Flue gas adsorption by single-wall carbon nanotubes: A Monte Carlo study

THE JOURNAL OF CHEMICAL PHYSICS 145, 074701 (2016) Flue gas adsorption by single-wall carbon nanotubes: A Monte Carlo study M. I. Romero-Hermida,1,2 J. M. Romero-Enrique,3V. Morales-Flórez,2,4 and L. Esquivias2,4 1Departamento de Química Física, Facultad de Ciencias, Universidad de Cádiz, Campus Río San Pedro s/n, 11510 Puerto Real, Spain 2Departamento de Física Condensada, Universidad de Sevilla, Av. Reina Mercedes s/n, 41012 Sevilla, Spain 3Departamento de Física Atómica, Molecular y Nuclear, Área de Física Teórica, Universidad de Sevilla, Av. Reina Mercedes s/n, 41012 Sevilla, Spain 4Instituto de Ciencia de Materiales de Sevilla (CSIC/US), Av. Américo Vespucio 49, 41092 Sevilla, Spain (Received 9 May 2016; accepted 2 August 2016; published online 19 August 2016) Adsorption of flue gases by single-wall carbon nanotubes (SWCNT) has been studied by means of Monte Carlo simulations. The flue gas is modeled as a ternary mixture of N2, CO2, and O2, emulating realistic compositions of the emissions from power plants. The adsorbed flue gas is in equilibrium with a bulk gas characterized by temperatureT, pressure p, and mixture composition. We have considered different SWCNTs with different chiralities and diameters in a range between 7 and 20 Å. Our results show that the CO2adsorption properties depend mainly on the bulk flue gas thermodynamic conditions and the SWCNT diameter. Narrow SWCNTs with diameter around 7 Å show high CO2 adsorption capacity and selectivity, but they decrease abruptly as the SWCNT diameter is increased. For wide SWCNT, CO2adsorption capacity and selectivity, much smaller in value than for the narrow case, decrease mildly with the SWCNT diameter. In the intermediate range of SWCNT diameters, the CO2adsorption properties may show a peculiar behavior, which depend strongly on the bulk flue gas conditions. Thus, for high bulk CO2concentrations and low temperatures, the CO2adsorption capacity remains high in a wide range of SWCNT diameters, although the corresponding selectivity is moderate. We correlate these findings with the microscopic structure of the adsorbed gas inside the SWCNTs. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4961023] I. INTRODUCTION The increase of the carbon dioxide content in the atmosphere since the start of the industrial revolution is a key cause of global warming, which is one of the most alarming worldwide environmental issues that mankind is currently facing.1,2Fossil-fueled power plants are responsible for roughly 40% of the total CO2emission, coal-fired plants being the main contributor.3,4Flue gases emitted from medium to large point sources are generally at or slightly above atmospheric pressure and fuel type, the chosen combustion system and operating conditions are the major factors affecting their composition.5Typically, the main component of the flue gas is N2, as in pure air, with a molar fraction around 80% and other major components are CO2, with a molar fraction typically between 3% and 15%, and O2with molar fraction between 5% and 15%. Water is usually also present in the flue gas, but it is possible to remove the moisture before the CO2sequestration process by using, for example, silica gel air dryers.6Finally, there are other minor components, such as SO2, NOx, and CO, as well as particulates in suspension. Currently, there is an increasing interest in reducing and controlling the CO2concentration in the atmosphere, and it has been suggested that several combined strategies could achieve the stabilization of atmospheric CO2concentrations at around 500 ppm.7One of these technologies is carbon capture and storage (CCS), which involves not only CO2separation and fixation3and underground storage,8but also mineral sequestration.9–11 As necessary starting steps in reversible capture and storage technologies and carbon reutilization, adsorption and membrane separation of CO2from flue gases have been deeply researched.12 Many possible materials have been considered for CO2adsorption, including zeolites,13,14 activated carbon,15,16 metal-organic frameworks,17,18 and single-wall carbon nanotubes (SWCNTs).19 The latter have been identified as vessels for short-term reversible storage of CO2at ambient temperatures.20 The performance of multiwalled carbon nanotubes to capture CO2from flue gases has been assessed in Refs. 6,21, and 22, finding that after a suitable chemical modification they can show larger CO2adsorption capacities than zeolites or granular activated carbons. Additionally, it has been experimentally found that electrical resistance of carbon nanotubes is sensitive to the adsorption of gaseous molecules such as those released on burning of fossil fuels.23,24 It was concluded that resistance decreases when oxidizing gas molecules adsorb on the surface, whereas adsorption of reducing gas molecules results in increasing it. These results, together with new experimental techniques, which allow controlled synthesis of monodisperse single-chirality SWCNT distributions,25 make carbon nanotubes suitable for the development of innovative gas sensor technologies. From a computational point of view, molecular simulations of the gas adsorption and separation by carbon nanotubes or related porous media have been extensively studied in the 0021-9606/2016/145(7)/074701/13/$30.00 145, 074701-1 Published by AIP Publishing. Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 150.214.182.116 On: Tue, 22 Nov 2016 15:35:06 074701-2 Romero-Hermida et al. J. Chem. Phys. 145, 074701 (2016) literature.20,26–41 Most of these simulation studies consider classical force fields, but ab initio calculations have also been reported.19,27,42 The capacity of carbon nanotubes to adsorb pure CO2has been tested by computer simulations in isolated19 and arrays of parallel SWCNTs,20 as well as isolated36 and parallel double-walled carbon nanotube bundles.38,40 On the other hand, CO2separation by carbon nanotubes from mixtures has been studied in CO2—CH4mixtures,30,39 in presence of water37 or in CO2—N2mixtures.33 This latter study, relevant for CO2capture from flue gases, studied the effect of pressure, temperature, and bulk gas composition on the CO2adsorption in SWCNTs with diameters between 8 and 10 Å. They find that the narrowest SWCNT (6,6) they considered presents an optimal CO2selectivity with respect to N2(of about 10) for T=300 K, p=0.15 MPa, and bulk CO2concentration yCO2=0.3.33 Our goal in this paper is the molecular simulation study of the adsorption properties of flue gases under experimentally typical conditions by SWCNTs, paying special attention to their performance to capture CO2. We will extend previous studies to a larger range of SWCNT diameters, spanning from around 7 Å, which can be obtained experimentally,43 to 20 Å. On the other hand, we will consider the effect of the presence of oxygen in the flue gas. We will restrict ourselves to the study of the gas adsorption inside the nanotubes. Although the flue gas can be also adsorbed in the outer surfaces of the SWCNTs, its effect will depend not only on the nanotube geometry, but also in the aggregation properties, i.e., in the way the SWCNTs form bundles. This work will be performed by Monte Carlo computer simulations,44,45 and thus dynamical properties such as diffusion cannot be considered. However, the Monte Carlo method is very suitable for the study of confined multicomponent fluids, where we do not know the adsorbed fluid compositions a priori. In this way we avoid those undesired finite-size effects that may arise in the simulation geometries. In order to characterize the effects of the carbon nanotube geometry, we have systematically studied the CO2adsorption properties of all the SWCNTs with a diameter smaller than 20 Å. The paper is organized as follows. In Section II we describe the molecular model of the flue gas and the carbon nanotubes. The simulation methods we will use are introduced in Section III. Our results will be presented and discussed in detail in Section IV, and we will end up our paper with the conclusions in Section V. II. THE MODEL We model the flue gas as a N2, CO2, and O2ternary mixture. Thus, the effect of the water or the minority components on its adsorption by SWCNT is not considered. The interactions between molecules are modeled by using the TraPPe force field.46,47 Each molecule of the flue gas is considered to be rigid and linear, with fixed chemical bond distances dbetween neighbour atoms: d=1.1 Å for N2, d=1.21 Å for O2, and d=1.16 Å for each C==O bond in CO2. Furthermore, the two C==O bonds in each CO2molecule are always collinear. The molecular interactions are assumed to be pairwise, where the interaction between the iand j molecules is given by v2(i,j)= α∈i, β ∈j(4ϵαβ      (σαβ rαβ )12 −(σαβ rαβ )6      +qαqβ 4πϵrαβ ), (1) where αand βrepresent the interaction centers of the iand jmolecules, respectively. Each molecule has three interaction centers, associated to the atom nuclei of each molecule and, in the case of the diatomic molecules N2 and O2, the molecular center of mass (CM). Lennard-Jones potentials are associated to the atoms of each molecule (not to the molecular CMs). On the other hand, molecular electric quadrupolar moments are modeled by a distribution of point charges qαassociated to each interaction center α. In particular, two equal charges qare located at the atoms of the diatomic molecules, and an additional charge −2qassociated to their CM. For CO2molecules, two equal charges qare located at the oxygen atoms, and a charge −2qat the carbon atom. Table Ishows the relevant interaction parameters for the intermolecular interaction potential. For the parameters of the Lennard-Jones potential between dissimilar nonbonded atoms, the Lorentz-Berthelot combination rules are used σαβ =σαα +σββ 2, ϵαβ =√ϵααϵβ β.