properties and applications of nanoporous materials (POSTER) IX International Conference on Porous Metals and Metallic Foams (Metfoam 2015), Barcelona (Spain), September 2015 S. Pérez-Tamarit, V. Bernardo, J. Martín-de León, E. Solórzano and M. A. Rodriguez-Perez Characterization of the solid phase of cellular materials by means of x-ray micro-CT (POSTER) IX International Conference on Porous Metals and Metallic Foams (Metfoam 2015), Barcelona (Spain), September 2015 S. Pérez-Tamarit, E. Solórzano and M. A. Rodriguez-Perez A numerical approach for solving the light scattering model applied to solid polymeric foams (ORAL) XI European Conference on Foams and Applications (EuFoam 2016), Dublin (Ireland), July 2016 S. Pérez-Tamarit, B. Notario, E. Solórzano and M. A. Rodriguez-Perez Towards transparent nano-cellular polymeric foams (POSTER) XI European Conference on Foams and Applications (EuFoam 2016), Dublin (Ireland), July 2016 Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scat tering 56 S. Pérez-Tamarit, E. Solórzano, E. Laguna-Gutierrez, B. Notario, A. Hilger, I. Manke and M. A. Rodriguez-Perez Characterization of fillers dispersion in composites and nanocomposites by means of synchrotron X-ray microtomography (ORAL) XIV Reunión del Grupo Especializado de Polímeros (GEP 2016), Burgos (Spain) September 2016 S. Pérez-Tamarit, E. Solórzano, S. Pardo-Alonso, R. Mokso and M. A. Rodriguez-Perez Pore Nucleation and growth in cellular polymers analysed by time resolved synchrotron μ-CT (ORAL) III International Conference on Tomography of Materials and Structures (ICTMS 2017), Lund (Sweden) June 2017 S. Pérez-Tamarit, E. Solórzano, E. Laguna-Gutierrez, B. Notario, A. Hilger, I. Manke and M. A. Rodriguez-Perez Novel quantification methods of fillers dispersion in polymer composites and nanocomposites based on high resolution synchrotron X-ray μ-CT (POSTER) III International Conference on Tomography of Materials and Structures (ICTMS 2017), Lund (Sweden) June 2017 S. Pérez-Tamarit, E. Solórzano, A. Hilger, I. Manke and M. A. Rodriguez-Perez Multiscale analysis of cellular polymers (POSTER) VIII Conference on Industrial Computed Tomography (iCT 2018), Wels (Austria) February 2018 S. Pérez-Tamarit, E. Solórzano, A. Hilger, I. Manke and M. A. Rodriguez-Perez Determination of solid phase corrugation ratio of polymeric foams (POSTER) VIII Conference on Industrial Computed Tomography (iCT 2018), Wels (Austria) February 2018 S. Pérez-Tamarit, E. Solórzano and M. A. Rodriguez-Perez Characterization of the cellular architecture of solid polymeric foams by means of optical light transmission measurements (ORAL) XII European Conference on Foams and Applications (EuFoam 2018), Liege (Belgium), July 2018 S. Pérez-Tamarit, P. Cimavilla, J. Martín-de León, V. Bernardo , E. Solórzano and M. A. Rodriguez-Perez X-ray tomographic homogeneity inspection in nanocellular polymers produced using different foaming conditions (POSTER) XII European Conference on Foams and Applications (EuFoam 2018), Liege (Belgium), July 2018 P. Cimavilla, S. Pérez-Tamarit, M. Santiago-Calvo and M. A. Rodriguez-Perez In-situ physicochemical analysis of the foaming process of aerogel-rigid polyurethane composite foams (ORAL) XII European Conference on Foams and Applications (EuFoam 2018), Liege (Belgium), July 2018 P. Cimavilla, S. Pérez-Tamarit, E. Solórzano, A. Hilger, I. Manke and M. A. Rodriguez-Perez Novel subresolution tomographic methods for quantifying fraction of mass in Plateau borders of solid polymeric foams (POSTER) XII European Conference on Foams and Applications (EuFoam 2018), Liege (Belgium), July 2018 D. Batey, S. Cipiccia, X. Shi, S. Williams, K. Wanelik, A. Wilson, S. Pérez-Tamarit, P. Cimavilla, M. A. Rodríguez-Pérez and C. Rau Coherence Branch at I13, DLS: The Multiscale, Multimodal, Ptycho-tomographic End Station (ORAL) XIV International Conference on X-Ray Microscopy (XRM 2018), Saskatoon (Canada), August 2018 1. Introduction 57 C. Rau, M. Storm, S. Marathe, A. J. Bodey, S. Cipiccia, D. Batey, X. Shi, M-C. Zdora, I. Zanette, S. Pérez-Tamarit, P. Cimavilla, M. A. Rodríguez-Pérez, F. Doring and C. David Multi-Scale Imaging at the Coherence and Imaging Beamline I13 at Diamond (ORAL) XIV International Conference on X-Ray Microscopy (XRM 2018), Saskatoon (Canada), August 2018 V. Bernardo, J. Martín-de León, F. Van Loock, N. A. Fleck, P. Cimavilla, S. Pérez-Tamarit and M. A. RodriguezPerez Nanocellular polymers based on PMMA/sepiolite nanocomposites: characterization of the mechanical behaviour (POSTER) V Cellular Materials (CellMat 2018), Bad Staffelstein (Germany), October 2018 Table 1-3 Research Projects Desarrollo y fabricación en continuo de aislantes térmicos avanzados basados en polímeros nanocelulares Neadfoam: Aditivos innovadores para espumas con mejores prestaciones de aislamiento térmico y comportamiento frente al fuego Desarrollo de bandejas de espuma de poliestireno extruido con baja densidad y propiedades mejoradas Table 1-4 Stays in Other Research Facilities XXXIV Berlin School on Neutron Scattering Helmholtz Zentrum, Berlin (Germany) 13th-21st March 2014 Synchrotron tomography of polymer foams: in the limits of resolution (Experimentation campaign) BESSY II Synchrotron, Berlín (Germany) 5th-8th June 2014 In-situ characterization of the foaming behaviour and exfoliation of nanoclays in nanocomposites using combined white-beam X-ray radioscopy & diffraction (Experimentation campaign) BESSY II Synchrotron, Berlín (Germany) 7th-10th May 2015 In-situ study of nanoclay exfoliation of polymeric nanocomposites during foaming with azodicarbonamide (Experimentation campaign) BESSY II Synchrotron, Berlín (Germany) 3rd-9th October 2016 Multiscale investigation of nanocellular polymers with synchrotron based tomography Diamond Light Source, Oxford (United Kingdom) September-December 2017 PhD Research Stay Multiscale investigation of nanocellular polymers with synchrotron based tomography (Experimentation campaign) Diamond Light Source, Oxford (United Kingdom) 18th-21st January 2018 2. Basic Concepts on Cellular Materials 65 This chapter describes the basic concepts related to the structural description of cellular materials, as well as the main notions about foaming mechanisms required to understand the contents included in the following chapters. In addition, the materials involved in this investigation are presented as well as a description of the foaming process to produce them. 2.1 Cellular structure Cellular materials are structures constituted by two phases, a continuous solid (or liquid) skeleton and a continuous or discontinuous gas phase dispersed on it [1-3]. The solid phase is generally called matrix. It is possible to find cellular materials based on a large variety of matrixes such as polymers, metals, wood, etc… According to the particular structural features cellular materials can be classified in three groups: lattice materials, engineered materials and foams. This investigation is focused on foams and more precisely on polymeric foams since they are one of the main topics covered by the research carried out at CellMat. These cellular materials are produced (or foamed) from the liquid/softened state using a blowing agent that produces cellular structures with a completely stochastic morphology and topology. 2.1.1 μ-structure model It is possible to distinguish different elements in the two mentioned phases (Figure 21). The main component characterizing any kind of cellular material are the cells, also called pores or bubbles indistinctively that are the principal constituent of the gas phase when the density is low. Cells could be geometrically described according to a polyhedral modelling. On the other hand, the topology of the solid phase of low density cellular materials permits distinguishing two main constituents, cell walls (or films) and struts (or Plateau borders). Cell walls are the polyhedron faces separating two contiguous cells whereas vertexes and edges together form the cellular struts, considered the main skeleton of the cellular structure. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 66 Figure 2-1. Conventional model of cellular structures. As it is well known, physical properties of cellular materials such as thermal conductivity, stiffness, permeability, acoustic absorption strongly depends on microstructure [1-3]. However, a description of gaseous phase is not enough to explain many of these properties. For this reason, the characterization of the features corresponding to the solid phase, typically not considered nowadays in the literature, is of vital importance. For example, obviating the influence of presence/absence of cell walls, the mechanical performance of such kind of materials for a fixed relative density is strongly dominated by the cell wall thickness. The thicker is the cell wall thickness, the higher is the material stiffness. The first and principal feature of cellular materials is their density [1-3]. The introduction of gas into the solid matrix leads to a weight reduction and thus a density reduction. However, in order to eliminate the influence of the matrix density it is more commonly used the so-called relative density (ρr) defined as the ratio between the cellular material density (ρf) and the density of the solid precursor (ρs) (Equation 21). It is also called solid fraction depending on the aggregate state of the matrix. 2. Basic Concepts on Cellular Materials 67 Equation 2-1 According to its relative density, cellular materials can be classified in three great groups: low density (ρr < 0.3), medium density (0.3 ≤ ρr ≤ 0.6) and high density cellular materials (ρr > 0.6). Linked to relative density, porosity (ψ) or void fraction is defined as the fraction of the volume of voids over the total volume of material (Equation 2-2). Equation 2-2 Another parameter related with relative density and normally employed when dealing with cellular materials is the expansion ratio (ER) calculated as the inverse value of the relative density (Equation 2-3). It indicates the volume ratio reached by the foamed materials, or more precisely, how many times the precursor material has been expanded during foaming. Equation 2-3 2.1.2 Microscopic descriptors This section deals with the description of the main descriptors concerning the microstructure of cellular materials. As these materials are biphasic, in this section the descriptors are classified accordingly. o Gaseous Phase The average cell size (ϕ) is one of the most representative parameters of the cellular structure. A lot of definitions of this parameter are possible but the most typical refers to mean diameter of the corresponding cell. In fact, another classification of cellular materials can be addressed regarding their mean cell size (Figure 2-2). Nanocellular materials are those with cell size lower than 0.3 μm, sub-microcellular materials are characterized by cell sizes ranging 0.3-1 μm, Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 68 microcellular materials are those with cell sizes between 1-10 μm and finally conventional cellular materials have cell sizes higher than 10 μm. Figure 2-2. Schematic view of cell size range classification of cellular materials. In practice, two main procedures are considered in order to determine this parameter. The first one consists on calculating the size of the three main axis of the equivalent ellipsoid. The average value of these three values is considered as the mean cell size. On the other hand, the mean cell size calculated as the equivalent diameter is that one obtained from an equivalent sphere containing the same volume as the considered cell. In fact, the two values are identical in spherical pores. Cell size is a key parameter for properties such as thermal conductivity, toughness and ultimate mechanical properties. For this reason, some of the most important research topics nowadays directly focus on reducing the cell size to the micro-scale (microcellular materials) and nanoscale (sub-microcellular and nanocellular materials). Finally, it is important to mention that the mean cell size is not enough to accurately characterize the gaseous phase of cellular materials. Cell size distribution can also strongly alter the physical properties since the resulting cellular structures can be homogeneous or highly inhomogeneous even if the average value of cell size is not modified (Figure 2-3). The influence of the cellular homogeneity on the physical properties of a cellular material is an analysed topic. In general, it has been found that non-uniform distribution of the cell sizes has in general a detrimental effect on the 2. Basic Concepts on Cellular Materials 69 properties of the material [2]. In this case the solid mass is not homogenously distributed which favours the appearance of cracks in the weaker areas [1]. Figure 2-3. Micrographs of two cellular polymers with homogeneous –leftand inhomogeneous –rightcellular structure. The standard deviation (SD) (Equation 2-4) or most recently the normalised standard deviation (NSD) (Equation 2-5), which permits eliminating the effect of mean cell size, are the numerical parameters that should be taken into account when comparing different structures [4]. √∑( ) Equation 2-4 ⁄ Equation 2-5 Where n is the total number of cells, ϕi is the diameter of each cell, and ϕ is the mean cell size. The smaller is the value of NSD, the more homogeneous is the cellular structure. Cell density (Nv) is defined as the number of pores per unit volume and is typically calculated using both mean cell size and relative density (Equation 2-6). ( ) Equation 2-6 However, in order to compare two cellular materials with different relative densities is more adequate to introduce the cell nucleation density (N0) which is closely related with cell density (Equation 2-7). Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 70 Equation 2-7 Due to the cubic dependence of cell density with mean cell size, reducing cell size dramatically increases cell density if the relative density remains constant (Figure 2-4). Focusing on the average cell size classification of cellular materials shown before, cell density is around 1014, 1011, 108 and 106 cells-3 for nanocellular, sub-microcellular, microcellular and conventional materials respectively [5-7]. Cell density is one of the most representative parameters of any cellular structure since it combines the influence of both cell size and relative density. In addition, it is crucial to understand the cellular structure evolution during the foaming processes. In our case, cell density is directly obtained in X-ray Tomography due to the 3D outputs of this technique. Figure 2-4. Tomographic 3D rendering of two cellular materials with similar relative density but different cell density. In order to justify the directionality of physical properties, cell anisotropy (Ri) is typically considered. It is defined as the mean cell size in that direction divided by the average cell size in the perpendicular plane (Equation 2-8). However, depending on processing peculiarities, cells are typically elongated along preferential directions (Figure 2-5) [8, 9] and therefore it is useful to identify some of them with the typical directions of a Cartesian reference system [1, 2, 10]. On the other hand, the pore orientation is typically described considering the two angles that form the main axis of the equivalent ellipsoid with the reference system in the 3D space. 2. Basic Concepts on Cellular Materials 71 Figure 2-5. Tomographic slices showing a slightly anisotropic cellular PS in the Y direction and an isotropic cellular PE. Equation 2-8 The topological information of the cellular structure is provided by the coordination number (ni). It indicates the average number of neighbouring cells, that is close connected wit the cell packing and cell shape in cellular materials. At this respect, a lot of possible cell topologies are possible in 3D space from tetrahedrons, triangular prisms, cubes, octahedrons, pentagonal dodecahedrons, etc… [1]. However, only few packing geometries are admissible for the minimisation of the energy. In 1873 Plateau deduced that the rhombic dodecahedron, polyhedron containing 12 faces with rhombic shape, was the most energy efficient single unit. Few years later (1887) Kelvin minimizes further the involved energy by using the tetrakaidekahedron cells (14 faces, 6 quadrilateral and 8 hexagonal), but with slightly curved surfaces [11]. In 1994 Weaire and Phelan minimized even more this energy by employing 14-sided polyhedrons made up of 12 curved pentagonal and 2 hexagonal plane faces [12]. Coordination number is, in addition, linked with other descriptors of the cellular structure like cell size distribution. For example, a wider cell size distribution should be linked to a higher average coordination number since large cells will be surrounded by many smaller neighbours. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 72 Open cell content (OC) is defined as the gas volume fraction of interconnected cells in the material. It is calculated typically using gas pycnometry that allows determining the displaced volume of the sample (Vp) considering the geometric volume of the sample (V) and also the volume of cells in the surface of the sample (Vs) (ASTM 622610, Equation 2-9) [13]. The grade of this parameter (ranging 0-1) allows establishing the classification of cellular materials between purely open and closed-cell materials (Figure 2-6). Figure 2-6. 3D rendering of two cellular materials. Closed cell cellular epoxy –leftand open cell cellular PU –right-. ( ) Equation 2-9 Closed cell materials are characterized by the absence of interconnected cells and therefore open cell content is 0 and in open cell materials the open cell content is close to 1. In this case, it is important to mention that the interconnection of cells is possible either by the total absence of cell walls in the structure or by the presence of holes in the cell walls. In fact, size, concentration and shape of holes in the cellular structure have a influence on several physical properties of cellular materials. However, gas pycnometry is not able to discriminate between these two situations, becoming tomography one of the only possible solutions for the characterization of the holes in the cell walls. 2. Basic Concepts on Cellular Materials 73 o Solid Phase The principal solid phase descriptor of cellular materials is the structure thickness. Several algorithms have been developed nowadays for the quantification of thickness in 3D [14]. One of the most used is called Local Thickness Algorithm [15-17], that assign to each point of the entity under study the diameter of the greatest sphere entirely enclosed within the entity and centred in the selected point. Once the algorithm is implemented, it is possible to obtain material thickness distributions on the analysed volume (Figure 2-7). For low density cellular materials, the typical material thickness distribution contains two differentiated peaks corresponding to the two mentioned parts of the solid phase, struts (thicker part peak) and walls (thinner part peak). Furthermore, depending on the characteristics of the cellular architecture the two peaks can be well separated or highly overlapped. Figure 2-7. 3D rendering of a cell of a PU foam showing the calculated material thickness along the structure –leftand the resulting material thickness distribution –right-. Analysing the materials thickness distribution it is possible to calculate the mean cell wall thickness (δ), the strut thickness (ξ) and the average thickness of the structure (t). All these thicknesses are crucial to understand physical properties of cellular materials such as stiffness [18] or thermal conductivity [19]. A detailed characterization of these non-well studied features has been carried out in low density cellular polymers during this research by using high resolution X-ray Tomography (Chapter 4). Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 80 2.3 Materials In this section, a description of the materials selected for this investigation as well as the foaming process to produce them is addressed. Three different types of cellular polymers based on different matrices (PU, PE and PS) were considered whereas nanocellular polymers based on PMMA as solid matrix were also used. In addition, the characteristic of the selected nanosilica (Aerosil R812) to evaluate the effect of nucleating agents in the foaming process are finally addressed. 2.3.1 Polyurethane (PU) and Reactive Foaming Polyurethane (PU) foams are the most extensively used and well-known cellular polymers, representing more than half of the global market of foams [42]. These materials are produced by the chemical reaction of two main components, polyol and isocyanate, being the main example of the so-called reactive foaming process [2, 43]. In this foaming process, two simultaneous reactions take place, gelling and blowing reactions. Figure 2-11 shows the typical reaction for water-blown PU foams, in which water is used as blowing agent. A mixing process of the three components, in which the main parameters are stirring time and rate (rpm), is required to promote both reactions. In the gelling reaction urethane groups are created due to the isocyanate (R-N=C=O) and hydroxyl (-OH) groups present on the polyol component. On the other hand, blowing reaction forms carbamic acid from isocyanate (R-N=C=O) and water (H2O). This acid decomposes in amine (RNH2) and CO2 thus creating the cells. Furthermore, the created amine is able to react with isocyanate resulting in urea groups [44]. 2. Basic Concepts on Cellular Materials 81 Figure 2-11. Chemical reactions involved in the reactive foaming of PU. The structure of PU foams is the result of these two chemical reactions. These materials own pentagonal dodecahedron shape cells. In addition, depending on the conditions of the foaming process (free or in mould) different cells anisotropy could appear. From the point of view of the solid phase, due to semisolid material drainage prior the gelling of the structure, PU foams concentrate a high amount of solid material in the struts, resulting in high values of fs (>0.6) and therefore very thin cell walls (1-2 μm) (Figure 2-12). Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 82 Figure 2-12. Tomographic slice –leftand separation in walls and struts –rightof a PU foam with fs of 0.7. For this investigation a commercial PU formulation from BASF was selected (Elastopor® H). The polyol component, Elastopor® H 1501/1 (1.07 gcm-3), is a mixture of polyols, catalysts, stabilizers and water. The isocyanate, IsoPMDI 92140 (1.23 gcm-3), is a diphenylmethane diisocyanate. By using four different commercial polyol blends with different amounts of water samples with different densities were produced (30100 kgm-3). In addition, using different mixing conditions different cell sizes were obtained (350-800 μm). As a result, a complete chart of materials with independent density and cell sizes were manufactured and used for developing this investigation (Table 2-1). 2. Basic Concepts on Cellular Materials 83 Table 2-1. List of PU samples produced during this research using 4 different formulations and 4 different mixing conditions (16 samples in total). Formulation 1 Density ~ 30 kg/m3 Formulation 2 Density ~ 55 kg/m3 Formulation 3 Density ~ 70 kg/m3 Formulation 4 Density ~ 100 kg/m3 Mixing conditions 1 (12s, 800 rpm) Cell size ~ 800 μm     Mixing conditions 2 (16s, 1000 rpm) Cell size ~ 600 μm     Mixing conditions 3 (20s, 1200 rpm) Cell size ~ 500 μm     Mixing conditions 4 (25s, 2000 rpm) Cell size ~ 350 μm     2.3.2 Polyethylene (PE), poly-methyl methacrylate (PMMA) and Gas Dissolution Foaming Polyethylene (PE) is the most common polyolefin, formed by simple repetition of the ethylene (-CH2-) group. In particular, low density polyethylene (LDPE) shows low density (910 kgm-3), chemical stability and mechanical strength and is frequently selected as base polymer in foaming for multiple purposes [45]. It is a semicrystalline thermoplastic polymer with approx. 40% of crystallinity. Polymethyl methacrylate (PMMA) is an amorphous thermoplastic polymer, optically transparent, with density of 1180 kgm-3 often used in sheet form as a lightweight or shatter-resistant alternative to glass. It is a strong, tough and lightweight material with very good impact strength. Both materials could be foamed by the so-called gas dissolution foaming [5, 46]. This foaming process consists on several steps (Figure 2-13): Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 84 Step I. Saturation: the polymer is placed inside a pressure vessel under controlled gas pressure and temperature. The gas diffuses into the polymer, occupying the free space between the polymer chains [5, 47-49]. This stage usually ends when the polymer sample is completely saturated by surrounding gas. Step II. Desorption: gas pressure is released, and the sample enters into a supersaturated state. The polymer starts to release the excess of gas, either by diffusion to the outside or by the formation of discontinuities/voids inside the matrix. These voids will act as nuclei for the cells formation [35]. Step III. Foaming: when the saturated sample reaches a temperature over or close to its glass transition temperature (Tg) for PMMA or the melting temperature (Tm) for PE the cell growth and then sample expansion takes place. In this process, the variation of the different processing parameters permits controlling the final structure of the produced materials (density and cell size). Figure 2-13. Gas dissolution foaming scheme. For this investigation a collection of commercial low density cellular polyethylene samples produced by the company Zotefoams (UK) [50] were considered (density 1560 kgm-3, cell size 300-800 μm). These materials are produced using N2 as blowing agent. Cell geometry in this case is tetrakaidecahedral with isotropic cells. In addition, the solid material is distributed throughout the structure more homogeneously than 2. Basic Concepts on Cellular Materials 85 in the case of PU foams, achieving therefore low-medium values of fs (0.2-0.4) owing also thin cell wall thickness (2-4 μm) (Figure 2-14). Figure 2-14. Tomographic slice –leftand separation in walls and struts –rightof a typical LDPE foam with fs 0.3. On the other hand, for the nanocellular polymers considered in this investigation a PMMA (Plexiglas® V825) from Altuglas-Arkema (France) was used as raw material. The foamed specimens manufactured present relative densities around 0.4-0.8 and cell sizes from 25 nm to a few microns. The exact shape of the pores in this type of materials is still unknown. However, it has been proven that the anisotropy of the pores is linked with the anisotropy of the solid precursor [51, 52]. Regarding the solid phase, 2D microscopy studies have shown that fs is proportional to relative density for constant cell size [5]. 2.3.3 Polystyrene (PS) and Extrusion Foaming Finally, polystyrene (PS) is an aromatic amorphous thermoplastic polymer produced from the monomer styrene with density of 1050 kgm-3. It is clear, hard and brittle and one of the most widely used plastics. Among all its uses, foaming is one of the most important. Both expanded polystyrene (EPS) and extruded polystyrene (XPS) are manufactured nowadays mainly for insulation applications. EPS is fabricated by the sintering in a mould of pre-expanded PS beads whereas XPS is produced following the so-called extrusion foaming. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 86 This is a continuous process working under similar principles of solid polymer extrusion [2, 41]. It allows producing simple geometries (pipes, sheets, etc…) of low and high density foams. However, temperature and pressure need to be controlled with care due to the presence of reactive and flammable gases acting as blowing agents. This process is composed by several steps: polymer melting, blowing agent injection and dissolution into the molten polymer, cooling of the blowing agentmolten polymer mixture to a temperature close to the glass transition temperature of the base polymer and pressure drop at the die which allows expansion. This pressure drop allows cell nucleation, followed by the sample expansion reaching stabilisation of the resultant cellular structure by cooling and solidification. The extrusion foaming can use a single extruder or tandem extruders. This last case permits manufacturing cellular materials with very low density. In this investigation two similar commercial XPS samples (density 35 kgm-3, cell size around 250 μm) have been considered. Cells in this material are typically oriented in the thickness direction. These kind of materials reaches ultra-low values of fs (<0.2) with very thin (~1 μm) flat cell walls and almost uniform material thickness distributions (Figure 2-15). Figure 2-15. Tomographic slice –leftand separation in walls and struts –rightof PS foam with fs 0.15. 2. Basic Concepts on Cellular Materials 87 2.3.4 Nanosilica Aerosil R812 These hydrophobic-fumed silica (pyrogenic silicon dioxide) post-treated with hexamethyldisilazane (90% of hydrophobic surface) [53] were provided by Evonik Industries (Germany). The nanometric silica powder has an extremely low density and high surface area. In fact, the specific surface area for this particle ranges 230-290 m2/g. Due to the post-treatment only a small fraction of the surface hydroxyl groups are free. Its three-dimensional structure may result in viscosity increase when used as reinforcing additive. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 88 References [1] L.J. Gibson, M.F. 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Rodríguez-Pérez, Rigid polyurethane foams with infused nanoclays: Relationship between cellular structure and thermal conductivity, European Polymer Journal, 80 (2016) 1-15. [33] E. Laguna-Gutierrez, C. Saiz-Arroyo, J.I. Velasco, M.A. Rodriguez-Perez, Low density polyethylene/silica nanocomposite foams. Relationship between chemical composition, particle dispersion, cellular structure and physical properties, European Polymer Journal, 81 (2016) 173185. [34] J. Lobos, S. Iasella, M.A. Rodriguez-Perez, S.S. Velankar, Improving the stability of polylactic acid foams by interfacially adsorbed particles, Polymer Engineering & Science, 56 (2016) 9-17. [35] J.S. Colton, N.P. Suh, The nucleation of microcellular thermoplastic foam with additives: Part I: Theoretical considerations, Polymer Engineering and Science, 27 (1987) 485-492. [36] R.D. Pattel, Bubble growth in a viscous Newtonian liquid, Chemical Engineering Science, 35 (1980) 2352-2356. [37] M. Favelukis, R.J. Albalak, Bubble growth in viscous newtonian and non-newtonian liquids, The Chemical Engineering Journal, 63 (1996) 149-155. [38] I. Cantat, S. Cohen-Addad, F. Elias, F. Graner, R. Höhler, O. Pitois, F. Rouyer, A. SaintJalmes, Foams Structure and Dynamics, Oxford University Press2013. [39] M.M. Bernal, S. Pardo-Alonso, E. Solórzano, M.A. Lopez-Machado, R. Verdejo, M.A. RodriguezPerez, Effect of carbon nanofillers on flexible polyurethane foaming from a chemical and physical perspective, RSC Advances, 4 (2014). Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 96 In the following paragraphs a description of the two great groups of X-ray generation systems (X-ray compact sources (tubes) and synchrotron large facilities) is addressed. o Conventional Laboratory X-ray Sources The main working principle of this kind of X-ray radiation generator is the strike of free electrons against a metal target thanks to a high voltage. In 1913 Coolidge source was invented. In this design the electron source was an incandescent filament. In this case the target (anode) was inside a glass tube under vacuum which allowed increasing the tube current and consequently the density of photons emitted. In addition, in this setup the acceleration voltage was tuneable and therefore the energy of the beam. In fact, some of the actual compact X-ray tubes are still working under this principle including improved components. The main limitation on this kind of Xray source was the heat generated into the target that might lead to the anode melting. To overcome this issue, different cooling systems were implemented until the establishment of the rotating anode. This improvement permitted distributing the generated heat and thus increasing the power of the X-ray sources (kW). Furthermore, due to the intrinsic conic geometry of the generated beam in these systems, depending on the spot size blurring artefacts could appear limiting the spatial resolution. For this reason, in order to improve the spatial resolution the main goal has been downsizing the focus area and thus reducing the size of the blurring area (Figure 3-4). Figure 3-4. Effect of focal spot size on spatial resolution for cone-beam configuration. 3. X-ray Imaging and Image Analysis 97 Mini, micro and sub-micro (nano) focus sources are nowadays available focusing the electrons onto a reduced zone of the target. As a consequence, the intensity current decreases proportionally to the spot area reducing the available number of photons. Latest developments to increase the X-ray flux in micro and nanofocus sources are basically focused on targets with improved heat dissipation. In this sense, liquid anode technology is based on liquid metal target continuously circulating providing optimum thermal dissipation and thus powerful X-rays from a quasi-punctual source. o Synchrotron Sources Alternatively, as mentioned before, X-rays can be generated in synchrotrons. A synchrotron machine exists to accelerate electrons to extremely high energy and then make them change direction periodically. The resulting X-rays are emitted (Figure 3-3) as dozens of thin beams, each directed toward a beamline next to the accelerator. The electrons are kept in the Storage Ring in which they circle for hours close to the speed of light. The tube is maintained at very low pressure (approx. 10-9 mbar) in order to avoid undesired collisions. The electrons pass trough several types of magnets in their trajectory producing X-rays (Figure 3-5). On one hand, Undulators (short period) and Wrigglers (large period) are magnetic structures made up of a complex array of small magnets and force the electrons to follow an undulating trajectory. The radiation emitted at each consecutive bend overlaps and interferes with that from other bends. This generates a much more focused, or brilliant, beam of radiation than that generated by a single magnet roughly in proportion to the number of magnets [8]. Also, the photons emitted are concentrated at certain energies (called the fundamental and harmonics). The gap between the rows of magnets can be changed to fine-tune the wavelength of the X-rays in the beam. On the other hand, Bending Magnets (Figure 3-5) bend the electrons into their racetrack orbit. However, as the electrons are deflected from their straight path when passing through these magnets, they emit a spray of X-rays tangentially to the plane of the electron beam. The synchrotron light from a bending magnet covers a wide and continuous spectrum, from microwaves to hard X-rays, and it is much less focused, or brilliant, than the fine beam of X-rays from an Undulator or Wriggler. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 98 Figure 3-5. Different magnetic devices present on synchrotron facilities. During the last decades a large number of synchrotron facilities have been built across the world. Synchrotrons have been developed from first to third generation rapidly increasing brilliance of these radiation sources [9-11]. Furthermore, X-rays are generated in synchrotrons far from the sample position leading to quasi-parallel configurations avoiding the influence of the focal spot size and enabling high resolution experiments using lenses to obtain small effective pixel sizes. In addition, even smaller pixel sizes can be achieved by using X-rays microscopes that allow reducing further the effective pixel size (nm) focusing the Xray beam. 3.1.2 X-ray-matter interaction The interaction of X-rays with matter is linked to the complex refractive index (n) of the involved materials, with real and imaginary parts containing the principal parameters dominating phase and absorption contrast respectively (Equation 3-1) [12]. { Equation 3-1 Where μ is the attenuation coefficient, ϕ is the phase shift and λ is the radiation wavelength. Absorption is represented as the attenuation in the intensity of the X-ray wave when passing through the material whereas phase contrast provokes a phase shift on it (Figure 3-6). Comparing the magnitude of both contributions, phase contrast generate 10-1000 times more signal, but requires coherent illumination [13- 3. X-ray Imaging and Image Analysis 99 15]. This fact is employed for either reducing the radiation dose or increasing the sensitivity. Figure 3-6. Attenuation and phase shift of X-ray wave propagating in medium with complex index of refraction. o Absorption Absorption contrast imaging is the most common imaging technique. An absorption contrast image is essentially a shadowgraph, the contrast being generated by the different attenuating power of materials and their thicknesses in the sample. The physical fundamentals of radiation absorption are based on Beer-Lambert law (Equation 3-2). This expression predicts the attenuation of incident monochromatic Xray radiation by an exponential function of the linear absorption coefficient (μ), the element concentration (c) and the thickness (t). In case of heterogeneous materials and/or polychromatic X-rays, an effective attenuation coefficient (μeff) is usually considered. In addition, in order to eliminate the influence of material density, the mass attenuation coefficient, μm, is introduced (μm = μeff/c). ( ) ( ) Equation 3-2 The attenuation coefficient varies with incident energy and basically with atomic numbers of elements in scanned object (Figure 3-7). On one hand, the lower is the energy of X-rays, the higher is the attenuation coefficient and therefore also the X-ray absorption. On the other hand, roughly speaking, materials with high atomic number Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 100 such as metals stop X-ray radiation, whereas materials with low atomic number (oxygen, carbon, hydrogen, nitrogen…) are almost transparent to X-rays. Figure 3-7. Dependence of mass attenuation coefficient with both atomic number and incident radiation energy. General view –upand particular cases –down-. o Phase contrast The phase of the waves travelling through the sample contributes to the modulation of the detected intensity in an X-ray phase-contrast imaging system. It is not possible to directly measure the phase of electromagnetic waves at optical frequencies and above, however, phase effects can play a significant role in the image formation also in the hard X-ray regime. Phase-contrast imaging techniques exploit the phase perturbations introduced by the sample to modulate the intensity recorded at the image receptor [16]. The simplest approach is the so-called Free-space Propagation [17-19] (Figure 3-8). According to this approach, the introduction of an appropriate distance between the sample and the detection system (R2) can be sufficient to make phase effects detectable. This phenomenon for a pure phase object is interpreted in terms of Fresnel diffraction (Equation 3-3). 