Selectivity transitions in carbon nanotubes

Grand canonical Monte Carlo simulations have been carried out to determine the adsorption selectivity of single walled, arm-chair carbon nanotubes towards a binary Lennard-Jones gas mixture. For species with differing molecular diameters, a complete transition in selectivity is observed as the temperature of the bulk gas is lowered. At high temperatures, the larger energetically favoured species is preferred, however at lower temperatures the smaller species completely eliminates the larger species. This transition is accompanied by a lowering in the total potential energy of the system. For species that have similar molecular diameters, the energetically favoured species is preferentially adsorbed at all temperatures, and transitions in selectivity are absen

Simulations of Binary Mixture Adsorption in Carbon Nanotubes: Transitions in Adsorbed Fluid Composition

The adsorption of equimolar binary Lennard-Jones gas mixtures into single-walled carbon nanotubes is investigated using grand canonical Monte Carlo simulations. For mixtures whose species have different molecular diameters, the larger energetically favored species is adsorbed at higher temperatures. However, at lower temperatures and intermediate nanotube diameters, a complete exclusion of the larger species in favor of the smaller species is observed. This transition in nanotube fluid composition is accompanied by a decrease in the total potential energy of the system. Although adsorption of the smaller species is favored, both species adsorb at lower temperatures in the larger nanotubes. In situations where the molecular diameters are similar, the energetically favored species is preferentially adsorbed at all temperatures. Axial pair correlations are used to relate the composition in the nanotube with the structure of the adsorbed fluid

Influence of temperature on mixture adsorption in carbon nanotubes: a grand canonical Monte Carlo study

Grand canonical Monte Carlo simulations are used to examine the adsorption of a binary Lennard-Jones (sigma(22)/sigma(11) = 1.426, epsilon(22)/epsilon(11) = 1.059) gas mixture into a single-walled structured carbon nanotube. At a temperature, T* = kT/epsilon(11) = 1.2 (388.88 K) and above, the larger species with greater fluid-wall interaction is preferentially adsorbed. At lower temperatures selectivity shifts toward the smaller species, completely eliminating the larger species below T* = 0.935 (303 K). Axial pair correlation functions indicate that the smaller species condenses into the pore at lower temperatures

Statistical thermodynamics of lattice models in zeolites: Implications of local versus global mean field interactions

The statistical thermodynamics of adsorption in caged zeolites is developed by treating the zeolite as an ensemble of M identical cages or subsystems. Within each cage adsorption is assumed to occur onto a lattice of n identical sites. Expressions for the average occupancy per cage are obtained by minimizing the Helmholtz free energy in the canonical ensemble subject to the constraints of constant M and constant number of adsorbates N. Adsorbate-adsorbate interactions in the Brag-Williams or mean field approximation are treated in two ways. The local mean field approximation (LMFA) is based on the local cage occupancy and the global mean field approximation (GMFA) is based on the average coverage of the ensemble. The GMFA is shown to be equivalent in formulation to treating the zeolite as a collection of interacting single site subsystems. In contrast, the treatment in the LMFA retains the description of the zeolite as an ensemble of identical cages, whose thermodynamic properties are conveniently derived in the grand canonical ensemble. For a z coordinated lattice within the zeolite cage, with epsilon(aa) as the adsorbate-adsorbate interaction parameter, the comparisons for different values of epsilon(aa)(*)=epsilon(aa)z/2kT, and number of sites per cage, n, illustrate that for -1 <epsilon(aa)(*)< 0 and n greater than or equal to 10, the adsorption isotherms and heats of adsorption predicted with the two approaches are similar. In general, the deviation between the LMFA and GMFA is greater for smaller n and less sensitive to n for epsilon(aa)(*)> 0. We compare the isotherms predicted with the LMFA with previous GMFA predictions [K. G. Ayappa, C. R. Kamala, and T. A. Abinandanan, J. Chem. Phys. 110, 8714 (1999)] (which incorporates both the site volume reduction and a coverage-dependent epsilon(aa)) for xenon and methane in zeolite NaA. In all cases the predicted isotherms are very similar, with the exception of a small steplike feature present in the LMFA for xenon at higher coverages. (C) 1999 American Institute of Physics. [S0021-9606(99)70333-8]