(2) With respect to the SWCNTs, they are modeled as rigid, regular distributions of carbon atoms following the ideal structure of the carbon nanotube, i.e., defectless and infinite along the axial nanotube direction. This structure is obtained by wrapping a two-dimensional layer of graphite or graphene, which has a honeycomb structure with a bond distance between nearest-neighbour carbons of a=1.421 Å, into a seamless cylinder. SWCNTs show periodic structures along its axis, characterized by the chiral indices (n,m), where the integer numbers nand mare the components of the chiral vector Chin the basis vector of the honeycomb lattice. Under wrapping, Chprovides the perimeter of a carbon nanotube section. So, the geometric characteristics of ideal SWCNTs are uniquely determined by the carbon-carbon bond distance and the chiral indices.48 In particular, the nanotube diameter TABLE I. Intermolecular interaction parameters. Underlined atom symbols correspond to the interaction centers that the interaction parameter refers to. Lennard-Jones parameters for dissimilar atoms are obtained via the Lorentz- Berthelot combination rules Eq. (2). The interaction center charges qare in units of the electron charge e=1.6×10−19 C. CM stands for the molecule center of mass. σ(Å)ϵ/kB(K)q/e CO2–CO22.8 27.0 0.70 CO2–CO23.05 79.0 −0.35 N2–N23.31 36.0 −0.482 CM(N2)–CM(N2)... ... 0.964 O2–O23.013 49.048 −0.123 CM(O2)–CM(O2)... ... 0.246 Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 150.214.182.116 On: Tue, 22 Nov 2016 15:35:06 074701-3 Romero-Hermida et al. J. Chem. Phys. 145, 074701 (2016) TABLE II. Parameters of the Steele potential between the SWCNT and the flue gas. Underlined atom symbols refer to the interaction center associated to the corresponding parameter. σ(Å)ϵ/kB(K) C–CO23.11 27.0 C–CO23.16 45.6 C–N23.36 33.4 C–O23.19 37.6 dtis given by dt=a√3 π√n2+m2+nm.(3) On the other hand, the wavelength Tassociated to the translational symmetry along the nanotube axis is given by T=√3πdt/dR, where dtis given by Eq. (3) and dRis the highest common divisor of (2n+m,2m+n). Without loss of generality, we can assume that n≥m. If m=0, SWCNTs are called zigzag nanotubes, and if n=m, SWCNTs are called armchair nanotubes. Otherwise, they are called chiral. For the adsorbed flue gas, the presence of the SWCNT is twofold. First, it acts as a confining pore. On the other hand, the interactions between the SWCNT and the flue gas molecules can be expressed as an external field acting on the adsorbed flue gas. In the present work this interaction is modeled by the Steele potential49–51 v1(i)= α∈i, β ∈SWCNT 4ϵαβ      (σαβ rαβ )12 −(σαβ rαβ )6      ,(4) where αruns over the interaction centers of the flue gas adsorbed molecule i, and βlabels the SWCNT carbon atoms. The parameters for the Steele potential are taken to be the same as for a fluid in contact with a flat graphite surface (see Table II). However, recent ab initio calculations of adsorbed gases on Schwarzite C168 show that the nanotube curvature may have an effect on the adsorption properties.27 III. METHODOLOGY As mentioned in the Introduction, we will study the physisorption of flue gases inside SWCNT in thermodynamic equilibrium with a bulk reservoir. So, in a first step we will characterize the thermodynamic properties of the bulk flue gas, and in particular the chemical potentials for each species for a given temperature, pressure, and mixture compositions yi. Although there are empirical equations of state which can provide these quantities, in the present work they will be evaluated by NpT Monte Carlo simulations. In addition, grand-canonical Monte Carlo simulations will be performed to check the accuracy of the NpT estimates. After that, we will study the flue gas adsorption inside SWCNTs via grandcanonical Monte Carlo simulations, using for each species the chemical potential obtained from the bulk simulations for the same temperature and pressure. In this way, the coexistence between the confined and the flue gas is ensured. In this work, we will restrict ourselves to the temperatures T=300 K, 350 K, and 400 K, and as values of the pressure 1–4 atm. These values span the range considered by experimental studies of flue gas adsorption on multiwalled carbon nanotubes.6Now we present a summary of the simulation details. A. Bulk simulations Bulk Monte Carlo simulations are performed on cubic boxes subject to periodic boundary conditions, using the Metropolis algorithm. Lennard-Jones interactions are truncated at a cutoffdistance rc=8.5 Å. The long-ranged character of the electrostatic interactions is handled by the use of the Ewald summation technique52 with real space damping parameter α=4 and a maximum wave vector kmax =10π/L for the Fourier part. In order to obtain the chemical potentials of each component of the flue gas, we performed NpT Monte Carlo simulations. The total number of molecules is set to N=1000, of which 800 correspond to N2molecules (yN2=0.8). In order to study the effect of the bulk CO2concentration of the flue gas on the adsorption, we have considered the cases (NCO2,NO2)=(0,200),(50,150),(100,100),(150,50), and (200,0), i.e., (yCO2, yO2)=(0.00,0.20),(0.05,0.15), (0.10,0.10),(0.15,0.05), and (0.20,0.00), respectively. We start from a configuration where the molecules are located at the sites of a simple cubic lattice of initial volume 2.7×107Å3. Each simulation typically consists of 55 000 Monte Carlo cycles, where the initial 5000 cycles are disregarded as an equilibration period, and averages are taken over the remaining cycles. Each