3. X-ray Imaging and Image Analysis 101 Figure 3-8. Schematic of the Free-space Propagation phase contrast. [ ] Equation 3-3 Where M=(R1+R2)/R1 is the geometrical magnification and R1 is the distance between source and sample, ϕ is the phase shift and λ the radiation wavelength. The contrast from a pure phase object vanishes when R2→0 and the phase term is directly proportional to the propagation distance R2. In addition, the monochromaticity of the radiation is not essential for this type of imaging. A necessary condition, however, is that the radiation must have a certain degree of spatial coherence [15, 20] (Equation 34). √ Equation 3-4 where σs is the standard deviation of the source intensity distribution. The coherence length (lc) has to be comparable to or larger than the inverse spatial frequency of the feature of interest [21] in order to obtain significant phase contrast. In practice this means that the source has to be small or that the object must be placed at large distance R1 from it. Another requirement is that the imaging system must have spatial resolution high enough to not wash out the interference fringes. The intensity projection image will contain a mixture of contributions from both the absorption and the phase shifts in the sample. Other experimental parameters, like the X-ray energy, the geometrical magnification, the radiation coherence and the system resolution, determine the modulation of intensity at the detector. The process that Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 102 calculates phase and amplitude at the exit surface of the sample is called phase retrieval [22, 23]. Quantitative retrieval algorithms are also a fundamental component for accurate three-dimensional reconstructions [24]. The determination of both amplitude and phase requires more than a single measurement (by changing either the propagation distance or the energy) unless some constraints can be imposed on the sample. Other imaging techniques using phase contrast are interferometry [25], analyser based imaging [26] and edge illumination [27]. The latter has been investigated in recent years as a possible way forward for the translation of phase-sensitive imaging techniques into mainstream applications by using two different apertures (or masks), before and after the sample even in conventional X-ray systems [28, 29]. The first mask allows separating the polychromatic beam in series of independent beamlets. Combined to the second mask, this technique has negligible spatial or temporal coherence requirements [30] providing high sensitivity on laboratory implementations. 3.1.3 X-ray detection Once the X-ray radiation passes through the object, the last step of the imaging process consists on collecting the transmitted radiation and converting it into a readable signal. Nowadays, there are a lot of detection systems depending on the required application. In particular, X-ray detectors for imaging purposes can be divided in two groups depending on the used technology for the conversion of X-rays to electrical signals (intensity currents) representing the X-rays intensity distribution (Figure 3-9). On one hand, in indirect detection a scintillating material converts X-ray photons into visible light by luminescence process. Then, a secondary system (CCD, photodiode) converts the visible photons into electrical current intensities. This detection principle is predominantly used in X-ray imaging since the energy response of the detector can be easily optimized varying the scintillating material and its thickness. In addition, the great variety of detector of light in the visible range permits selecting the best option in each case. Some common scintillating materials are 3. X-ray Imaging and Image Analysis 103 ceramics, phosphor (P), silicium (Si), cesium iodide (CsI), etc. One of the main disadvantages of this detection technique is that spectral information is lost and the light scattering inside the scintillator strongly limits the resolution. Doping scintillators with rare earths or fluorescent ions permits increasing the quantum efficiency of the scintillator (emit more light photons per X-ray photon) and therefore reducing scintillator thickness improving the final image quality. Typical examples of such kind of scintillator materials are Cerium-doped Lutetium Yttrium Orthosilicate (LYSO), Cadmium Tungstate (CWO) and Gadolinium Oxysulfide (GOS). On the other hand, the direct detection is based on materials that convert directly the X-rays to intensity currents (sensitive layers or photoconductors) such as amorphous selenium or Cadmium Telluride (CdTe). This mechanism counts every single photon and its energy avoiding light scattering of indirect detection, increasing quantum efficiency and maintaining the spectral information, but the X-ray flux needs to be low in order to match the frame rate of the used electronics avoiding in this way the overlap of photons in the acquired signal. Figure 3-9. Scheme of main steps of X-ray detection for indirect and direct detection systems. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 104 3.2 X-ray Computed micro Tomography (μ-CT) X-ray tomography, also known as CT (Computed Tomography) is a non-destructive technique which provides 3D information of materials [31]. The micro-structure characterization must be carried out at the relevant scale. X-ray Tomography permits the inspection from centimetres to few microns, the so-called micro-Tomography (μCT). It is consequently very attractive in materials science to study the structure of materials. X-ray tomography is employed in several research topics besides materials science such as in medicine, in paleontology, archeology [32-34]. Nowadays, X-ray tomography can really compete with classical optical and electronic microscopy techniques due to several reasons: - The technique is non invasive and there is no need for sample preparation like polishing or metal deposition. - Very brittle samples can be easily handled. - In situ tests can be monitored on the tomography stage (depending on resolution and kind of test). - Spatial resolution is up to 1 μm in lab-scale equipments and ever further in novel devices. - And the most important is obtaining representative data in 3D. The general concept of X-ray tomography is an extension of classical X-ray radiography, and is based on the attenuation of the X-ray beam through the specimen. X-ray radiography provides only a projection of the sample volume on one single plane. X-ray tomography overcomes this disadvantage by combining the information from hundreds of radiographs, each being recorded with different orientation of the sample in front of the detector. The variation of X-ray attenuation in the volume of the sample can be reconstructed by combining a sufficient number of radiographs with an appropriate algorithm. The data is obtained in the form of a 3D array of voxels, for 3. X-ray Imaging and Image Analysis 105 which the grey-level of each voxel describes the calculated X-ray attenuation at that position. A detailed description of all the involved steps in the tomography process (Figure 3-10) is addressed hereinafter. Figure 3-10. Main steps of the tomography process. Projections acquisition, sinograms generation and reconstruction. 3.2.1 Acquisition The first step of every tomography experiment is the acquisition of the so-called projections, each of the radiographs of the scanned sample at different angles. It is the crucial step since optimum raw data leads to suitable reconstructed results. To this purpose, several parameters play an important role: beam conditions (voltage and current), detector exposure time, number of projections and the acquisition mode (single projection or multiple projection integration). Firstly, depending on the characteristics of the scanned sample (geometrical dimensions and constituents) mainly voltage but also current should be adapted to achieve the maximum contrast in every projection using as a consequence most of the dynamical range of the detector. In this sense, several efforts have been carried out in order to establish simple criterion to select suitable illumination conditions. One of the most representative methods is the following [35]. Considering an irregular sample, the normalized transmissivity (defined as the intensity divided by the intensity Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 112 o Filtered Back Projection (FBP) The Fourier Slice Theorem resulted essential to solve the reconstruction equation system. It states that the reconstruction of the object from its projections is possible by using Fourier transforms as long as the number of projections (angles) fills the Fourier space along radial lines. Collecting projections from 0º to 180º can fill the entire Fourier space, but in cone-beam geometry 360º are covered to minimize the distortions induced in the projections due to beam geometry and thus improving the final reconstruction. Finally, the scanned object is recovered by the inverse Fourier transform. In order to exemplify these statements we can consider a 2D object as the cross section of a 3D object and the following definitions: f (x,y) 2D Object R [f (ρ, ϕ)] 1D projection of f (x,y) at angle ϕ (Sinogram – Radon Transform) F [f (ν, ϕ)] 2D Fourier transform of f (x,y) in polar coordinates Fρ ([R f (ν, ϕ)]) 1D Fourier transform of the projection R f (ρ, ϕ) in polar coordinates at angle ϕ Hence, the Fourier Slice Theorem states that the Fourier transform of the sinogram is linked to the Fourier transform of the original projection (Figure 3-15) (Equation 3-8). Figure 3-15. Schematic representation of the main statement of Fourier Slice Theorem. 3. X-ray Imaging and Image Analysis 113 { [ ( )]} [ ( )] Equation 3-8 From this theorem, the bases of the Filtered Back Projection (FBP) algorithm are easily derived. In this algorithm, the spreading and sum (Back Projection) over the full Fourier space (over 180º) of the inverse Fourier transforms of the sinograms, adequately filtered with a high-pass filter in order to suppress background and thus enhance sample contrast, permit the reconstruction of the scanned object (Equation 39). ( ) ∫ [ { [ ( )]} ( )] Equation 3-9 FDK (Feldkamp, Davies and Kress) reconstruction algorithm is the mainstream method in practice to develop FBP reconstructions [44] mainly in cone-beam configurations. o Statistical Iterative Reconstruction (SIR) The iterative reconstruction algorithm first synthesizes forward projection and mathematically compares and corrects the actual measurement with the measured projection at the detector. The technique then iterates this comparison and correction step to achieve close proximity between actual and measured projections. These algorithms incorporate a better statistical noise model, which uses noise information in the measured projection data to accurately model the behaviour of attenuated photons and electronic noise (referred to as photon and noise statistics, respectively). These algorithms also include accurate mathematical information of actual focal spot size, detector size and shape, and image voxel shape (referred to as the system optics). Inconsistencies in the projection measurement owing to limited photon statistics and electronic noise are corrected with multiple iterations. The forward projection and multiple iterative corrections lead to increase in reconstruction time (100 times higher than FBP) but help to lower image noise and artefacts [45]. A pure iterative reconstruction technique includes mathematical probability likelihood functions to compute a more accurate noise model as well as a forward Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 114 model or a projector, which is mathematically more complex and accurate. These algorithms also incorporate prior functions, which take into account prior appropriate information about the image reconstruction and the CT imaging system such as actual focal spot size, image voxel model, exact detector size, raw data statistics, and the desired image behaviour. These techniques compute a cost function to include all of the above inputs and perform the optimal number of iterations to generate a final desired CT image as output under a convergence criterion or after a predetermined number of iterations is performed (Figure 3-16) [46]. Figure 3-16. Several iterations on the iterative reconstruction of a test sample until the convergence criterion is reached. Finally, comparing the two mentioned reconstruction algorithms FBP permits obtaining reconstructed information without very specific computation requirements. Moreover, reconstruction process is accomplished in moderate computation times (few seconds in GPU). However, in order to achieve ideal results a lot of projections are required therefore increasing the radiation dose in the sample. On the other hand, SIR allows obtaining very good results with few raw information, but requiring more computation power and reconstruction time. o Reconstruction artefacts Some specific artefacts occurring in X-ray Tomography are briefly described in the following paragraphs. Ring artefacts, beam hardening, metal and scattering artefacts 3. X-ray Imaging and Image Analysis 115 are addressed. There are strategies to solve them that imply the slice modification both before and after the reconstruction process [47]. Ring artefacts result from pixel deviation due to miss-calibration. This is usually caused by imperfections in the scintillating detectors [48] (Figure 3-17). They are concentric rings centre around the rotation axis. They can be corrected by filtering the image during the reconstruction process. In some cases, an additional correction after the reconstruction process is required to avoid this artefact. The reconstructed slices are translated to polar coordinates, in which ring artefacts become vertical stripes. Then, a stripe-wavelet filter is applied in order to supress the lines. Finally, the images are retranslated to the Cartesian space to recover the original image, but without rings [49]. Figure 3-17. Ring artefacts and typical protocol to post-process the reconstructed slices to correct them. Beam hardening is the result of the dependence with energy of attenuation coefficient when using polychromatic illumination [50, 51] (Figure 3-18). Since the attenuation coefficient is higher for low energies, low energy photons are attenuated by samples more frequently than high energy ones. As a consequence, the transmitted beam contains a higher proportion of high energy photons. The effect is conceptually similar to a high-pass filter. Beam hardening may result in two characteristic artefacts: streaking (dark bands) and cupping. Streaking artefact appears as multiple dark streaking bands positioned between two dense objects whereas cupping artefact refers to a falsely bright appearance along the periphery of an object. Since higher energy photons are less attenuated by tissue, the beam will be less attenuated versus identical Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 116 tissue near the skin entry site. If uncorrected during CT reconstruction, these differences in expected attenuation profile lead to a peripherally dense appearance. Beam hardening is usually corrected by using filters of an attenuating substance (often metallic) that harden the beam before it reaches the sample. In addition, there are image methods that substitute every value of the natural logarithm of the sinograms (s) with the corresponding value of a 5th polynomial whose four parameters (ai) can be adjusted (Equation 3-10). Equation 3-10 Figure 3-18. Schematic view of a cylindrical sample with and without Beam Hardening artefact (cupping). In the presence of high attenuation objects, the reconstruction algorithms such as FBP give rise to streak and star artefacts, condensed as metal artefacts [52] (Figure 3-19). The metal artefact reduction (MAR) algorithms can be divided mainly in two classes: the projection completion based methods and the statistically based iterative methods that interpolates the missing data using the neighbouring projections. Figure 3-19. Metal artefact and corresponding corrected slice. 3. X-ray Imaging and Image Analysis 117 Finally, the additional share of scattered X-rays during the acquisition of projections may result in increased measured intensities, since the scattered intensities add to the primary intensity. As a result, in the final reconstruction an underestimation on the attenuation coefficient takes place, known as scattering artefact [53]. The reconstructed error is dependent on the object and is proportional to the amount of scatter present. Scatter causes streak artefacts in the reconstruction that are very similar to those caused by beam hardening. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 118 3.3 μ-CT device at CellMat The X-ray system of CellMat laboratory was built as part of a previous PhD. Thesis [54]. The critical elements are the X-ray tube (microfocus L10101 from Hamamatsu photonics, Japan) and flat panel detector (C7940DK-02 also from Hamamatsu). Both elements were carefully selected since polymers are low absorbing materials. To overcome this constraint, low energy X-rays are required in order to guarantee enough contrast in the images. For this reason, the spectral response of the selected detector should be focused on the low energy range to maximize the sensibility and efficiency. Moreover, dimensions of cellular structure are in the order of microns and therefore high spatial resolution is also relevant, needing small focus spot size and small pixel size in the detector. In addition, tomography experiments are carried out by locating a high precision rotation stage (DT-65 N from PI miCos, Germany) between source and detector. 3.3.1 X-ray Source A closed air-cooled micro-focus X-ray source is the X-ray generator. The main technical characteristics of the X-ray source are summarized in table 3-1. In this tube an ultrafine electron beam strikes on a tungsten target in high vacuum atmosphere. The tungsten anode, irradiated by the electrons, produces X-rays. X-rays come out the source through a Beryllium 150 μm-thick window forming an X-ray cone-beam of 39º of aperture. The micro-focus spot size of 5 μm tends to slightly broaden as electron acceleration voltage or current become increased up to a maximum of 20 μm. Nevertheless, the spot size remains in its minimum size for values below 40% of its maximum power (20 W). In addition, the maximum intensity is limited by the produced voltage (Figure 3-20). 3. X-ray Imaging and Image Analysis 119 Table 3-1. Technical characteristics of Hamamatsu L10101 X-ray source Spot size (μm) 5-20 Voltage (kV) 20-100 Current (μA) 0-200 Maximum output power (W) 20 Figure 3-20. Maximum output power curve of the X-ray source. 3.3.2 Flat Panel detector This high resolution detector is composed by a matrix of 2240 x 2344 pixels2 with a pixel size of 50 μm (therefore 111.50 x 117.20 mm2). The digital output is a 12 bits depth resolution (4096 real grey levels) with maximum acquisition velocity up to 9 fps working at 4 x 4 binning mode. In this detector, the CsI scintillator layer is directly grown over the CMOS detector. In this way the light transmission is maximized reducing light scattering resulting in high sensibility of the detected X-rays. It is important that the diameter of the grown scintillator material is smaller or similar than CMOS pixel size. Further, the detector area is covered by a 1 mm-thick carbon fibre plate. The communication between detector and CPU is accomplished using a frame grabber (Dalsa-Coreco, USA). X-ray tube and detector are located in front of each other inside a lead shielded cabinet (Figure 3-21). Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 120 Figure 3-21. X-ray system at CellMat laboratory. Due to the conical spread of the X-ray beam, source-detector distance (SDD) could be in the range 0.3-1.2 m. In our case, due to the spatial limitations marked by the cabinet, SDD is commonly fixed at 580 mm, becoming a compromise distance for all the involved factors such as beam intensity decay and apparition of artefacts. Thanks to a linear stage the scanned object could be placed at any position between source and detector thus changing the optical magnification factor (M). Magnification factor is calculated considering the distances between source and detector (SDD) and source and scanned object (SOD) (Equation 3-11). Equation 3-11 As magnification increases sample position in reference to the rotation axis plays a more important role. In addition, wobble of the rotation stage (and thus of the rotation axis) can become into a horizontal sample displacement during the scan that increases with vertical distance between rotation stage and sample position. These two facts can preclude the correct reconstruction of the tomography. During this thesis, in order to avoid these two constrains and enhance the X-ray Tomography results the X-ray system has been optimized. On one hand, the position of the sample in the X-ray beam can be adjusted in height by a specific Z lab-jack that maintains constant and reduced the distance between sample and rotation stage, reducing therefore the wobble problems. On the other hand, the sample can be easily 3. X-ray Imaging and Image Analysis 121 placed on the centre of rotation by an X-Y micrometre table connected to the rotation stage (Figure 3-22). These two updates in the X-ray system permit nowadays performing with ease and optimum contrast X-ray tomography at CellMat Laboratory with an effective pixel size of 2.5 μm. Finally, all the functions corresponding to all the devices (source, detector, motors of the linear and rotation stage, etc.) have been counted in a unique application developed under LabView framework. Figure 3-22. 3D rendering of the X-ray system indicating the distances required to calculate optical magnification and focused zone of the Z-labjack and positioning micrometres. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 128 On the other hand Octopus Analysis, formerly known as Morpho+ was used at the start of the thesis for the morphological analysis of the tomograms. It is a powerful 3D analysis software package due to its intuitive and user-friendly interface which provides quick access to the powerful algorithms implemented in the package and allows for a complete 3D analysis of very large datasets (>8 gigavoxel) [67]. 3.5.3 Avizo Fire/Amira Avizo/Amira is a general purpose commercial software application for scientific and industrial data visualization and analysis developed by FEI Visualization Sciences Group [68]. It enables to perform interactive visualization and computation on 3D data sets. It includes a large amount of different kernels for filtering, object separation algorithms, quantification tools and rendering for visualization. This software was used in this investigation for the computing of surface curvatures on high resolution μ–CT and for visualization purposes. 3. X-ray Imaging and Image Analysis 129 3.6 Image processing Finally, to obtain quantifiable information of the acquired data it is required to perform specific image processing protocols onto the tomographic data. As the structure of cellular materials is characterized by a multi-scaled architecture (solid+gaseous phases), the developed protocols have considered the analysed phase (or scale). As a result, parameters concerning gaseous phase (conventional parameters) and solid phase (advanced parameters) are analysed separately, as explained hereinafter. 3.6.1 Conventional features characterization The analysis of the gaseous phase of cellular materials by means of X-ray μ–CT has been broadly performed within the literature [69-72]. It is accomplished following several steps aiming at the end of the process to extract quantitative data about the gas phase of these materials such as cell size, anisotropy, etc… (Figure 3-26). - An edge preserving filter (typically median) is applied in order to enhance the contrast between gas and solid phase in the images. - Thresholding and binarization allows separating the solid material from gaseous phase background. In low density cellular materials, as the cell walls are commonly extremely thin, the spatial resolution employed is not high enough to correctly binarize these parts of the structure. - As a consequence, a watershed based algorithm is required in order to separate artificially joined gaseous phase thus creating digital walls that permit obtaining separated pores to analyse. - Prior the 3D analysis of the cells, cells touching the border edges of the volume considered are eliminated in order to improve the results statistics. - Finally, several quantitative parameters are evaluated for every remaining single pore. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 130 Figure 3-26. Visualization of the main steps of the image analysis protocol for the gas phase characterization by μ–CT. As a result of this workflow several parameters can be extracted of the 3D images. - The ratio of the gaseous phase volume fraction and the total volume, i.e., porosity. - The cell size of the pores by means of the equivalent diameter procedure. - The anisotropy and orientation of the pores using the bounding box approach and the equivalent ellipsoid. - The neighbourhood distribution of the pores that enables characterizing their 3D geometry. 3.6.2 Advanced features characterization High resolution μ-CT opens the possibility to reconstruct even the cell wall in low density cellular polymers. As a result, advanced features of the solid phase, not widely studied in the literature, can be accurately characterized. In this sense, few studies have been carried out considering several criterions to separate the two constituents of the solid phase: cell walls and struts. The two main ways are the destructuration by a succession of erosions-dilations in 3D [73] and a solid classification 3. X-ray Imaging and Image Analysis 131 algorithm in with the inertia moment of each pixel is calculated considering its neighbourhood to discriminate between the two mentioned constituents [74]. However, in this thesis, the determination of the local thickness has been considered as a key point to extract the basic parameters of the solid phase such as the fraction of material in the struts or the thickness of the different constituents (Figure 3-27). After filtering and binarizing (as well as in the previous case) en Euclidean transform local thickness algorithm allows assigning to every pixel belonging to the solid phase a thickness value corresponding to the diameter of the maximum sphere selfcontained in that phase and centred in that pixel [75]. As a result, material thickness distributions can be obtained typically containing two separate peaks, each of them corresponding to the main constituents of the solid phase (Figure 3-27). Figure 3-27. Main steps in the imaging analysis protocol for the characterization of the parameters concerning the solid phase. After that, by analysing the relative area of the two peaks the fraction of material in each zone of the solid skeleton can be calculated. In addition, from every thickness distribution (cell walls, struts and total) the average thickness can be determined obtaining then the mean cell wall thickness, strut thickness and total structure average thickness. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 132 During this research, additional image analysis protocols have been developed to quantify specific features in X-ray Tomography. A detailed description of all these methodologies is included in the corresponding papers of the next chapter (Chapter 4). 3. X-ray Imaging and Image Analysis 133 References [1] J. Banhart, Advanced tomographic methods in materials research and engineering., Oxford University Press2008. [2] J. 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Laguna, M.A. Rodriguez-Perez, muCT-Based Analysis of the Solid Phase in Foams: Cell Wall Corrugation and other Microscopic Features, Microscopy and Microanalisis, 21 (2015) 13611371. [75] T. Hildebrand, P. Rüegsegger, A new method for the model-independent assessment of thickness in three-dimensional images, Journal of Microscopy, 185 (1997) 67-75. Chapter 4 X-ray Tomography Studies on Cellular Polymers Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 144 topologically separated in cell walls and struts, it is usually difficult to select a suitable criterion to distinguish them. For this reason, we have developed a novel methodology for solid classification in low density cellular solids, which allows identifying both parts of the solid phase. This new approach could become an ideal characterization route for the cellular materials scientific community. 2. Experimental 2.1 Materials Closed-cell rigid polyurethane foams and cross-linked closed-cell polyolefin foams are comparatively analysed in this work. Polyurethane (PU) foams have been fabricated by a reactive foaming process [28]. In this type of process two different reactants are mixed in order to obtain a foamed solid specimen. In our particular case, the two reactants are dior polyisocyanate (part A) and a polyol blend (part B) provided by BASF Poliuretanos Iberia S.A. Polyol blends are composed by catalysts (amines), surfactants to stabilize the foam structure, the base polyol, which can be a polyether polyol, a polyester polyol or a blend of different types of polyols, and finally, water as blowing agent (that decomposes during the reaction generating CO2). According to the supplier technical data sheet parts proportion were fix to 100 (part B)/160 (part A) for the polyol and isocyanate. The mixture of the two components was carried out using an overhead stirrer (EUROSTAR Power control-visc P1), equipped with a 50 mm diameter propeller stirrer from IKA. The mixing process (25s at 1200 rpm) was carried out in order to promote the blowing and curing reactions. By using four different polyol blends supplied by BASF (part B) in which the difference was only the amount of water it was possible to produce PU foams with four different densities between 30 and 100 kg/m3 (Table 1). Cross-linked closed-cell polyolefin foams manufactured by a high-pressure nitrogen gas solution process [29] were generously provided by Zotefoams Plc. (Croydon, United Kingdom). They were produced with low density polyethylene (LDPE) as base polymer. In this process, an extruded and cross-linked LDPE sheet was placed in an autoclave, in which it was subjected to a high pressure of nitrogen gas at temperatures above the polymer softening point. Under these Table 1. Summary of the samples in this study. Sample Density (kg/m3) Relative density Sample Density (kg/m3) Relative density PU-1 32.5 0.028 LDPE-1 16.4 0.018 PU-2 54.8 0.046 LDPE-2 20.2 0.022 PU-3 76.0 0.064 LDPE-3 31.2 0.034 PU-4 94.9 0.080 LDPE-4 41.3 0.045 4. X-ray Tomography Studies on Cellular Polymers 145 conditions, the nitrogen dissolved into the polymer matrix. At the end of the solution stage and after cooling, the pressure was reduced to ambient pressure. Then, the materials were placed in a second autoclave under low pressure and again heated above the polymer melting point. The release of the pressure resulted in full expansion. Finally, the slabs were cooled down to room temperature. For this study we have analysed four samples with densities in the range of 15-45 kg/m3 (Table 1). A more detailed description of the production process of these foams can be found elsewhere [30, 31]. These two collections of foams were selected for this study due to their structural differences. On the one hand, the microstructural solid distribution of PU foams shows a high concentration of polymer in the struts, (rounded-edge polyhedral pores) whereas, on the other hand, LDPE foams owe a likely sharpedge polyhedral structure since the material is distributed all over the solid foam structure, and is not concentrated in the struts (Fig. 1). The density and names of the samples characterized in this study are summarized in Table 1. 2.2 Experimental set-up Two different series of tomographies were carried out. The samples were analysed in a laboratory system (Fig. 2). The set-up consists of a micro-focus conebeam X-ray source L10101 from Hamamatsu (spot size: 5 µm, Voltage: 20100 kV, Current: 0-200 µA) with a maximum output power of 20W and a flat panel detector C7940DK-02 also from Hamamatsu (2240x2344 pixels2, 50 µm of pixel size). A rotation stage is mounted over a linear stage with a total travel of 600 mm thus varying the magnification factor, M, as described in Eq. 1 –SDD: source-detector distance, SOD: sourceobject distance-. (1) In our experiments the linear stage was placed in a position to achieve a magnification value M=10 (SDD=581.8 mm, SOD=58.18 mm) and thus an effective pixel size of 5 microns was (a) (b) Fig 1. Representative tomographic slices of (a) rigid PU foams –PU-2and (b) cross-linked LDPE foams –LDPE-4-. Fig 2. 3D rendering of X-ray μ-CT device at CelMat Laboratory Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 146 reached. A tube voltage of 55 kV and current of 150 µA were found to be optimal for the selected samples characterization. The detector exposure time was 1500 ms and the rotation step was 0.4º. In order to enhance the contrast in the reconstructed images each projection was the result of integrating two consecutive images. The samples were cylinders of 6 mm in diameter and 15 mm in height. Once all the projections were acquired, the reconstruction process of the tomogram was carried out using Octopus reconstruction package [32]. High resolution X-ray synchrotron µ-CT experiments were performed using the same samples. Measurements were performed at BAM-Line [33], a beam line located at Bessy II facility in Berlin (Germany). In this case, the detector of the X-rays was a PCO 4000 camera (4008x2672 pixels2, 9 µm of pixel size) near to a CWO scintillator. The analysed sample was placed very near the scintillator (9 mm) in order to minimize phase contrast artefacts. A specific optical system between scintillator and camera yielded a final pixel size of 0.438 µm. The energy of the X-rays in the line was fixed in a value of 9.8 keV. The selected exposure time of the detector was 3000 ms and the rotation step in this case was 0.08º. Samples with a reduced size (prisms of less than 1 mm2 of base and 4 mm in height) were used due to the limited field of view of 1.8x1.2 mm2 at such resolution. 2.3 Density characterization Density (ρ) for all the samples was determined over five cubes of 30x30x30 mm3 using the geometric method [1]. Values of 1160 kg/m3 and 910 kg/m3 respectively for PU and LDPE solid matrixes were used to calculate the relative density (ρ*). 2.4 Laboratory μ–CT analysis Quantitative data analysis of the gaseous phase was carried out using Octopus Analysis package [2]. Sub-volumes of 6503 voxels were analysed for each sample after a previous 3D median filter of 1 pixel of radius. Image analysis under this software leads several steps (Fig. 3): image binarization, removal of isolated pixels, cells identification, cells separation by a watershed-based algorithm [3] and, finally, quantitative computation of every cell and its neighbourhoods [4-6]. In addition, the incomplete cells touching the limit of the analysed volume were removed. It is important to remark that watershed algorithm was required at this resolution since the cell walls of the foam present lower contrast than bulky regions (strut). Once this procedure is applied, several cellular and topological descriptors of the foams such as cell size distribution, cell size, anisotropy, coordination number and cell density can be extracted. 4. X-ray Tomography Studies on Cellular Polymers 147 The mean cell diameter corresponds with the equivalent diameter which can be defined as the diameter of a sphere containing the same number of voxels than the current cell. In addition, the anisotropy of each individual cell was determined using the bounding box descriptor which represents the smallest prism that includes all the voxels of the object/cell. This descriptor outputs 3 cell dimensions (width, depth and height) referred to the Cartesian space directions (X, Y, Z). Moreover, the cell coordination number is defined as the number of cells in contact with a specific one. Finally, cell density informs about the number of cells per unit volume. It can be calculated by using Eq. 2. As several cells in contact with the border of the volume are removed during the analysis, only the foam volume occupied by the analysed cells is considered in this calculation. To calculate this volume, the total volume of gas (Vgas) calculated as a sum of all the volumes of the individual cells is corrected by using the gaseous fraction of the material (1-ρ*=Vgas/Vfoam). Once the foam volume is determined, NvTOMO is directly calculated considering the involved number of cells (n). (2) 2.5 Synchrotron μ-CT data analysis Quantitative data analysis of the solid phase was carried out using the open source image analysis application ImageJ/Fiji [7, 8]. Three different subvolumes of 13003 voxels were analysed for each sample after a previous 3D median filter of 2 pixel of radius. The method of analysis is different for this type of images (Fig. 4). Volumes were carefully binarized selecting a binarization level that preserves completely the cell walls in the binarized images (Fig 4(b)). Euclidean Distance Transform procedure (in 3D) [9] was applied (Fig. 4(c)) to determine the thickness distribution of the solid phase. Thickness histogram reveals that the thickness distribution of the mentioned constituents of the solid phase –struts and (a) (b) (c) Fig. 3. Graphical representation of software workflow. (a) Filtered grey-level (b) binarized without nonresolved cell walls and (c) final individual cell identification with suppressed border cells. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 148 cell wallsis overlapped. To separate these two contributions, two different strategies have been implemented. The first one consists in fitting the thickness histogram data by using a two-peak deconvolution process, using one peak for each constituent of the solid phase (Fig 4(d)). Considering the distinctly different thickness distributions for PU and LDPE foam materials, Log-normal or Gaussian fitting were used respectively. The correlation coefficient was better than 0.95 in all cases. With this methodology the determined area of these two peaks (Aw and As respectively) represents the fraction of each constituent. Then, the fraction of mass in the struts can be accurately calculated using the expression of Eq. 3 (Method-1). In addition, using the fitted data for these two overlapped thickness distributions it is possible to calculate the mean thickness values for cell walls and struts. (3) Alternatively, a simpler thickness threshold method (Fig. 4(e)) has been applied to classify struts and cell walls obtaining reasonably good results as observed in Fig. 4(f) (Method-2). The thickness value was selected in each case (a) (b) (c) (d) (e) (f) Fig. 4. Graphical scheme of the procedure for the analysis of high-resolution tomography volumes. (a) Filtered grey level slice. (b) Binarized slice including the cell walls (c) 3D local thickness with scale bar (d) two curves fitting of the material thickness distribution for the determination of fs (Method-1) (e) thickness threshold selected for the determination of fs (Method-2) and (f) final separation between cell walls –greenand struts –redafter Method-2. 4. X-ray Tomography Studies on Cellular Polymers 149 in order to reproduce the results of the erosion-dilation methodology, extensively applied in the literature [4, 10]. In this case, fs is calculated as the ratio between the area of the thickness distribution above the selected thickness threshold and the total area of the material thickness distribution. Finally, the mean thickness of the structure (t) is obtained calculating the weighted average of the original thickness distribution without fitting process. These methodologies improve the proposed methods for solid classification in foams described elsewhere [4, 11]. 3. Results and discussion The cellular structure descriptors are analysed here in three different sections. In the first section we discuss the characteristics of the individual entities of the gaseous phase. In the second section, we will analyse the topology of the cells. Finally, the descriptors of the solid phase are examined. 