Influence of Internal Convection during Microwave Thawing of Cylinders

Numerical simulations were carried out for microwave thawing of 2-D cylinders of pure materials with internal convection in the liquid regions. Enthalpy formulation of the energy balance equation was used with a superficial mushy region around the melting point. Electric field, energy and momentum balance equations were solved using the Galerkin finite-element method with the penalty finite element formulation of the momentum balance equation. Microwave power absorption, temperature, and stream functions were studied for various cases. For samples of diameter D, thawing was contrasted between samples for $0.032<D/D_p<3.73$ and $0.10<D/\lambda_m<1.58$. These ratios were $D_p$ computed based on the liquid-phase penetration depth D and wavelength of microwave radiation in the medium $\lambda_m$. In all cases, Pr=0.5 was used and the Rayleigh m number varied from $1.067\times10^3$ for the smallest diameter to $1.33416\times10^5$ for the largest sample (D=2 cm) . Thawing was contrasted for MWs being incident from the top and bottom faces of the cylinder and with the thawing dynamics in the absence of convection in the liquid. Our simulations indicate that convection plays a small role for $D/D_p \ll 1$ and thawing is independent of the direction of MWs. At intermediate values p of $D/D_p$ where a strong maximum occurs in the power, the influence of convection with p primary and secondary cell formation in the liquid regions was a strong function of the direction of incident microwaves. In the presence of multiple connected thawed regions convection was suppressed

Solid–solid transitions in slit nanopores

The structure of Lennard–Jones (LJ) fluids confined in smooth slit-like pores have been investigated using grand canonical Monte Carlo simulations for a bulk state point lying close to the liquid-solid freezing line. The structure of the fluid is examined by computing the in-plane pair correlation function and bond orientational order parameters. Simulations reveal that the fluid not only freezes into the pore but also undergoes a solid–solid transition from a square to a triangular lattice for small changes in pore widths. This transition occurs at pore widths that accommodate two and three fluid layers. Classification of solid structures based on the 3D counterparts, indicate that the transition occurs between solids that correspond to a body centred tetragonal structure to the hexagonal close packed structure. In the two layer structures the pore fluid consists of the first two basal planes of the bct and hcp structures and in the three layer system a complete unit cell of bct and hcp forms in the direction of confinement

Structure and Dynamics of Octamethylcyclotetrasiloxane Confined between Mica Surfaces

Using a molecular model for octamethylcydotetrasiloxane (OMCTS), molecular dynamics simulations are carried out to probe the phase state of OMCTS confined between two mica surfaces in equilibrium With a reservoir. Molecular dynamics simulations are carried out for elevations ranging from 5 to 35 K above the melting point for the OMCTS model used in this study. The Helmholtz free energy is, computed for a specific confinement using the :two-phase thermodynamic (2PT) method. Analysis of the in-plane pair correlation functions did not reveal signatures of freezing even under an extreme confinement of two layers. OMCTS is found to orient with a wide distribution of orientations with respect to the mica surface, with a distinct preference for the surface parallel configuration in the contact layers. The self-intermediate scattering function is found to decay with increasing relaxation times as the surface separation is decreased, and the two-step relaxation in the scattering function, a signature of glassy dynamics, distinctly evolves as the temperature is lowered. However, even at 5 K above the melting point, we did not observe a freezing transition and the self-intermediate scattering functions relax within 200 ps for the seven-layered confined system. The self diffusivity and relaxation times obtained from the Kohlrausch-Williams-Watts stretched exponential fits to the late alpha-relaxation exhibit power law scalings with the packing fraction as predicted by mode coupling theory. A distinct discontinuity in the Helmholtz free energy, potential energy, and a sharp change in the local bond order parameter, Q(4), was observed at 230 K for a five-layered system upon cooling, indicative of a first-order transition. A freezing point depression of about 30 K was observed for this five-layered confined system, and at the lower temperatures, contact layers were found to be disordered with long-range order present only in the inner layers. These dynamical signatures indicate that confined OMCTS undergoes a slowdown akin to a fluid approaching a glass transition upon increasing confinement, and freezing under confinement would require substantial subcooling below the bulk melting point of OMCTS