Monte Carlo cycle consists of N+1 trial movements, which in average correspond to Nrandom translations and rotations of a molecule chosen also at random, and a box volume change (keeping its cubic shape), where the molecular positions are rescaled accordingly. The maximum molecular displacement is set to 100 Å, and the maximum angle rotation with respect to the original orientation is of 70◦. Finally, maximum volume change is V0/2, where V0is the current simulation box volume. With these values, the molecular movement acceptance ratio is about 99%, due to the low density of the flue gas under the considered conditions of temperature and pressure. On the other hand, the volume change acceptance ratio is about 20%. Different thermodynamic properties, such as the inner energy or the virial pressure, are obtained as run averages of their microscopic analogues. The chemical potentials of the flue gas species are obtained by Widom’s test particle method.53 In particular, the activity coefficient ziof the ispecies is obtained as zi=eβµi Λ3Λr =1 4π(Ni+1)dridωiexp       − N  j=1 βv2(i,j)      −1 ,(5) where Λ=h/√2πmkBTand Λr=h2/(4π2IkBT), with mand Ibeing the molecular mass and inertia moment, respectively. Niis the number of particles of speciesi,v2is the pair potential Eq. (1), and ⟨. . .⟩corresponds to the thermal average. Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 150.214.182.116 On: Tue, 22 Nov 2016 15:35:06 074701-4 Romero-Hermida et al. J. Chem. Phys. 145, 074701 (2016) In order to check the obtained values for the chemical potential from our NpT simulations, we also performed grandcanonical Monte Carlo simulations of the bulk flue gas. As in the NpT simulations, the simulation box is cubic, with a volume which, depending on the thermodynamic conditions, is between 8 ×106Å3and 2.7×107Å3, in order to have an average total number of particles of about one thousand. We considered runs of typically 3 ×107Monte Carlo steps after an equilibration period of 3 ×106steps, starting from an empty box. In these simulations, a Monte Carlo step is trial insertion or deletion of a molecule. The species of the molecule is chosen randomly between those present in the flue gas with the same probability. Again, the low densities of the flue gas under the considered thermodynamic conditions lead to insertion and deletion acceptance ratios of around 99%. We use as an input of the chemical potentials the estimated values from the previous NpT simulations. As an output, we obtain the average mole fractions yi=⟨Ni⟩/⟨N⟩, where Niand Nare the instantaneous values of the i-species number of particles and total number of particles, respectively. Comparison between these values and the input values of the corresponding NpT simulations provides an accuracy test for the activity coefficients. B. Simulations in SWCNTs Flue gases under confinement in SWCNTs have been studied by grand canonical Monte Carlo simulations, with the activity coefficients obtained from the bulk NpT simulations for the selected values of temperature, pressure, and bulk flue composition. In this way, the confined fluid will be in equilibrium with the corresponding bulk gas. The simulation procedure is similar to the one outlined above for the grand canonical Monte Carlo simulations of the bulk flue gas. However, now the simulation box is a cylinder of diameter dt given by Eq. (3), and an axial length Lzwhich is a multiple of the wavelength Tof the carbon nanotube. The integer number of proportionality is chosen in such a way that Lzis around 100 Å. Periodic boundary conditions are only considered along the nanotube axis direction, and the cylinder wall is impenetrable for the interaction centers of each molecule. In addition to the fluid-fluid interactions, the external potential Eq. (4) acts on each molecule. Finally, we do not use the Ewald summation to deal with the electrostatic interactions. The reason for this is that, at large distances, the electrostatic interactions are basically quadrupole-quadrupole interactions, which decay with the intermolecular distance as 1/r5. In the quasi-one dimensional situation we are considering, this potential decays fairly fast to zero as r→ ∞, so we can truncate it for distances larger than Lz/2. We have considered a large set of narrow SWCNTs in the microporous range, i.e., with nominal diameters less than 2 nm: armchair nanotubes with n=6,7, . . . ,14; zigzag nanotubes with n=9, . . . ,25; and the chiral nanotubes (6,5), (7,4),(7,5),(7,6),(8,3),(8,4),(9,1),(9,3),(10,1),(10,5), (11,2),(12,4),(20,5), and (21,7). Their nominal nanotube diameters dtspan a range between 7.05 Å for the (9,0) nanotube, and 19.76 Å for the (21,7)nanotube. In each case, we compute the average mole fractions xi=⟨Ni⟩/⟨N⟩(note that in general they will differ from the bulk values yi), the flue gas number density ρ, and the inner energy. From these data we evaluate the selectivity of the minority species relative to the flue gas major component N2as SCO2|N2=xCO2/xN2 yCO2/yN2 ,SO2|N2=xO2/xN2 yO2/yN2 .