3.1 Gaseous phase descriptors Fig. 5 shows the analysed cell structure of two of the foams under study, PU-2 and LDPE-4, in order to exemplify the structural differences between them at the two scales analysed. These two foams have been selected for most of the comparisons in this work since they present nearly the same relative density (Table 1). Evident differences can be observed comparing these two materials. On the one hand, the cells of PU foams are slightly oriented in the Z-direction while LDPE foams show nearly isotropic (a) (b) (c) (d) Fig. 5. Tomographic 3D renderings of the gas phase for PU-2: (a) and (c), and LDPE-4: (b) and (d). Laboratory resolution: (a) and (b), and synchrotron resolution: (c) and (d). Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 150 cells (figures 5(a) and 5(b)). On the other hand, (figures 5(c) and 5(d)), it is possible to elucidate a different shape of the cells. PU cells are rounded-edge polyhedral pores whereas LDPE pores are sharpedge polyhedrons. Analysing the dependence of cell size with the foam density it is possible to find two different trends (Fig. 6). For PU foams, in which mean cell sizes are between 310 and 390 µm, there seem to be a relation between cell size and foam density, the cell size decreases as the foam density increases, whereas in the case of LDPE foams there is no correlation between these two parameters. The mean cell size in these materials is ranged between 260 and 320 µm. The different behaviour is caused by specific particularities of each foaming process. On one hand, in reactive foaming (PU foams) when the mixing conditions are fixed (pale, stirring velocity and time) the density can only be controlled by the amount of blowing agent. If stabilizing additives are also kept the constant coarsening and coalescence effect should take place similarly too [12, 13]. As a result, final cell size is slightly higher for less-dense samples and decreases with sample density. On the other hand, for gas dissolution foaming process the most important parameters to control cell size are the first stage pressure (in addition to the pressure release rate) and the temperature during the different steps. As a consequence, it is known that this process allows controlling in a precise and independent way density and average cell size and for this reason it is not expected to find out a relation between these parameters [14, 15]. Furthermore, foaming process also affects the cell size distributions (Fig. 7). All the specimens are likely mono-disperse because the cell size distributions contain a single peak. PU foams present wider distributions. This might be caused intrinsically by the reactive foaming process used to produce these foams, in which cells are nucleated at slightly different times and degeneration mechanisms (coalescence, coarsening, and drainage) promote the apparition of smaller (due to delayed nucleation) and larger cells (due to degeneration mechanisms). On the other hand, in gasdissolution foaming process nucleation of all the cells occurs in a very short period (when the pressure is released) and the high melt strength of the polymer (that is cross-linked before foaming) reduces the intensity of the degeneration mechanisms, leading to a more homogeneous cellular structure. Fig 6. Mean cell size versus relative density for all the samples under study. 4. X-ray Tomography Studies on Cellular Polymers 151 As it is shown by the error bars of Fig. 6 PU foams have in average a normalized standard deviation (ratio between standard deviation of the cell size distribution and average of a distribution) of 0.35 whilst it is only 0.17 for LDPE foams. In addition, PU foams show a cell size distribution that contains a tail at larger cells. These large cells might be caused by inclusion of external air bubbles during the mixing process of the two components. In addition, the anisotropy of the cells in the Z-direction has been analysed. We have selected this direction because it corresponds with the growing direction in the analysed foams. As it has been indicated before, we have employed the bounding box in order to calculate this parameter. To this end, we calculate the ratio between the cell size in Z direction - heightand the average value of two remaining (and equivalent) cell sizesX and Y directions– to calculate the anisotropy of every cell considered within the analysed volume. Then, the average value of the cell anisotropy considering all the cells in the analysed volume is calculated. As it is shown in Fig. 8, LDPE foams are isotropic in this direction but also in the other directions (results not shown). This fact is explained, once again, taking into account the specific foaming process. In this process the material expands in a free expansion process without any physical constrains. As a consequence, the foam is fully isotropic. However, PU foams are anisotropic with cells oriented in Z direction since the expansion in these materials takes place in a cylindrical mould that limits the expansion of the foam in the horizontal plane [15]. In addition there is a clear dependence with (a) (b) Fig. 7. Cell size distributions for all the samples under analysis. (a) PU foams and (b) LDPE foams. Fig 8. Anisotropy in Z-direction versus relative density for all the specimens in this work. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 152 density. Anisotropy increases when density is reduced. This dependence is explained since different amounts of blowing agent –waterwere included in polyol blends in order to obtain specimens with different density. Thus, less dense foams contain a higher amount of water that promotes quicker foaming process and in consequence a higher elongation of the cells in the growing direction of the foam. 3.2 Topological features The coordination number, which represents the number of neighbours of every single cell, is closely connected with the shape and size in-homogeneity of the cells. In our particular case (Fig. 9), there are clear disparities in the coordination number. In both cases, foams contain cells with a high variation of cell shapes. It is possible to detect cells with geometries such as cubic (ni=6), octahedral (ni=8), dodecahedral (ni=12), tetrakaidecahedral (ni=14), or even icosahedral (ni=20). The most probable value of the coordination number is around 12 or 14, for PU or LDPE foams respectively (Fig. 9). This interesting result indicates that in average cells in PU foams can be modelled as pentagonal dodecahedrons while a likely tetrakaidecahedral shape should be considered for modelling LDPE foams [16]. In contrast to the precedent parameters, foam density does not affect the cell geometry since all the distributions are very similar in shape. Calculated values of cell density via tomographic methods (NvTOMO) are ranged between 104-105 cells/cm3 (Table 2), which are expected values for cell sizes previously measured [17]. In addition, LDPE foams contain a higher number of cells per unit volume due to both its lower density and reduced cell sizes in comparison with PU samples. (a) (b) Fig. 9. Coordination number distributions for (a) PU foams and (b) LDPE foams under study. The dashed line corresponds to a coordination number of 12 in PU foams and 14 in LDPE foams. Table 2. Cell density values determined by Xray μ-CT of samples of this study. Sample NvTOMO (cells/cm3) Sample NvTOMO (cells/cm3) PU-1 2.2·104 LDPE-1 5.4·104 PU-2 3.1·104 LDPE-2 8.0·104 PU-3 3.8·104 LDPE-3 8.6·104 PU-4 4.1·104 LDPE-4 4.1·104 4. X-ray Tomography Studies on Cellular Polymers 153 Also packing of the sharp-edged polyhedral cells is expected to be higher complementary contributing to a higher cell density. 3.3 Solid phase analysis Clear differences in the solid material distribution can be observed in Fig. 10 (a) and (b) in the 3D rendering of the solid phase of typical cells. We will use the extracted data for material thickness distribution (Fig. 10, (c) and (d)) to objectively compare the specimens in this work. Results for two foams with similar densities based on a different polymer matrix are shown in this figure. It can be observed that PU foams present much more asymmetric material thickness distributions. Due to this reason, we have used asymmetric lognormal functions for processing peak deconvolution and final data fitting. The high amount of material concentrated in the struts will output high values for fs next to one. In the case of LDPE foams, the thickness distributions are concentrated in much lower values, having a higher weight in the zone of low thickness with rather overlapped peaks. As a consequence, the solid material is well distributed along the entire structure of the foam, resulting in low fractions of mass in the struts. In addition, for LDPE foams it is possible the use of symmetric functions (combination of two Gaussian curves) to have a more accurate fitting of the experimental data. This difference in the structure of the solid phase and therefore between material thickness distributions for the two kinds of foams under study is explained again (a) (b) (c) (d) Fig. 10. 3D rendering of the separated solid phase (a) and (b), and material thickness distributions (c) and (d) for PU-1 and LDPE-3 samples respectively. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 256 separate factors. On one hand, the anisotropy characterized by tomography varies around 10-16% for the samples themselves. On the other hand, the thickness of the tested samples (5 mm) involves the interaction of light with roughly around 13 cells (considering cell sizes of 400 μm, the average value for the selected samples). In this travel through the material, light could encounter cells with different anisotropy values and finally resulting in not perfectly output. In fact, considering these two obstacles the obtained results are so accurate to consider these measurements as a confident methodology to calculate pore anisotropy. 4. Conclusions In summary, this paper presents the results of characterizing the cell anisotropy by analysing the dimensions of the transmission pattern through cellular polymer slabs. In addition, the cell anisotropy was also determined by means of X-ray tomography in order to evaluate the accuracy of the obtained results. Three different cellular polymers have been tested in the three space planes obtaining reliable relationships between the two characterization methods. Consequently, the methodology presented within this manuscript is valid for a fast, easy and straightforward characterization of cell anisotropy of cellular polymers, even for in-situ experiments. Materials with different densities, thickness and cellular architectures (cell sizes and anisotropies) will be studied in further investigations in order to verify the global applicability of the developed methodology. Acknowledgements Financial assistance from MINECO and FEDER program (MAT2012–34901) MINECO, FEDER, UE (MAT2015-69234R) and the Junta de Castile and Leon (VA011U16) are gratefully acknowledged. Predoctoral contract of S. Perez-Tamarit by University of Valladolid and Banco Santander (E-472015-0094701) is acknowledged. References [1] L.J. Gibson, M.F. Ahsby, Cellular Solids: Structure and Properties, Pergamon Press, Oxford, England, 1988. [2] A. Cunningham, N.C. Hilyard, Low Density Cellular Plastics: Physical Basis of Behaviour, Ed. Chapman and Hall, London, 1994. [3] L. Oliveira-Salmazo, A. Lopez-Gil, F. SilvaBellucci, A.E. Job, M.A. Rodriguez-Perez, Natural rubber foams with anisotropic cellular structures: Mechanical properties and modeling, Industrial Crops and Products, 80 (2016) 26-35. [4] S. Estravís, J. Tirado-Mediavilla, M. SantiagoCalvo, J.L. Ruiz-Herrero, F. Villafañe, M.Á. Rodríguez-Pérez, Rigid polyurethane foams with Fig. 4. Relationship for the cell anisotropy using both tomography slices and transmission patterns showing the good agreements of the light transmission anisotropy characterization. 6. Light Scattering in Solid Cellular Polymers 257 infused nanoclays: Relationship between cellular structure and thermal conductivity, European Polymer Journal, 80 (2016) 1-15. [5] J. Pinto, E. Solorzano, M.A. Rodriguez-Perez, J.A. de Saja, Characterization of the cellular structure based on user-interactive image analysis procedures, Journal of Cellular Plastics, 49 (2013) 555-575. [6] Y. Mu, G. Yao, H. Luo, Effect of cell shape anisotropy on the compressive behavior of closedcell aluminum foams, Materials & Design, 31 (2010) 1567-1569. [7] S. Pardo-Alonso, E. Solórzano, S. Estravís, M.A. Rodriguez-Perez, J.A. de Saja, In situ evidence of the nanoparticle nucleating effect in polyurethane– nanoclay foamed systems, Soft Matter, 8 (2012) 11262. [8] K.S. Lim, M. Barigou, X-ray micro-computed tomography of cellular food products, Food Research International, 37 (2004) 1001-1012. [9] D. Klempner, K.C. Frisch, Handbook of polymeric foams and foam technology, Passavia Druckerei GmbH Passau1991. [10] E. Solórzano, J. Pinto, S. Pardo, F. GarciaMoreno, M.A. Rodriguez-Perez, Application of a microfocus X-ray imaging apparatus to the study of cellular polymers, Polymer Testing, 32 (2013) 321329. [11] K. Mader, R. Mokso, C. Raufaste, B. Dollet, S. Santucci, J. Lambert, M. Stampanoni, Quantitative 3D characterization of cellular materials: Segmentation and morphology of foam, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 415 (2012) 230-238. 6. Light Scattering in Solid Cellular Polymers 259 References [1] D.J. Durian, D.A. Weitz, D.J. Pine, Multiple Light-Scattering Probes of Foam Structure Dynamics, Science, 252 (1991) 686-688. [2] M.U. Vera, A. Saint-Jalmes, D.J. Durian, Scattering optics of foam, Applied optics, 40 (2001) 4210-4214. [3] A. Cunningham, N.C. Hilyard, Low Density Cellular Plastics: Physical Basis of Behaviour, Ed. Chapman and Hall, London, 1994. [4] L.J. Gibson, M.F. Ahsby, Cellular Solids: Structure and Properties, Pergamon Press, Oxford, England, 1988. [5] D.F. Swinehart, The Beer-Lambert law, Journal of Chemical Eduacation, 39 (1962) 333-335. [6] C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles, WILEY‐ VCH Verlag GmbH & Co. KGaA1983. Chapter 7 X-ray Tomography and Light Scattering in Non-Conventional/ Nanocellular Polymers 7. X-ray Tomography and Light Scattering in Non-Conventional/Nanocellular Polymers 263 As commented in previous chapters, nanocellular polymers are a novel class of cellular materials with impressive enhanced physical properties [1-4]. These materials have been developed in the recent decades by mainly gas dissolution foaming. As a consequence, the development of novel or modified characterization techniques is required for the accurate study of these materials. In this respect, the two involved techniques during this investigation have been applied for the study of nanocellular polymers. This Chapter deals with the main experimental results of these characterizations. On one hand, two of the main nano-imaging techniques were selected to perform nano computed Tomography (n-CT) [5, 6]. On the other hand, the samples were tested in our equipment to measure optical transmissivity finding the first evidences of the possibility of manufacturing transparent nanocellular polymers. 7.1 Nano-tomography applied to nanocellular polymers As well as in the micrometre range, X-ray Tomography is a powerful technique that allows the structural inspection in 3D. However, the experimental set-up and the involved interaction mechanisms for n-CT are much more complicated than in the case of μ–CT. In this respect, two different kinds of techniques dominate in the case of imaging with nanometre spatial resolution: X-ray transmission microscopy (TXM) and coherent diffraction imaging (CDI) depending if the imaging is accomplished in the real or reciprocal space respectively. The main principles of both techniques and the obtained results are addressed in the following paragraphs. These experiments were carried out in I13 beamline at Diamond Light Source synchrotron (Oxford, UK). 7.1.1. Zernike phase contrast X-ray transmission microscopy (TXM) In transmission X-ray microscopy (TXM) Fresnel zone plates (FZP) are employed as high resolution X-ray optics. These are circular diffraction gratings with radially decreasing line spacing. The X-ray beam is condensed onto the object in a region of approx. 50 μm thus increasing the photon density several orders of magnitude. The numerical aperture of the illumination is well matched with the aperture of the objective FZP by means of an order sorting aperture (OSA). The objective FZP guides Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 264 the transmitted beam to an image plane in which the detector is located. In order to avoid radiation damage in the high sensitivity detector by the direct undiffracted beam a central stop (CS) manufactured of a high absorption material (of typically 500 μm of diameter) is located before the condenser (Figure 7-1). The interaction of X-rays with structures in a sample leads to the generation of diffracted light in addition to the direct beam passing through the sample. According to Abbe theory, diffracted light from an object is required for image formation in a microscope. However, the reduced phase shift in typical phase contrast imaging results in a very weak contrast for the sample structure in TXM. For this reason, to obtain valuable contrast it is required according to Zernike to phase shift the undiffracted light [7-9]. This is accomplished with a phase shifting optical element located in the back focal plane of the objective. By these means, the direct beam can be phase shifted either 90º (positive phase shift) or 270º (negative phase shift). This kind of X-ray optical configuration permits reaching effective pixel sizes up to 50 nm. Figure 7-1. Basic scheme of a TXM optical equipment. This configuration, joined to a high precision rotation stage, permits reaching n-CT with effective pixel sizes up to 50 nm. During the research stay carried out at Diamond synchrotron a collection of TXM tomographies were performed at 100 nm effective pixel size. In those experiments 3 reference images (at 0º, 90º and 180º of rotation) were acquired before and after the tomography in order to evaluate the stability of the sample during the process. In our case, the high X-ray flux concentrated onto the sample provokes a temperature 7. X-ray Tomography and Light Scattering in Non-Conventional/Nanocellular Polymers 265 increase that provokes the sample expansion and thus drifts in the projections that hindered the correct reconstruction of the tomographies (Figure 7-2). Figure 7-2. TXM projections and drift in a nanocellular polymer with 780 nm cell size and 0.5 of relative density. Only in two samples the induced expansion was as small as required to obtain an acceptable reconstruction. However, in both cases the mean cell size of the samples was 225 nm therefore hindering the correct observation of the cells using 100 nm of effective pixel size (Figure 7-3). For this reason, it is required another technique that does not require the focus of the beam onto the sample, the scanning coherent diffraction microscopy, also called ptychography. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 272 with a temperature profile set from 160 ºC to 200 ºC, and the screw speed equal to 40 rpm. Solid sheets (4 mm thick) from the extruded material were produced by compression molding using a hot plate press provided by Remtex (Spain). The temperature set on the press was 250 ºC and processing time was 9.5 minutes, 8.5 for melting the polymer and 1 minute more for compression under pressure (1.7 MPa). From these sheets, squares of 25x25 mm2 were cut for the foaming experiments. Cellular material was produced using a two-step foaming process in a highpressure vessel (model PARR 4681) provided by Parr Instrument Company. The pressure was set to 6 MPa and it is controlled via a pressure pump controller (model SFT-10) provided by Supercritical Fluid Technologies Inc. The temperature was fixed at 25 ºC, and it was kept constant with a clamp heater controlled with a CAL 3300 temperature controller. The foaming step was carried out in a thermal bath with water. The foaming temperature used to was 40 ºC. The foaming time was 1.5 minutes. A SEM image of foamed specimen is shown in Figure 1. 