Modeling velocity autocorrelation functions of confined fluids: A memory function approach

Velocity autocorrelation functions (VACF) of a fluid confined in a slit pore have been modeled using the memory equation. Models for the VACF are based on both the truncation and analytic closure approximations of the Mori's continued fraction representation. The performance of the models is evaluated for gas to liquid-like pore densities and pore widths which accommodate one to four atomic layers. In all cases we compare the predictions from the models with the VACF obtained from molecular dynamics simulations. The truncation models predict an oscillatory behavior for the in-plane VACF with better agreement at lower densities. Among the analytical closure models we observe that the sech model applied at the first level of closure is not only able to capture the short-time dynamics but is also seen to give the best predictions to the in-plane diffusivities at liquid-like pore densities. Although the minima in the VACFs are captured accurately by the sech model, the subsequent plateau regions in the VACF typically observed in confined systems are not predicted. This aspect is due to the slower relaxation of the actual memory kernel, which is not captured by the model. Predictions of the in-plane diffusivities using different levels of analytic closure have been compared with diffusivities obtained from the simulations

Role of length scales on microwave thawing dynamics in 2D cylinders

Microwave (MW) thawing of 2D frozen cylinders exposed to uniform plane waves from one face, is modeled using the effective heat capacity formulation with the MW power obtained from the electric field equations. Computations are illustrated for tylose (23% methyl cellulose gel) which melts over a range of temperatures giving rise to a mushy zone. Within the mushy region the dielectric properties are functions of the liquid volume fraction. The resulting coupled, time dependent non-linear equations are solved using the Galerkin finite element method with a fixed mesh. Our method efficiently captures the multiple connected thawed domains that arise due to the penetration of MWs in the sample. For a cylinder of diameter D, the two length scales that control the thawing dynamics are D/D-p and D/lambda(m), where D-p and lambda(m) are the penetration depth and wavelength of radiation in the sample respectively. For D/D-p, D/lambda(m) much less than 1 power absorption is uniform and thawing occurs almost simultaneously across the sample (Regime I). For D/D-p much greater than 1 thawing is seen to occur from the incident face, since the power decays exponentially into the sample (Regime III). At intermediate values, 0.2 < D/D-p, D/lambda(m) < 2.0 (Regime II) thawing occurs from the unexposed face at smaller diameters, from both faces at intermediate diameters and from the exposed and central regions at larger diameters. Average power absorption during thawing indicates a monotonic rise in Regime I and a monotonic decrease in Regime III. Local maxima in the average power observed for samples in Regime II are due to internal resonances within the sample. Thawing time increases monotonically with sample diameter and temperature gradients in the sample generally increase from Regime I to Regime III. (C) 2002 Elsevier Science Ltd. All rights reserved

Adsorption and diffusion of Lennard-Jones fluids in carbon nanotubes

With the discovery of carbon nanotubes, we have a realistic cylindrical nanopore that can potentially be used for separating fluid mixtures. In the present work, we investigate the adsorption and diffusion of pure L-J fluids in single walled carbon nanotubes. These pure fluid studies will serve as a prelude to understanding the adsorption of mixtures in carbon nanotubes. We perform GCMC simulations to obtain the equilibrium distribution of the fluid inside the nanotube exposed to a pure bulk liquid. Molecular dynamics simulations are subsequently used to obtain self-diffusivities of the adsorbed fluid. An issue while carrying out molecular dynamics in narrow structured cylindrical pores like carbon nanotubes, is the generation of a non-zero net momentum in the pore fluid. To overcome this problem we introduce and evaluate a constrained molecules dynamics method to calculate self-diffusivities of the fluid in the carbon nanotube