(6) In addition, we evaluate the i-species absolute adsorption capacity, qi, in a (n,m)SWCNT as qi=Pmi⟨Ni⟩ PatCNC ,(7) where ais the carbon-carbon bond length in the SWCNT, ⟨Ni⟩and NCare the average number of particles of i-species in the confined flue gas and the number of carbon atoms in the simulated nanotube section, respectively, and Pmiand PatCare the molecular weight of the i-species and the atomic weight of carbon, respectively. In order to compare to experimental results, the excess adsorption capacity qexc imust be evaluated by subtracting from ⟨Ni⟩in Eq. (7) the contribution of the bulk fluid into the available volume ⟨Ni⟩exc =⟨Ni⟩−nb iVfree,(8) where nb iis the bulk number density at the same thermodynamic conditions. The definition of the available volume Vfree is somewhat ambiguous as the nanotube has soft boundaries. We estimate as the volume of a cylinder of the same length the simulation box along the CNT axis, and radius as dt/2−σ0, where σ0≈(2.7±0.1)Å is estimated from the closest distance between the carbon nanotubes and the atoms which compose the flue gas molecules. In a similar way, an excess selectivity Sexc i|jis defined when considering the excess mole fractions of the adsorbed flue gas by subtracting the corresponding bulk contribution as in Eq. (8). The isosteric heat of adsorption Qst which characterizes the adsorption strength of the confined fluid by the adsorbate can be obtained as54 Qst =xCO2QCO2+xN2QN2+xO2QO2,(9) where the molar quantities Qiare obtained as Qi≈kBT−(∂⟨U⟩ ∂⟨Ni⟩)T,p,⟨Nj,i⟩ (10) with Ubeing the intermolecular energy of the adsorbed phase. The second term in the right-hand side of Eq. (10) can be obtained in simulation by the fluctuation formula (∂⟨U⟩ ∂⟨Ni⟩)T,p,⟨Nj,i⟩ = j ⟨UNj⟩−⟨U⟩⟨Nj⟩(κ−1)i j,(11) where κ−1is the inverse of the matrix κ, with elements κi j ≡⟨NiNj⟩−⟨Ni⟩⟨Nj⟩.54 We also evaluated structural properties such as the interaction center radial density profiles nα(r)and axial pair Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 150.214.182.116 On: Tue, 22 Nov 2016 15:35:06 074701-5 Romero-Hermida et al. J. Chem. Phys. 145, 074701 (2016) distribution functions gαβ(z), defined as nα(r)=1 2πrNα  m=1 δ(rm−r),(12) gαβ(z)=Lz ⟨Nα⟩⟨Nβ⟩Nα  m=1 Nβ  n=1 ′ δ(|zmn|−z),(13) where δis the Dirac delta, Nαis the total number of interaction centersoftype α,rmand zmaretheradialandaxialcoordinates of the interaction center m, and zmn ≡zm−zn. Finally, the prime in Eq. (13) means that we exclude the case m=nif α=β. IV. RESULTS AND DISCUSSION A. Bulk simulations We have performed the bulk simulations of the flue gas followingtheprocedure outlined inSec.III. Table IIIshowsthe most relevant results from the NpT simulations for p=1 atm. Similar results are obtained for higher pressures, although the virial pressure shows larger fluctuations for p=4 atm. However, even in this case the standard deviation is less than 1%. Note that densities are similar to the corresponding one to pure air under normal conditions. The potential energy contribution to the inner energy per molecule, U, is small, which is consistent with the fact that the flue gas density is low. Actually, the obtained pair distribution functions between center of interactions show a microscopic structure which is typical for diluted gases. Although in general we obtain accurate values for the thermodynamic properties of the flue gas, the activity coefficients obtained from the Widom insertion method show uncertainties of about 10%. However, the obtained values are consistent with the ideal gas limiting values zi→Ni/⟨V⟩, with Nibeingthe numberofmoleculesof thespeciesiandVthe box volume. This fact is not surprising because of the low density of the flue gas under the considered conditions. However, we have to confirm that the obtained values are appropriate for the grand-canonical simulations in the confined case. In order to check this, we performed grand-canonical simulations of the bulk flue gas, using the activity coefficients obtained from the NpT simulations. Table IV shows the grand-canonical simulation results for the same thermodynamic conditions considered for the simulations with results shown in Table III. The agreement between the data obtained by both procedures is excellent, validating the NpT simulation estimates for the activity coefficients. B. Simulations in SWCNTs: Adsorption capacities, selectivities, and isosteric heat of adsorption Grand-canonical Monte Carlo simulations of the flue gas confined in SWCNT are performed using the same conditions as those considered for the bulk gas simulations. In particular, we select the same values of temperature, pressure, and chemical potentials for all the species, ensuring in this way thermodynamic equilibrium between the bulk and the confined flue gas. The acceptance ratio of insertion/deletion of molecules differs from that corresponding to the bulk simulations. Furthermore, it depends on the nanotube diameter, spanning a range from 0.1%–2% for the narrowest SWCNT to 20%–25% for the widest nanotubes. We observe that for each species the adsorption capacity increases with the pressure. CO2and O2adsorption capacities decrease when the temperature is raised, but for N2this observation is only true for wide or very narrow SWCNT. However, for