2.3. X-ray ptychography at I13-1 (Diamond Light Source) Ptychography is a scanning coherent diffraction imaging (CDI) technique in which the sample is scanned perpendicular to the path of X-ray beam, collecting diffraction patterns at each point. As a mandatory condition, there is always enough overlap of probe between adjacent points. The resulting far-field diffraction patterns are then processed through iterative phase retrieval algorithms to obtain high resolution, phase contrast projections [22]. A natural extension of two dimensional ptychographic imaging is the so-called ptycho-tomography, a combination of ptychography with tomography. We exploit the high resolution 2D ptychographic projections obtained at various angles as a starting point which are then taken through the conventional tomographic process of alignment and 3D reconstruction thus obtaining a threedimensional reconstruction of the sample under study. Ptychographic imaging was carried out at the I13-1, the coherence branchline of the I13 beamline at Diamond light source, UK [18]. The samples were imaged with X-rays at a photon energy 9 keV and 0.05s exposure time per diffraction pattern. The detector to sample distance was ~7 m. The photon counting Excalibur detector with a pixel size of 55µm and ~2000x1800 pixels2 was used [23]. Other elements Fig 1. SEM micrograph of the sample under study. 7. X-ray Tomography and Light Scattering in Non-Conventional/Nanocellular Polymers 273 such as a zone plate (FZP), beam-stop (CS), and order sorting aperture (OSA) were employed to obtain a X-ray probe in order to illuminate the sample (as schematically shown in Figure 2). The effective reconstruction pixel size in this geometry was 133nm. 600 projections were collected to finally reconstruct the 3D volume. 3. Results and Discussion The main characteristics (density and cell size) of scanned sample have been determined by classical procedures and are summarized in Table 1. The bulk density has calculated using the Arquimedes’ water-displacement method. Further, the cell size has been obtained analyzing SEM images (Figure 1) by a self developed tool [24] in imageJ/Fiji image analysis environment [25, 26]. Focusing on the ptychography scan, observing the shown projection (Figure 3 left) it is possible to observe several parts on the sample that are totally visible observing the ptycho-tomography reconstruction (Figure 3 right). Due to the high relative density of the sample (0.65) and the particularities of the gas dissolution foaming, the sample owns both solid and foamed parts, not a continuous foamed specimen with high density. In the case of the cellular part of the sample, we can conclude that even the thinnest parts of the structure are well reconstructed with the selected effective pixel size of 133 nm. In addition, a qualitative inspection of the tomography volume outputs a relative density of 0.7 and a mean cell size of (3.1±1.5) μm, which are in concordance with measurements of bulk density and analysis of the cell size by means of SEM images (in 2D). 4. Conclusions A combination of X-ray ptychography and tomography (ptycho-tomography) has been used to visualize the structure of Fig. 2. Schematic of the ptychography elements and geometry present at I13-1 beamline of Diamond Light Source (from [21]). Table 1. Sample included in this study Density [kg/m3] Mean cell size [μm] 760 2.3±1.2 Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 274 non conventional cellular polymers for the first time. Due to the unique characteristics of the used technique tomography experiments with 133 nm of effective pixel size have been performed. As a result, even the thinnest parts of the solid structure of the scanned samples. In addition, thanks to phase information obtained in ptychographic projections the final reconstructions owned also suitable contrast even for low absorbing and diffracting materials such as amorphous PMMA, used as raw material for the selected cellular materials. With the results of this manuscript in mind and knowing the potential of ptychography to reach spatial resolutions of 10 nm, the inspection presented here will be applicable for scanning more challenging samples with reduced cell size. Acknowledgments Financial assistance from MINECO and FEDER program (MAT2012–34901) MINECO, FEDER, UE (MAT2015-69234R) and the Junta de Castile and Leon (VA035U13) are gratefully acknowledged. Predoctoral contract of S. Perez-Tamarit by University of Valladolid and Banco Santander (E-472015-0094701) is also acknowledged. Financial support from Junta de Castile and Leon (Grant Paula Cimavilla) (Grant Judith Martín-de León) and from Spanish Ministry of Education (FPU grant FPU14/02050, Victoria Bernardo) is gratefully acknowledged. We thank Diamond Light Source for access to beamline I13 (proposal MT17625-1) that contributed to the results presented here. References [1] L.J. Gibson, M.F. 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Pinto, E. Solorzano, J.A. de Saja, M. Dumon, M.A. Rodríguez-Pérez, Experimental validation of the Knudsen effect in nanocellular polymeric foams, Polymer, 56 (2015) 57-67. [8] B. Notario, J. Pinto, R. Verdejo, M.A. RodríguezPérez, Dielectric behavior of porous PMMA: From the micrometer to the nanometer scale, Polymer, 107 (2016) 302-305. [9] B. Notario, A. Ballesteros, J. Pinto, M.A. Rodríguez-Pérez, Nanoporous PMMA: A novel system with different acoustic properties, Materials Letters, 168 (2016) 76-79. [10] S. Pérez-Tamarit, B. Notario, E. Solórzano, M.A. Rodriguez-Perez, Light transmission in nanocellular polymers: Are semi-transparent cellular polymers possible?, Materials Letters, 210 (2018) 39-41. [11] C. Forest, P. Chaumont, P. Cassagnau, B. Swoboda, P. Sonntag, Polymer nano-foams for insulating applications prepared from CO2 foaming, Progress in Polymer Science, 41 (2015) 122145. [12] D. Miller, V. 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X-ray Tomography and Light Scattering in Non-Conventional/Nanocellular Polymers 277 Several physical properties have been already studied on nanocellular polymers such as mechanical [2], thermal [3], dielectric [4], or even acoustic properties [13]. These novel materials have shown enhanced properties in comparison with similar materials but with cells sized in the micrometre range. Nevertheless, the optical properties of such kind of materials have been scarcely considered. For this reason, one part of this Thesis has been focused in the study of optical behaviour of nanocellular polymers. 7.2 Light Scattering in nanocellular polymers. Transparency Among all the possible existing parameters in order to characterize the optical properties we have selected the optical transmissivity (T). The simplicity for measuring this parameter permitted us evaluating the effect of changing the scale of the cell size in cellular polymers. To this end, a collection of cellular polymers based on PMMA was selected for this work with similar relative density (~0.5) and cell sizes from 11 μm to 30 nm. The experimental details and the obtained results about this investigation are detailed in the following paragraphs. The work entitled “Light transmission in nanocellular polymers: are semi-transparent cellular polymers possible?” shows how decreasing the cell size of cellular polymers up to nanometre range it will be possible to manufacture cellular polymers with valuable transparency. 7. X-ray Tomography and Light Scattering in Non-Conventional/Nanocellular Polymers 279 Materials Letters 210 (2018) 39-41 http://dx.doi.org/10.1016/j.matlet.2017.08.109 Light transmission in nanocellular polymers: are semi-transparent cellular polymers possible? S. Pérez-Tamarit*, B. Notario, E. Solórzano, M.A. Rodriguez-Perez CellMat Laboratory, University of Valladolid, Paseo de Belén 7 47011, Spain * Corresponding author: [email protected] Tel.: +34 983 423572; fax: +34 983 433192 Abstract This work presents the light transmission through a collection of solid cellular polymers based on poly (methyl methacrylate) (PMMA) with cells sizes covering the micro and nano-scale. The obtained results showed that the behavior of light transmission when cell size is in the nano-scale is opposite to the one shown by microcellular foams or the one predicted by theoretical models of light scattering (LS). In fact, the expected trend is that a reduction of cell size increases the opacity of the samples. However, for nanocellular polymers based on amorphous polymers reducing the cell size increases the light transmission. Therefore, this result indicates that a further reduction of the cell size could result in cellular polymers optically semi-transparent. Keywords: polymers; poly (methyl methacrylate); light transmission; nanocellular foams; porous materials. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 280 1. Introduction Nano-cellular polymers represent a new kind of materials which have attracted the attention of the scientific community in the last years due to their surprising properties [1, 2]. Nowadays, some papers have been published on the thermal [3], acoustical [4], mechanical [5] or dielectric [6] properties of these materials showing promising results. However, the optical properties of these materials have been less considered [7]. Moreover, similar materials as those studied in this work are silica aerogels [8]. An aerogel is an open-celled, mesoporous, solid cellular material that is composed of a network of interconnected nanostructures. It exhibits a porosity (non-solid volume) greater than 50% and cells with sizes in the nano-scale (ca. 50nm) [9]. These materials have a combination of properties that no other cellular material possesses simultaneously [10]. For instance, silica aerogels have very low densities and thermal conductivities (Knudsen effect), among other extraordinary properties [11, 12]. In addition, these materials, produced from transparent solid matrix (silica) and with pores in the nano-scale, are almost transparent to light in the optical wavelength range (400-750nm) [9]. Therefore the aim of this paper is to study the optical properties of nanocellular polymers produced from an amorphous polymer (PMMA) trying to elucidate if reducing the cell size to the nanoscale could induce some transparency in the materials. To this end light transmission (T) through samples has been measured. This property characterizes the transparency of the materials. Transmissivity (T) is defined as the ratio between transmitted (I) and incident (I0) intensity reaching the light detector (Eq. 1). ⁄ (1) 2. Experimental 2.1 Materials The PMMA was kindly provided by Altuglas-Arkema Company (France) in the form of pellets. The material used presents a glass transition temperature (Tg) of 115ºC, density (ρs) of 1180kg/m3 and due to its amorphous structure a high transparency. 2.2 Samples production PMMA pellets were first dried in a vacuum furnace (680 mm Hg) at 80ºC during 4h. Then, the pellets were molded into precursors of 155x75x4mm3 by using a two-hot plate press. The temperature of the press was fixed at 250ºC. The material was molten without pressure for 9 minutes, then it was compacted under a constant pressure of 21.8bar for another minute and finally it was cooled under the same pressure. Foaming experiments were performed in a pressure vessel (PARR4681, Parr Instrument Co.). The pressure system comprises an accurate pressure pump controller (SFT-10, Supercritical Fluid Technologies Inc.). The vessel is equipped 7. X-ray Tomography and Light Scattering in Non-Conventional/Nanocellular Polymers 281 with a clamp heater (1200W) controlled via a CAL3300 temperature controller. Therefore, a collection of experiments were implemented following the solid state foaming process [3, 13]. The pressure and temperature were selected in order to produce four samples with cells in the micrometer range (ϕ>500nm) and five materials with cells in the nanoscale (ϕ<500nm). The analyzed foamed specimens (12x12x1mm3) were prepared by using a precision buzz saw. 2.3 Characterization techniques Density of the samples was measured by the water-displacement method using the density determination kit for an AT261 Mettler-Toledo balance. Relative density (ρr) is calculated as the ratio between cellular material density (ρf) and solid polymer density (ρs) resulting for all analyzed samples values close to 0.5 (Table 1). Although the effect of sample density is corrected in transmissivity theoretical models, comparing samples with similar densities is crucial to obtain accurate conclusions. Cellular structure was determined using a scanning electron microscope (JSM820, Jeol and Quanta 200FEG). Samples were cooled in liquid nitrogen, fractured and finally coated with gold using a sputter coater (SCD005, Blazers Union) for the microscopic visualization. Microscopy images were analyzed using a selfdeveloped application [14] based on ImageJ/Fiji image analysis software [15]. Microcellular materials with cell sizes between 1-11μm have been selected (Fig. 1 right). The nanocellular samples have cell sizes ranging 25-400nm (Fig. 1 left). Fig. 1. Micrographs of the two kinds of samples. Nanocellular (25-400nm) –leftand microcellular (0.811μm) –right-. Samples are Nano-3 and Micro-4. Table 1. Labels, cell size (ϕ), density (ρr) and relative density of samples under study. Sample ϕ (nm) ρ (kg/m3) ρr Nano-1 25 625.4 0.53 Nano-2 90 568.9 0.48 Nano-3 200 531.5 0.45 Nano-4 350 508.1 0.43 Nano-5 400 519.2 0.44 Micro-1 820 623.3 0.53 Micro-2 1080 638.6 0.54 Micro-3 7000 592.8 0.50 Micro-4 11000 649.0 0.55 8. Conclusions and Perspectives 289 8.1 Conclusions This final chapter presents the main conclusions that have surged from this thesis as well as the most remarkable achievements of the investigation. This investigation was built around three main objectives: o The application of X-ray tomography to reveal the process-structure-properties relationship on microcellular polymers. o The development and application of a novel non destructive technique for the characterization of cellular polymers based on Light Scattering methodologies. o The application of both techniques on nanocellular polymers for the first time. Therefore, the main conclusions of this thesis are closely related with these objectives and separated in three great groups, X-ray Tomography, Light Scattering and Application on nanocellular polymers. 1. X-ray Tomography We have design and upgrade the X-ray imaging system located in CellMat laboratory into a μ-CT scanner allowing the acquisition of tomograms with up to 2.5 μm/pixel resolution and optimum image contrast for the study of cellular polymers. In addition, this upgrade is totally compatible with the established radioscopy set-ups of the X-ray imaging system resulting in a unique and versatile characterization equipment of cellular polymers. With this system it was possible to develop detailed structural characterizations of the cellular structure of several kinds of cellular polymers focusing on the gas phase (cell size, anisotropy, neighbourhood distribution and cell density) due to the limitations of spatial resolution. Moreover, the cell size and anisotropy tomographic values obtained in our X-ray μ-CT scanner have been used to evaluate the reliability of the Light Scattering results. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 290 Furthermore, the experimentation has been completed by means of synchrotron campaigns in different European facilities such as Swiss Light Source (SLS, Switzerland) and Bessy II (Germany). On one part of these experiments (Bessy II) we were able to increase the spatial resolution of the acquired tomograms (up to 0.45 μm/pixel), allowing the reconstruction of the thinnest parts of the cellular structure on conventional low density cellular materials. Therefore, by using specific and advanced image analysis protocols developed during this investigation based on analysing the material thickness distributions a detailed characterization of the solid phase of these materials has been carried out. The analysed parameters were the fraction of material in the struts and the thickness of different parts of the structure (walls and struts) and also the full structure average thickness. Combining these results with the in-house system results a full detailed characterization could be obtained nowadays. In addition, by using these tomographies we were able to compute the solid structure corrugation of low density flexible cellular polymers and to evaluate and model its influence on both thermal and mechanical properties of these materials (thermal expansion coefficient and collapse stress respectively). On the other hand, synchrotron experiments on SLS enabled the study of cell nucleation and growth on cellular polymers for the first time in 3D. The increased temporal resolution in this facility allows acquiring tomography sequences at 20 Hz rate. In our particular case, the used rate (6 Hz) was selected in order to follow the foaming dynamics of both nanocomposite and pure PU with suitable temporal (156 ms/tomography) and spatial resolution (3.2 μm/pixel). 2. Light Scattering During this investigation it was possible to develop a novel theoretical model of Light Scattering applied to solid cellular polymers in a semi-empirical way. In that model the influence of light absorbed by the material is considered, in opposite to Light Scattering models for aqueous cellular systems in which the absorption is considered negligible. A collection of semi-transparent (non-coloured) cellular polymers based on PE, PU and PS with different cell sizes (200-1000 μm) and densities (15-110 kg/m3) was considered. The experimental output of this model was compared with X-ray 8. Conclusions and Perspectives 291 tomography results obtaining good findings in all cases, with variations in cell size below 20%, which is the typical width of cell size distributions on such kind of cellular polymers. The light diffusion within the material provokes the widening of the light beam forming a light halo in the output of the sample that grows with sample thickening. This fact forced us to change the light detector from a photodiode coupled to an integration sphere to a digital camera. Therefore the field of view of our system changed from 12.7 mm (window size of the photodiode) to the full surface of the sample, registering the transmitted light from all the points of the surface of the sample. With these findings, a milestone of this investigation was the design and building of a dedicated laboratory equipment for the characterization of solid cellular polymers by means of Light Scattering. On the other hand, using the digital camera as light detector we were able to measure the spatial dimensions of the transmitted light halo in the surface of the sample. Analysing its anisotropy and the cellular anisotropy of the material on the perpendicular plane to the light beam propagation direction we found that both anisotropy values are closely related. Therefore, cellular anisotropy is obtained also by means of Light Scattering methodologies. The possibility of measure both cell size (linked to the transmitted light intensity) and cellular anisotropy (linked to the relative geometry of the transmitted beam) encouraged us to patent Light Scattering as a valid methodology for the structural characterization of semi-transparent solid cellular polymers, as final conclusion of this investigation regarding Light Scattering. 