yCO2=0.15 and 0.20, a non-monotonic behavior of the N2 adsorption capacity with the temperature for large pressures and SWCNTs with intermediate diameters spanning from 8 Å to 10 Å is observed. Under these conditions, the N2adsorption capacity can be larger for T=350 K than for T=300 K. We first analyze the adsorption properties of narrow and wide SWCNT. In order to characterize each scenario, we will consider as examples the SWCNT with chiral indices (9,1)(dt=7.4 Å) and (25,0)(dt=19.58 Å). The adsorption isotherms of each species are compared in Fig. 1for bulk TABLE III. N pT simulation results for the bulk gas with p=1 atm. The 1σstatistical uncertainties, shown as subindexes, refer to the last decimal places. p(atm)T(K)yCO2ρ(kg/m3)U(kJ/mol)pvirial (atm)zCO2(10−6Å−3)zN2(10−5Å−3)zO2(10−6Å−3) 1 300 0.00 1.1551−0.005711.0001... 1.9313 4.93 1 300 0.05 1.18116 −0.006331.00214 1.2414 1.923.74 1 300 0.10 1.2022−0.007010.99922.4416 1.9412 2.4415 1 300 0.15 1.2272−0.007710.99913.631.9415 1.2310 1 300 0.20 1.2522−0.008311.00024.941.9414 ... 1 350 0.00 0.9901−0.005011.0001... 1.6694.22 1 350 0.05 1.0101−0.005430.99911.061.6573.1114 1 350 0.10 1.0301−0.005910.99912.121.6514 2.0919 1 350 0.15 1.0511−0.006310.99913.151.641.03 1 350 0.20 1.0722−0.006910.99914.241.6614 ... 1 400 0.00 0.8661−0.004211.0001... 1.4610 3.63 1 400 0.05 0.88316 −0.004710.99910.9371.4592.7416 1 400 0.10 0.9021−0.005011.00011.8291.4571.828 1 400 0.15 0.9201−0.005410.99912.731.4614 0.939 1 400 0.20 0.9381−0.005811.00013.741.4614 ... Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 150.214.182.116 On: Tue, 22 Nov 2016 15:35:06 074701-6 Romero-Hermida et al. J. Chem. Phys. 145, 074701 (2016) TABLE IV. Grand-canonical simulation results for the bulk flue gas. The thermodynamic conditions are the same as those shown in Table III. T(K)zCO2(10−6Å−3)zN2(10−5Å−3)zO2(10−6Å−3)pvirial (atm)ρ(kg/m3)yCO2yN2 300 0.00 1.939 4.86 1.00321.15920.00 0.7993 300 1.23 1.937 3.65 1.00421.18430.050820.7984 300 2.44 1.936 2.44 1.00331.20830.100940.7984 300 3.64 1.939 1.23 1.00431.23330.150360.7984 300 4.86 1.942 0.00 1.00621.25920.200570.8003 350 0.00 1.661 4.17 1.00320.99320.00 0.7993 350 1.05 1.651 3.11 0.99821.00920.050920.7994 350 2.08 1.654 2.09 1.00021.03120.100540.7984 350 3.10 1.633 1.04 0.98831.04020.151660.7984 350 4.17 1.663 0.00 1.00521.07820.200670.7993 400 0.00 1.456 3.65 1.00420.87020.00 0.7993 400 0.925 1.453 2.74 1.00430.88820.050920.7984 400 1.82 1.445 1.82 0.99830.90120.100740.7994 400 2.75 1.457 0.927 1.00730.92720.150860.7984 400 3.67 1.464 0.00 1.01120.94820.200470.8003 flue gases with CO2mole composition yCO2=0.15, and the nanotube selectivities of CO2and O2for both SWCNTs are shown in Fig. 2. Similar results are obtained for other bulk flue gas compositions. For narrow nanotubes, first we note that absolute and excess adsorption capacities are virtually identical, as it is shown in Fig. 1for the (9,1)SWCNT. This is not surprising since the bulk phases have very low densities, and the free volume is very small. The adsorption isotherms are compatible with Type I (Langmuir) isotherms in the limited range of pressures which we have considered. Fig. 1shows that CO2 adsorption capacity is much larger than that corresponding to N2, which in turn is one order of magnitude larger than for O2. The latter observation is common for every SWCNT which we have considered. The CO2adsorption capacity increases with the bulk flue gas CO2mole fraction, whereas N2and O2 FIG. 1. Adsorption isotherms of CO2(top), N2(middle), and O2(bottom) for yCO2=0.15, associated to the (9,1)(left) and (25,0)(right) SWCNT. Symbols correspond to different isotherms: circles for T=300 K, squares for T=350 K, and triangles for T=400 K. Open symbols correspond to absolute adsorption capacities, and filled symbols to excess adsorption capacities. Lines only serve as eye guides. adsorption capacities decrease as yCO2increases. Regarding the selectivities, Fig. 2shows that the CO2selectivity for the (9,1)SWCNT is quite large. It decreases with the pressure, being larger for smaller temperatures. The O2selectivity, on the other hand, is quite insensitive to pressure, temperature, and bulk flue gas composition (within statistical uncertainties). These observations indicate that narrow SWCNTs have a strong affinity to CO2with respect to N2or O2, these two being the latter components almost identical for adsorption properties. For wide nanotubes, absolute and excess adsorption capacities show larger discrepancies, which do not exceed 10% for CO2adsorption, and 20% for the other components. The adsorption capacities are proportional to the pressure (Henry’s law), although Type I behavior, which is typical for micropores, is expected for higher pressures. Fig. 1shows FIG. 2. CO2(top) and O2(bottom) selectivities for yCO2=0.15 as functions of the pressure, associated to the (9,1)(left) and (25,0)(right) SWCNT. Symbols correspond to different isotherms: circles for T=300 K, squares for T=350 K, and triangles for T=400 K. Open symbols correspond to absolute adsorption capacities, and filled symbols to excess adsorption capacities. Lines only serve as eye guides. Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 150.214.182.116 On: Tue, 22 Nov 2016 15:35:06 074701-7 Romero-Hermida et al. J. Chem. Phys. 145, 074701 (2016) FIG. 3. CO2(circles) and N2(squares) excess adsorption capacities as a function of the bulk CO2composition yCO2for the (25,0)SWCNT at T=300 K and p=1 atm. Lines only serve as eye guides. that for the (25,0)SWCNT the CO2adsorption capacity has decreased in a large proportion with respect to the (9,1)case, while for N2and O2remains in the same order of magnitude. We observe that N2is the preferentially adsorbed species for small bulk CO2mole fractions, but CO2adsorption capacity is larger than for N2when yCO2=0.2, as shown in Fig. 3. On the other hand, the CO2selectivity of the (25,0)SWCNT is one order of magnitude smaller with respect to the (9,1)SWCNT, and now it increases with the pressure, being also a decreasing function of the temperature. In any case, the dependence on pressure of the CO2selectivity for the (25,0)SWCNT is weaker than for the (9,1)SWCNT. Again the O2selectivity is almost unity regardless the pressure, temperature and bulk flue gas composition (within statistical uncertainties). In fact, this observation is true for almost every SWCNT we have considered. The exception is the narrowest SWCNT (9,0), in which the O2selectivity shows an unusual behavior. Except for this case, O2selectivities have values between 0.7 and 2, and for nanotubes of diameter larger than 10 Å is approximately equal to 1. The effect of the SWCNT geometry on the adsorption properties is shown in Figs. 4-8. We see that the nanotube diameter dtis the main geometrical feature of the SWCNT for these properties. This is shown by their smooth dependence on dt, and by the fact that different SWCNTs with different chirality indexes but the same diameter (such as the (6,5) and (9,1)SWCNTs) have, within the statistical uncertainties, the same adsorption properties, in agreement with previous results in the literature.20 We focus on CO2adsorption capacity and selectivity, which are the most relevant properties for applications to CO2sequestration. Figs. 4–6summarize the obtained results for CO2adsorption capacity. As we observed for the (9,1)and (25,0)SWCNTs, the adsorption capacity increases with the pressure or CO2mole fraction of the bulk fluegas, andingeneral whenthetemperature isdecreased.As a function of the SWCNT diameter, the CO2adsorption capacity shows a peak for the narrowest SWCNT (dt=7.05 Å), and decreases steeply as the nanotube diameter increases, at least up to dt≈8 Å. On the other hand, for wide nanotubes FIG. 4. CO2excess adsorption capacity as a function of the SWCNT diameter for T=300 K and (a) yCO2=0.05, (b) yCO2=0.10, (c) yCO2=0.15, (d) yCO2=0.20. From bottom to top: p=1 atm (circles), p=2 atm (squares), p=3 atm (diamonds), and p=4 atm (triangles). Lines only serve as eye guides. (dt&1 nm), the CO2adsorption capacity decays smoothly with the nanotube diameter. For the intermediate range of SWCNT diameters, 8 Å .dt.10 Å, we observe different scenarios when the thermodynamic conditions of the bulk flue gas are varied. For the highest temperatures T=400 K, the CO2adsorption capacity is a monotonic decreasing function of dt, except for narrowest SWCNT, where the extreme confinement can reduce its adsorption capacity for high temperatures (see Fig. 6). However, for high pressures this function displays a plateau for values of dtbetween 8.1 and 8.7 Å. When the temperature is reduced to T=350 K, two different scenarios are observed (see Fig. 5). When the bulk CO2mole fraction is yCO2=0.05, the dependence of the adsorption capacity on the SWCNT diameter is similar to the case T=400 K. As yCO2is increased, the CO2 adsorption capacity develops a non-monotonic behavior with FIG. 5. The same as Fig. 4for T=350 K. Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 150.214.182.116 On: Tue, 22 Nov 2016 15:35:06 074701-8 Romero-Hermida et al. J. Chem. Phys. 145, 074701 (2016) FIG. 6. The same as Fig. 4for T=400 K. dt, in such a way that it is an increasing function for dt between 8.1 and 8.7 Å. This feature is even more evident in the lowest temperature, see Fig. 4. For T=300 K, the maximum values of CO2adsorption capacity are between 60 and 70 mg/g, which are similar to those obtained for activated carbons at much higher values of yCO2.6Furthermore, for narrow SWCNTs the CO2adsorption capacity depends only weakly on the pressure. Finally, for high pressures and bulk CO2mole fractions, an additional maximum of the CO2 adsorption capacity emerges at dt≈10.4 Å, which can be even higher than that corresponding to the narrowest SWCNT for p=4 atm and yCO2=0.2. Figs. 7–9show the CO2selectivities with respect to N2 as a function of the SWCNT diameter. We observe that the dependence on the pressure and yCO2is quite weak. As a function of dt, a steep decay is observed for narrow SWCNTs, FIG. 7. CO2excess selectivity with respect to N2as a function of the SWCNT diameter for T=300 K and (a) yCO2=0.05, (b) yCO2=0.10, (c) yCO2=0.15, (d) yCO2=0.20. From bottom to top: p=1 atm (circles), p=2 atm (squares), p=3 atm (diamonds), and p=4 atm (triangles). Lines only serve as eye guides. FIG. 8. The same as Fig. 7for T=350 K. whereas for wide nanotubes it decreases smoothly with the SWCNT diameter. In all the cases there is an overall decrease of two orders of magnitude for the selectivity, being about 100 for the narrowest SWCNT, and of order of unity for wide nanotubes (note the semi-log scales in these figures). As it happened for the CO2adsorption capacity, at the highest temperature the dependence of SCO2/N2on dtdisplays a plateau for dtbetween 8.1 and 8.7 Å, from which a local maximum emerges as the temperature decreases and/or yCO2increases. Finally, the isosteric heat of adsorption shows a relatively small dependence on the thermodynamic properties of the bulk flue gas. The pressure dependence is more evident for the lowest temperature T=300 K. Fig. 10 shows that it decays monotonically with the SWCNT diameter from about 45 kJ/mol for the narrowest nanotube to about 12 kJ/mol for the widest one. These values are about one order of magnitude above the thermal energy or the typical fluid-fluid interactions (see Table I). This fact, together with the relative insensitivity to the thermodynamic properties, indicates that FIG. 9. The same as Fig. 7for T=400 K. Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 150.214.182.116 On: Tue, 22 Nov 2016 15:35:06 074701-9 Romero-Hermida et al. J. Chem. Phys. 145, 074701 (2016) FIG. 10. Isosteric heat of adsorption as a function of the SWCNT diameter for T=300 K and (a) yCO2=0.05, (b) yCO2=0.10, (c) yCO2=0.15, (d) yCO2=0.20. Circles correspond to p=1 atm (circles) and squares to p=4 atm. Lines only serve as eye guides. the physisorption of the flue gas under the thermodynamic conditions we are considering is mainly controlled by the adsorbent-adsorbate interactions. Furthermore, this is also suggested by the fact that the isosteric heat can be estimated by kBT−⟨U⟩/⟨N⟩for most of the cases we have considered. Fluid-fluid interactions will have a relatively larger impact in the intermediate range of SWCNT diameters. We will come back to this point later. C. Simulations in SWCNTs: Microscopic structure From the results in Subsection IV B we conclude that the adsorption properties in SWCNT show different behaviors for narrow and wide nanotubes, with a transition between these regimes for SWCNTs with diameters between 8.1 and 8.7 Å. In order to understand this, we have studied the microscopic structure of the confined flue gas for the (9,1),(6,6), and (25,0)SWCNTs, corresponding to the narrow, intermediate, and wide cases. Results will be shown for T=300 K, and p=1 atm, although similar conclusions are found for different thermodynamic conditions. Fig. 11 shows typical molecular configurations of the confined flue gas. In the (9,1)and (6,6)SWCNT, we observe that the particle density is larger than that corresponding to the bulk gas. Furthermore, the number of CO2molecules exceeds the number of N2molecules, and in these particular configurations no O2molecules are present. However, we see some differences between them: in the (9,1)SWCNT the CO2molecules are oriented along the nanotube axis, whereas their orientations are distributed more randomly in the (6,6)SWCNT. In the (25,0)SWCNT, the configuration is completely different: the particle density is much smaller, and molecules are preferentially localized close to the nanotube wall. In order to quantify these observations, the number density profiles corresponding to the αatom, nα(r), are shown FIG. 11. Typical snapshots for the confined flue gas inside the (9,1), (6,6), and (25,0)SWCNTs. The bulk flue gas conditions are p=1 atm, T =300 K, and yCO2=0.10. Triatomic molecules represent CO2and the diatomic molecules to N2(in these configurations there are no O2molecules). The network shows the positions of the carbon atoms in the SWCNT. in Figs. 12–14 for the (9,1),(6,6), and (25,0)SWCNTs, respectively. We suppose that these functions only depend on the radial coordinate rwith respect to the nanotube axis, which is a reasonable assumption as the nanotube inner surface is not very rough. Note that these profiles are non-zero only for values of r.dt/2−σ0, where σ0≈2.7 Å ∼σαC∼3 Å (see Table II). This is because the atoms of the flue gas molecules cannot be at a distance closer than σαCto any nanotube carbon, which are located on a cylinder of nominal radius, dt/2. First, we note that for each SWCNT the CO2 local densities increase with the bulk CO2mole fraction yCO2, whereas the N2and O2densities decrease. In Fig. 12 we see that all the density profiles show maxima at or near r=0. Carbon atom densities from CO2show a clear peak at FIG. 12. Number density profiles nα(r)of the atom αas a function of the radial coordinate r: continuous lines for C from CO2, dashed lines for O from CO2, dotted-dashed lines for N from N2, and dotted lines for O from O2. The flue gas is confined inside the (9,1)SWCNT, and it is in thermodynamic equilibrium with a bulk flue gas at p=1 atm, T=300 K and (a) yCO2=0.05, (b) yCO2=0.10, (c) yCO2=0.15, and (d) yCO2=0.20. Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 150.214.182.116 On: Tue, 22 Nov 2016 15:35:06