3. Application on nanocellular polymers Nanocellular polymers are a new class of cellular materials. In consequence, novel techniques must be developed or adapted in order to characterize them. In regard to Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 292 this fact, this investigation is completed by applying the two used techniques, suitably adapted, to this kind of materials. On one hand, X-ray n-CT techniques (with spatial resolution around 100 nm/pixel) have been considered for the 3D structural characterization of these materials. These experiments were carried out at Diamond Light Source (United Kingdom) during both the research stay corresponding to this thesis and a synchrotron measurements campaign. The obtained results represent the first reported 3D characterization of nanocellular polymers in which the gas phase of these materials with varied characteristics is analysed in detail. On the other hand, a collection of nanocellular polymers with constant relative density and different cell size (30-11000 nm) permitted us elucidating that in the micrometer range (ϕ>800 nm), the higher is the cell size, the higher is light transmissivity whereas in the nanometer range (ϕ<800 nm) the tendency is the opposite. The lower is the cell size; the higher is the light transmissivity. This result is one of the first evidences about the possibility of manufacturing transparent nanocellular polymers. 8. Conclusions and Perspectives 293 8.2 Perspectives We have presented the capabilities of two different characterization techniques, X-ray and Light Scattering. In the case of X-ray Tomography, this is a continuation and confirmation of a previous thesis about the application of this kind of technique on cellular materials research. We have demonstrated how this technique is a powerful tool to understand the mechanisms governing the process-structure-properties relationship in cellular polymers, even in novel nanocellular materials. For this reason, we think in the following topic to even extend the capabilities of this technique: - Develop novel image analysis protocols for the detailed structural characterization of foams in an easier way. In particular, analysis routines that allow calculating parameters concerning the solid phase in conventional X-ray tomographies (subresolution). - Continue investigating the possibilities on nanotomography for the 3D characterization of nanocellular polymers, in particular, further increasing the spatial resolution. - Evaluate other features of the solid phase of cellular materials such us tortuosity, connections between cells etc… - New experiments about 4D imaging could be conceived and carried out thank to the improvements of synchrotron facilities. - Apply the developed methodologies to materials based on other solid matrices such as glass, metals, etc… - Push the limits of the actual X-ray μ-CT system to increase the spatial resolution up to 1 μm/pixel. On the other hand, this is the first investigation in CellMat about Light Scattering applied to the structural characterization of solid cellular polymers. As this technique has been proved to be a powerful tool to extract in an easy way fundamental structure features of cellular polymers, we expect that this dissertation could be a reference Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 294 book and a starting point for new research works, focused probably in the following topics: - Investigate factors none contemplated during this thesis such as the influence of particles (type, size and shape), colour of the samples, etc… on the Light Scattering response and model the corresponding behaviour. - Combine X-ray radiography and Light Scattering to obtain surface distributions of density and thus cell size. - Develop a novel theoretical model that allows determining the cell size even in the case of nanocellular polymers. Annex Other Applications of X-ray Imaging Techniques Annex. Other Applications of X-ray Imaging Techniques 297 In the last Chapter of this Thesis, listed as an additional Annex to the main results of this research, other applications of X-ray imaging techniques are summarized. These two works are none directly related with the main subject of the Thesis but also intends to characterize key factors in the cellular materials scientific framework. On one hand, as previously commented throughout this Thesis the fast, simple and accurate determination of mean cell size is crucial since most of physical properties of these materials strongly depend on this parameter. For this reason, in addition to Light Scattering, this investigation was focused on developing a novel methodology to extract quantifiable values of mean cell size of X-ray transmission images (radiographies) making use of the Fast Fourier Transform (FFT). A.1 Cell size determination in X-ray transmission images It is well known that Fourier transform procedures are capable to determine the size, shape and number density of spherical particles distributed in a projected image in a volumetric monodisperse distribution of particles [1]. In fact, the two dimensional Fourier transform of a circularly symmetric object corresponds essentially to the Hankel transform of order zero [2]. It has been previously demonstrated that the frequency of oscillation of the Hankel transform in such cases corresponds with the size of the entities in the volume [3]. Nevertheless, the polydispersity of the size distribution of particles in the volume hinders the correct visualization of several peaks on the Hankel transform plot and only the first peak is available to extract valuable information. Making use of the penetration power of X-rays it is simple to obtain 2D projections (radiographies) of a volumetric sample (Figure A-1). In fact, radiographies of cellular materials, adequately treated, seem a non-monodisperse distribution of quasi-circular particles. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 304 imaging up to 9 fps (at 4x4 pixel binning). Finally a frame grabber records the radiography sequences for later image processing. The setup is customized for low absorbing materials such as polymers and typically works at low energies 20-60 kV and high currents 100-200 μA in order to achieve an optimum contrast keeping small exposure times (600ms, typically) and high acquisition rates (1.66 fps). Nonetheless, in the case of very low dense samples (density about 25-30 kg/m3) the weak absorption of X-rays results low contrast radiographs. Particularly, for this study the X-rays source parameters were 45 kV, 140 µA, the exposure time was 1500 ms and magnification used is 2 times with effective pixel size of 25 microns by using a source-detector distance of 580 mm and source-object distance of 290 mm. Additional measurements have carried out considering a magnification 4 times with effective pixel size of 12.5 microns by using a source-object distance of 145 mm maintaining constant the sourcedetector distance. A 3D drawing of the Xray imaging system is shown in (Fig 4). 2.4 Fast Fourier algorithm The methodology is similar to the one described by [3]. In this methodology the pore size (ΦFFT) is analysed in the Fourier space after removing the grey level fluctuations in the background (density in-homogeneities in the meso-scale). This step was done by using a high-pass filter based on large 2D median filter (15 pixels neighbourhood) and subsequently subtracting the original image from the filtered one. The output image was analysed in the reciprocal domain. The radial profile in Fourier space is plotted, then smoothed (5 pixels of SavitzkyGolay filter [15]) and finally, the spatial frequencies corresponding to the average pore size are identified as a broad peak. The peak position is identified by an automatic Gaussian fit, which allows evaluating the peak position with statistical accuracy. To this end, a MATLAB language algorithm was implemented using a commercial software package (MATLAB 8.2, The MathWorks Inc., Natick, MA, 2013). A resume of this procedure can be found in (Fig. 5). In this algorithm, different parameters may be fixed by the user (2D median filter index, smoothing filter index and name of the experiments) and Fig. 4. Microfocus cone beam radiography setup. Fig. 5. Scheme of FFT algorithm procedure. Annex. Other Applications of X-ray Imaging Techniques 305 others are required for output calculations (pixel size of the setup of the images in study). In addition, the algorithm permits to select between two different modes to analyse the collection of images, one for foaming experiments (or spatial correlation between consecutive images) and another for a collection of different samples. The maximum of data analysed nowadays is a collection of 507 images with 700x700 pixels size [16] taking 437s of full-process time with successful results. 3. Results and Discussion 3.1 Simulation of monodisperse particle distributions The first step and the main motivation of this methodology concern the simulation of a collection of hand-draw images with the particularity of containing monodisperse distributions of particle size. To this end, the algorithm described in the previous section was applied ignoring the 2D median filter in order to avoid blurring in the borders of the particles. The images under study consist in five different images varying the particle size in each of them, from 10 to 40 pixels, but not the position of each point in the images. The collection of images is shown in (Fig. 6). Once implemented the FFT algorithm to these images, radial plots of reciprocal space images can be represented (Fig 7.a) and, by identification of the position of the first oscillation peak in every image, a first correlation between selected particle size and these position can be found (Fig 7.b). Furthermore, due to the foregoing correlation, it is possible to develop a new and better correlation taking into account the inverse value of first position peaks in radial plots (or associated spatial frequency to this point in the Fourier space) (Fig 7.c). The oscillations Fig. 6. Succession of images used in the simulation in order to verify the validity of FFT procedures to correlate mean particle size with the response measured by the FFT based algorithm. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 306 presented in (Fig. 7.a) corresponds to the first order Hankel transform. In addition, the correlation between particle size and the inverse of the first peak position is almost perfect, which may be principally due to two reasons. First, all the particles in the succession of images are located in the same positions, that introduce less level of noising in the radial profiles and the second one, as it has been mentioned above in the manuscript, the polydispersion in the particle size distributions provokes that the radial profiles loses the oscillations to become only one peak. As it is shown in (Fig 7.a) and also in (Fig 7.c) the frequency of spatial oscillations in the reciprocal space increases linearly as the particle size become higher in each image. Therefore, in the case of real foams, it will be possible to correlate mean pore size with the spatial frequency associated to the first oscillation (and single oscillation, due to cell size distribution) in the radial plots of the reciprocal space images. To this end, several parameters of foams were taken separately in the analysis. First of all, the influence of sample density (four groups of samples, depending on described formulations in previous sections) in FFT algorithm response was analysed, secondly, the parameter under study was the mean pore size of the different foams (3 different values, depending mainly on stirring conditions) and finally, the effect of overlapping of pores in the final response was also studied. In addition, the applicability of this procedure in foaming process radioscopy experiments was complementarily analysed. 3.2 Influence of foam density In X-ray imaging, contrast in the transmission images is due to differences in X-ray absorbance of the material under study [17]. The absorbance of X-rays of Fig. 7. (a) Radial plots of reciprocal space images of (Fig. 6). (b) Representation of the particle size versus first oscillation peak of the radial plot for each image and (c) Representation of particle size versus the spatial frequency associated to first oscillation peak for every image. Annex. Other Applications of X-ray Imaging Techniques 307 the material is related with sample density and thickness via Lambert-Beer law [18]: ( ) ( ) (2) where ρ(x,z) is the density of the system, t is the sample thickness in the beam direction assumed to be constant, μ is the attenuation coefficient and I0 is the initial beam intensity. Thus, higher is the foam density under study; better is the contrast in X-ray transmission images. This fact causes that samples with highest density (100 kg/m3) have a superior response in measured cell size by FFT procedures independently of the sample thickness (Fig. 8). In addition, good general trends are achieved both for samples with thickness 11 mm and 33mm. Nonetheless, in the case of very low dense samples (30 kg/m3) the X-ray absorbance is not enough for obtaining images with a suitable contrast, thus, the FFT response for this type of foams lacks of accuracy. 3.3 Influence of real mean pore size Considering all the samples under study, it is possible to discriminate well three different cell sizes in whole density range although samples with density 30 kg/m3 present again deviations from the general trend of the rest of specimens. Furthermore, the slope for the three different pore sizes is almost the same and decreases as the foam thickness increases to the point to turn to zero as it is shown in (Fig. 9). Moreover, it is remarkable that in all cases, ignoring lowest dense samples, the FFT response of different trends concerning each pore size is arranged such that the minor real mean pore size (490 µm) is located in the bottom of the graphs, the major (670 µm) in the top, and the remaining one (520 µm) between them. Finally, as last consideration, taking into account that in our setup the pixel size of the X-ray imaging system is 25 µm, the differences between 490 and 520 µm are reduced to one pixel, making possible that the response of these two different pore sizes results overlapped. 3.4 Influence of pore overlapping In X-ray transmission imaging, due to high penetration power of the X-rays, it is possible that the surface of the object Fig. 8. Measured pore size by FFT procedures versus real mean pore size measured by optical microscopy for samples with 11 mm of thickness (top) and 33 mm of thickness (bottom). Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 308 under study may be perturbed by the irregularities inside the material, resulting low quality images. In our case, these irregularities are inherent, and can be disastrous for the study that we are carried out. In fact, the overlapping of pores may result in an effective pore size higher than the original cell size, becoming even more noticeable as the sample thickness increases. In order to alleviate this fact, as well as other irregularities, the 2D median filter is implemented in the algorithm, as it is mentioned above in the text. Therefore, as it is shown in (Fig.10), disregarding again samples with 30 kg/m3 of density, the possibility of overlapping of pores has no effect in the final response of FFT algorithm. Consequently, within the thickness range in which are the samples selected for this work, the FFT signal is not influenced by sample thickness. In addition, in this figure are discernible all the trends involving pore size measured by FFT procedures and real mean cell size measured by optical microscopy. 3.5 Study of a foaming process At this point, it is clear that the real mean pore size of the samples is highly correlated with the mean pore size associated to the spatial frequency of the first oscillation peak in the radial plot of the reciprocal space image of the samples. Thus, by X-ray radioscopy experiments of foaming processes it is possible to discern the relative evolution in real time of mean pore size by means of the procedure implemented in this algorithm. A succession of isolated radiographs of a radioscopy foaming experiment is shown in (Fig. 11) where it can be seen the evolution in time from plastic pellets to foamed by heating structure of the material. In our case, the algorithm is implemented since the foam has been completely formed (this is our time origin for representations) to the final of the Fig. 9. Measured pore size by FFT procedures versus sample density considering three different real pore sizes. The foam thickness varies between 11 mm (a) to 33 mm (c) considering an intermediate point (21 mm, b). Annex. Other Applications of X-ray Imaging Techniques 309 experiment, in 700x700 pixels region of interest (ROI). As it is shown in (Fig. 12), the cell size of the sample under study increases with time and, although the exact value of real mean pore size is unknown, this is it real evolution, therefore, measuring simply the final value of real mean pore size of the sample it is plausible to calculate the mean cell size in the whole foaming process. 4. Conclusions Using PU foam samples with a number of different characteristics varied independently (pore size, density, thickness, etc.) and a X-ray imaging system we have been able to show that fast Fourier transform procedures applied to X-ray transmission images allow to correlate real mean pore size of the samples under study. Furthermore, varying independently main characteristics of the foams it is possible to discern which parameters affect in the final response of the FFT algorithm presented in this work. Thus, concerning foam density, taking into account that the absorption of X-rays by the material is related to material density (via Lambert-Beer law) and the Xray absorption determines contrast in final images, more dense samples result in more contrasted images, therefore, as Fig. 10. Cell size measured by means of FFT algorithm versus number of pores in thickness for three different foam densities, (a) 30 kg/m3, (b) 50 kg/m3 and (c) 100 kg/m3. Fig. 11. Isolated radiographs of the whole foaming process. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 310 higher is sample density, major is the final response of the FFT algorithm. Moreover, we have shown that for constant mean pore size, the measured cell size by means of FFT algorithm is correctly ordered for every density (excepting very low dense samples under study). Finally, varying sample thickness between 11 and 33 mm, we have demonstrated that in this range of foam thickness the overlapping of pores doesn’t affect to FFT signal. A 2D highpass median filter was applied to all the images under study, eliminating, by subtracting filtered image to original image, the irregularities in original image. In addition, the applicability of this procedure to real time foaming processes radioscopy has been studied, achieving quite good results concerning relative mean pore size during the foaming process. Further work is required in order to characterize in detail other foam parameters like cell anisotropy that can be studied by identifying the symmetry of the radial plot of the reciprocal space images. The potential applicability of these results as a fast and non-destructive technique to measure the average cell size is of a capital utility for the cellular plastics scientific and technical community. Due to the simplicity of the set-up this could be a useful technique for the in-situ characterisation of cell size evolution during processing. Acknowledgments Pre-doctoral contract of S. Perez-Tamarit by University of Valladolid (E-47-20150094701) and co-financed by Banco Santander is acknowledged. In addition, financial support from MINECO, FEDER, UE (MAT2015-69234-R) and the Junta de Castile and Leon (VA011U16) are gratefully acknowledged. Joan Ferrer and Luis Vela from BASF Spain are also acknowledged for supplying the materials used in this investigation. References [1] P. Duhamel, M. Vetterli, Fast Fourier Transforms: A tutorial review and a state of the art, Signal Processing, 19 (1990) 259-299. [2] W.T. Cochran, J.W. Cooley, D.L. Favin, H.D. Helms, R.A. Kaenel, W.W. Lang, G.C. Maling, D.E. Nelson, C.M. Rader, P.D. Welch, What is the fast Fourier transform?, Proceedings of the IEEE, 55 (1967) 1664-1674. [3] C.D. Chan, M.E. Seitz, K.I. Winey, Disordered spheres with extensive overlap in projection: image simulation and analysis, Microscopy and microanalysis : the official journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada, 17 (2011) 872-878. [4] Y. Li, Y. Lu, Deriving the integral representation of a fractional Hankel transform from a fractional Fourier transform, Optics Letters, 23 (1998) 11581160. [5] V. Magni, G. Cerullo, S. De Silvestri, Highaccuracy fast Hankel transform for optical beam propagation, Journal of Optical Society of America A, 9 (1992) 2031-2033. Fig. 12. Measured by FFT algorithm cell size evolution versus foaming experiment time. Annex. Other Applications of X-ray Imaging Techniques 311 [6] A. Cunningham, N.C. Hilyard, Low Density Cellular Plastics: Physical Basis of Behaviour, Ed. Chapman and Hall, London, 1994. [7] L.J. Gibson, M.F. Ahsby, Cellular Solids: Structure and Properties, Pergamon Press, Oxford, England, 1988. [8] J.A. Reglero Ruiz, C. Saiz-Arroyo, M. Dumon, M.A. Rodriguez-Perez, L. Gonzalez, Production, cellular structure and thermal conductivity of microcellular (methyl methacrylate)-(butyl acrylate)-(methyl methacrylate) triblock copolymers, Polymer International, 60 (2011) 146152. [9] E. Solórzano, S. PArdo-Alonso, J.A. de Saja, M.A. Rodriguez-Perez, X-ray radioscopy in-situ studies in thermoplastic polymer foams, Colloids and Surfaces A: Physicochemical and Engineering aspects, 438 (2013) 167-173. [10] S. Pardo-Alonso, E. Solórzano, S. Estravís, M.A. Rodriguez-Perez, J.A. de Saja, In situ evidence of the nanoparticle nucleating effect in polyurethane– nanoclay foamed systems, Soft Matter, 8 (2012) 11262. [11] D. Klempner, K.C. Frisch, Handbook of polymeric foams and foam technology, Passavia Druckerei GmbH Passau1991. [12] M.D. Abràmoff, P.J. Magalhaes, J. Sunanda, Image Processing with ImageJ, Biophotonics International, 11 (2004) 36-42. [13] C.A. Schneider, W.S. Rasband, K.W. Eliceri, NIH Image to ImageJ: 25 years of image analysis, Nature Methods, 9 (2012) 671-675. [14] E. Solórzano, J. Pinto, S. Pardo, F. GarciaMoreno, M.A. Rodriguez-Perez, Application of a microfocus X-ray imaging apparatus to the study of cellular polymers, Polymer Testing, 32 (2013) 321329. [15] R.W. Schafer, What is a Savitzky-Golay filter?, IEEE Signal Processing Magazine, (2011) 111-117. [16] E. Solórzano, E. Laguna-Gutierrez, S. PerezTamarit, A. Kaestner, M.A. Rodriguez-Perez, Polymer foam evolution characterized by timeresolved neutron radiography, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 473 (2015) 46-54. [17] M.M. Bernal, S. Pardo-Alonso, E. Solórzano, M.A. Lopez-Machado, R. Verdejo, M.A. RodriguezPerez, Effect of carbon nanofillers on flexible polyurethane foaming from a chemical and physical perspective, RSC Advances, 4 (2014). [18] E. Solórzano, S. Pardo-Alonso, J.A. de Saja, M.A. Rodríguez-Pérez, Study of aqueous foams evolution by means of X-ray radioscopy, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 438 (2013) 159-166. Annex. Other Applications of X-ray Imaging Techniques 313 On the other hand, it is well known that in the cellular materials manufacturing the inclusion of particles in the polymer matrix serves either as blowing agents and nucleating sites depending on the type of particle. Several aspects influence the optimum performance of additives (both for blowing or nucleating purposes) such as the amount of additive [5], its size [6] or its compatibility with the employed polymer matrix [7]. In addition, the filler dispersion onto the polymer matrix plays an important role to optimize the purpose of the filler (blowing, nucleating or even as enhancer of a determined physical property) [8]. Several works have been performed in order to characterize all these aspects focused on typical characterization techniques such as SEM or SAXS, but owning critical experimental skews such as the 2D information or the compromise between resolution and statistics. Other techniques based on rheology could be considered in order to study the particle dispersion, but they are not applicable in the case of blowing agents due to the decomposition of the filler. For this reason this investigation is focused in obtaining a novel methodology to characterize the particle dispersion in polymer composites by means of high resolution X-ray Tomography. A.2 Quantification of additive dispersion in polymers using X-ray Tomography In this work entitled “Novel quantification methods of fillers dispersion in polymer composites based on high resolution synchrotron X-ray μ-CT” the dispersion quality of azodicarbonamide (ADC) particles in three different polypropylene matrixes is studied by means of synchrotron X-ray μ-CT. The high resolution achieved in the performed tomographies (0.438 μm voxel size) permitted reconstructing in detail the ADC particles thanks to phase retrieval (Figure A-2). Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 320 particle space was separated in individual objects by means of a 3D distance transform (quasi-Euclidean) watershed algorithm (Fig. 3b) [40]. After that, the objects connected with the edges of the VOI were eliminated in order to improve the statistics of the results (Fig. 3c). Finally, the volume of the remaining objects (around 750 in all cases) was determined. All the workflow steps of this method of analysis were carried out by using MorphLibJ plugin [41] for imageJ/Fiji. The computation time was around 2h in order to complete all the steps of this analysis method. In this case, the inter-partice distance is calculated as the equivalent diameter (ED) of the volume (V) of the analysed objects (Eq. 1). This parameter represents the average inter-particle distance for groups of particles and allowed also obtaining inter-particle distance distributions (interparticle distance 2). √ (1) Once the inter-particle distance distributions were determined for the two presented methods, we defined a new parameter characterizing the quality of the particle dispersion based on parameters of these distributions. We called it normalized full with at half maximum (NFWHM) and is calculated as the ratio between the full with at half maximum (FWHM) and the average value (A) of the inter-particle distance distributions (Eq. 2). As a criterion, the lower is the NFWHM of the inter-particle distance distributions; the better is the filler dispersion in the analysed VOI. ⁄ (2) In addition, the average values of the inter-particle distributions of the analysed VOIs should be linked to the concentration of particles contained therein (directly obtained from the (a) (b) Fig. 2. Computation workflow for the continuous analysis of the inter-particle space in one of the analysed VOIs of the HMS-PP polymer composite. (a) 3D rendering of the binarized particles and (b) result of the local thickness algorithm. Annex. Other Applications of X-ray Imaging Techniques 321 binarized VOIs). The higher is the particle concentration within a volume; the lower is the inter-particle distance. As a consequence, this relation might allow discriminating the quality of fillers dispersion within a volume. However, as shown below in the manuscript, the latter criterion is less precise than the previous one. 2.4.3 Statistical evaluation of the fillers dispersion on the space The last developed method consisted on the calculation of the Morishita index (IM) [42] in 3D for the selected volumes. It was usually determined in 2D images but not in 3D. To this end, a selected volume was iteratively subdivided in smaller parts of the same volume. In each iteration (n) the number of particles of all the subvolumes was recorded. The Morishita index is then calculated according to Eq. 3. ∑ (3) where q=3n is the number of subvolumes of the iteration n, ni is the number of particles contained in the subvolume i (a) (b) (c) (d) Fig. 3. Computation steps for the effective separation of the space into particles method for one VOI of the HMS-PP polymer composite. (a) Binarization of the particles (b) watershed segmentation of the inter-particle space (c) removal of the objects connecting the VOI edges and (d) remaining objects volume analysis. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 322 and N is the initial number of particles. The analysis process ended when the number of subvolumes was equal or greater than the number of particles contained in the initial volume. In our case, a little script was developed in MatLab language to calculate this index for the selected VOIs. To this end, the mass center of particles was selected as the position reference of every particle in the space. Then, comparing these values with the bounding coordinates of the subvolumes was possible determine all the ni values for every iteration and consequently IM. Nevertheless, this index does not permit discerning the dispersion quality, but the type of particle distribution within the material. It is possible analysing its evolution with number of subvolumes (or iterations). Among all the possibilities, we focus on three main cases. Firstly, if the Morishita index increases with the number of subvolumes, the distribution of the particles in the material is Aggregate distribution (Fig. 4a). Moreover, if this parameter remains at a constant value of 1 independently of the number of subvolumes, the distribution is Poisson distribution (Fig. 4b). Finally, if this index decreases when the number of iterations increases, the particle distribution is Normal (Fig. 4c) [24]. 2.5 Particle granulometry Finally, an interesting output of this analysis was the particle granulometry within the material. To this end, the volume of the binarized particles was analysed, again by means of MorphLib plugin. Once the volume was computed, the particle size (D) was determined as the equivalent diameter of the particle volume (VP) (Eq. 4) even if these particles are not spherical. √ (4) 3. Results and Discussion 3.1 Continuous analysis of the inter-particle space First of all, the homogeneity of the particle dispersion within the material was evaluated analysing the inter-particle distributions for the three analysed zones in each material (Fig. 5). In principle, all the distributions corresponding to each material are similar. Therefore, the dispersion quality is similar in all the analysed zones. In addition, HMS-PP is qualitatively the polymer in which there are less differences between zones (Fig. 5b) whereas in the two remaining polymers (50-50 and Linear-PP) the differences between the particle Fig. 4. Examples of the Morishita index outputs. (a) Aggregate distribution (b) Poisson distribution and (c) Normal distribution. Annex. Other Applications of X-ray Imaging Techniques 323 distribution on the different zones are higher but similar between them (Fig. 5 a and c). Moreover, we have determined the average inter-particle distance in all the zones calculating the average value of the inter-particle distributions. These distances are related hereinafter with the particle concentration of the analysed VOIs. Furthermore, in order to compare between materials, the histograms of the three regions have been suitably averaged (Fig. 6). This fact allowed us discriminate the dispersion quality of ADC particles in the three analysed materials. Regarding then the NFWHM values for the three distributions (Table 1), the particles are slightly better and worse dispersed in the Linear-PP and HMS-PP respectively. In addition, the dispersion quality of the 50-50 is in between of the two precedent limits. Comparing these results with viscosity values of the raw polymers measured by rheological techniques (Table 1) [43] the relationship is clear. The higher is the zero-shear viscosity of the raw PP; the better is the ADC dispersion in the polymer by the dispersion method employed. However, the small differences in the NFWHM for all the materials (approx. 2%) seem to indicate that the dispersion (a) (b) (c) Fig. 5. Inter-particle distance distributions for the continuous analysis of the space (interparticle distance 1) showing the homogeneity of the results between the selected ROIs (or VOIs). (a) 50-50 (b) HMS-PP and (c) Linear-PP. Fig. 6. Average inter-particle distributions obtained by the continuous analysis of the inter-particle space for the three tested polymer composites. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 324 quality is more linked to the manufacture process of the polymer composite and not to the characteristics of raw materials. 3.2 Effective separation of the space into particles The second method that separated the space into particles allowed extracting similar conclusions. On one hand, the differences in the inter-particle distributions for the analysed zones in the polymer composites are also small (Fig. 7). From the point of view of this method, the polymer in which the particle dispersion is more homogeneous comparing the different zones is the 50-50 (Fig 7a) whereas the opposite corresponds to the Linear-PP (Fig. 7c). Furthermore, we have extracted the average inter-particle distance from these distance distributions for this type of analysis. Again, these results allowed us discerning the relationship between the inter-particle distance and the particle concentration within a volume. The inter-particle distributions were then averaged (Fig. 8). Analysing the resulting distributions we were able to calculate the NFWHM for this method of analysis (Table 1). In this case the distributions are broader although the average interparticle distance is similar. As a result, both the NFWHM and the differences in Table 1. Viscosity characteristics and quantitative results of particle dispersion by the two image analysis methods Polymer Zero-shear viscosity (Pa·s) NFWHM Continuous analysis NFWHM Effective separation 50-50 9700 0.45 0.71 HMS-PP 8800 0.46 0.76 Linear-PP 10700 0.44 0.69 (a) (b) (c) Fig. 7. Inter-particle distance distributions for the effective separation of the space (interparticle distance 2) showing the homogeneity of the results between the selected ROIs (or VOIs). (a) 50-50 (b) HMS-PP and (c) Linear-PP. Annex. Other Applications of X-ray Imaging Techniques 325 this parameter between materials (approx. 6%) are higher in this case as shown in Table 1. In fact, the same conclusion as before could be addressed from these results relating the particle dispersion and the raw polymer shear zero viscosity. The higher is the zero-shear viscosity of the raw PP; the better is the ADC dispersion in the polymer by the dispersion method employed. Furthermore, the calculated average inter-particle distances were compared with the obtained particle concentration within every selected VOI (Fig. 9). The particle concentration was between 1.5·108 and 2.4·108 cm-3. We could see a clear separation between materials regarding the particle concentration. The concentration in the zones corresponding to the HMS-PP and 50-50 is lower than 1.9·108 cm-3 whereas the particle concentration in the analysed zones of the Linear-PP is higher than this value. The high shear viscosity of this polymer (Table 1) might provoke that a few amount of particles were fractured during the polymer composite manufacture. As a result, the number of particles within the material was slightly increased and also the average size of the particles was reduced, as shown in the granulometry results. Investigating the average inter-particle distances, it is clear that the continuous analysis of the space (Fig. 9a) results in lower values of inter-particle distance (between 30 and 35 μm). On the other hand, the average inter-particle distances determined by means of the efficient Fig. 8. Average inter-particle distributions obtained by the effective separation of the space into particles for the three tested polymer composites. (a) (b) Fig. 9. Inter-particle distance versus particle concentration for the three analysed ROIs of the tested materials. (a) Continuous analysis of the inter-particle space and (b) effective separation of the space into particles. Structural Characterization of Solid Cellular Polymers by X-ray Tomography and Light Scattering 326 separation of the space into particles was slightly higher (ranging 33-38 μm), as shown in Fig. 9b. Furthermore, a clear tendency was established in both cases. The higher is the particle concentration within a volume; the lower is the interparticle distance in this volume. The only exception to this tendency is one of the selected zones of the Linear-PP by means of the second method of analysis. 3.2 Morishita index characterization By using the same volumes and the procedure described before the Morishita Index was calculated. As explained before, the information related with this parameter is not the absolute value but the tendency when increasing the number of subvolumes. In this case the results concerning the different analysed volumes are not shown since they are essentially identical. For these reasons, only the average result for the three polymer composites is displayed (Fig. 10). Taking into account that the Morishita index is reduced when the number of subvolumes is increased, the particles are distributed within the polymer matrix according to Normal distributions. In this case there is no difference between materials. The variance of viscosity of the raw polymers is not enough to provoke a critical change in the particle distribution type since both the amount of additive and the production process of the polymer composites were the same. Consequently, the Morishita Index curves are also identical. 3.3 Particle granulometry Finally, analysing the distributions of particle size within the polymer matrixes (Fig. 11) it is possible to elucidate that the particles are slightly modified during the production of the composite precursors. As a result, the main parameters of the size distributions, summarized on Table 2 are also different. Linear PP material provokes a higher shear during production due to higher viscosity leading to smaller particles (both average size and d50) whereas in HMS-PP the effect is the inverse. Finally, the PP blend is in the middle of both extreme Fig. 10. Morishita Index calculation for several iterations in the analysed volumes and for the three materials under study. Table 2. Results of the particle granulometry analysis. Polymer Average size (μm) Standard deviation (μm) d50 (μm) 50-50 4.08 2.15 3.76 HMS-PP 4.11 2.14 3.79 LinearPP 3.88 2.03 3.56 Annex. Other Applications of X-ray Imaging Techniques 327 materials. Particle size is mostly between 0 and 12 μm in all the materials with average values around 4 μm (Fig. 12). 4. Conclusions In conclusion, we have defined new methodologies to investigate the quality of particle dispersion in polymer composites by using synchrotron X-ray μCT and image analysis. Two different methods have been developed and applied in three polymer composites based on polypropylene and azodicarbonamide. Both methods investigate the inter-particle space and quantify the inter-particle distance distributions. In addition, independently of the selected method, it was clear that the higher was the viscosity of the matrix polymer; the better was the particle dispersion within the polymer. Moreover, using the position in the space of the particles (assigned to the center of mass), the Morishita Index was calculated in 3D. Analysing the tendency of this parameter when sequentially dividing the space into subvolumes, we could extract that the particles in these systems were dispersed according to Normal distributions. Finally, by means of the same tomographies, the particle granulometry inside the materials was characterized. As (a) (b) (c) Fig. 11. Particle granulometry characterized by X-ray tomography for the three zones analysed on the materials. 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