Lev D. Gelb

Monte Carlo simulations using sampling from an approximate potential

A simulation algorithm is proposed in which the potential energy function used in a Monte Carlo simulation is replaced with one that is less expensive to evaluate, coupled with a correction step based on the difference between the two potentials. This can result in a substantial reduction in computational cost. A formal derivation of the appropriate sampling criteria is given, as well as estimates of the possible improvements in code performance. The method is demonstrated on the Lennard-Jones fluid at several state points, where speedups of as much as fourfold are achieved with negligible loss in precision.

Predicting gas adsorption in complex microporous and mesoporous materials using a new density functional theory of finely discretized lattice fluids.

We introduce a nonlocal on-lattice version of density functional theory (DFT) that allows for efficient modeling of fluids in complex inhomogeneous materials. In its previous implementations, classical DFT has required fine discretization of the fluid density. As a result, in studies of gas adsorption it has been used only in idealized pore models with high symmetry. Our new lattice DFT dramatically reduces the computational demand required to model simple fluids and hence can be efficiently applied to complex materials with multiple directions of asymmetry. We apply our new lattice DFT to study nitrogen adsorption in a slit pore with open ends and directly obtain the correct desorption hysteresis. We also apply our DFT to predict hydrogen adsorption accurately in an atomistic model of a metal-organic framework.

A Monte Carlo Simulation Study of Methane Clathrate Hydrates Confined in Slit-Shaped Pores

Monte Carlo simulations are used to study the structure, stability, and dissociation mechanisms of methane hydrate crystals inside carbon-like slit-shaped pores. The simulation conditions used mimic experimental studies of the dissociation of methane and propane hydrates in mesoporous silica gels (Handa, Y. P.; Stupin, D. J. Phys. Chem. 1992, 96, 8599). Simulations are performed under conditions of fixed methane pressure and fixed water loading, with the temperature increased in steps, with long equilibrations at each temperature. The initial structures of the confined hydrates are taken to be bulk-like, and pore widths chosen to accommodate integer or half-integer numbers of hydrate unit cells. Density profiles and orientational order parameter profiles are obtained and used to understand the structural changes associated with hydrate dissociation. Three different common water models, SPC/E, TIP4P, and TIP4P/2005, are used and the results compared. For water modeled using either the TIP4P or TIP4P/2005 potentials, dissociation temperatures are depressed proportionally to the inverse pore width, as predicted by the macroscopic Gibbs-Thomson equation. This behavior is observed for pores small enough that only half-cages of the clathrate structure are present. Experimental work has verified Gibbs-Thomson behavior for pores as small as 2 nm (Seshadri, K.; Wilder, J. W.; Smith, D. H. J. Phys. Chem. B 2001, 105, 2627); micropores of the size studied here have not yet been studied by experiment. Interestingly, the dissociation of hydrates modeled using the SPC/E water potential does not display the predicted pore-size dependence, and the dissociation mechanisms in this model seem to be quite different than those in the TIP4P-type models. In the SPC/E hydrates, with increasing temperature, cage dissocation occurs before methane desorption. In TIP4P-type hydrates, these processes occur either at the same temperature (to within the resolution of this study) or with dissociation occurring at higher temperatures than desorption. These simulations show that a variety of interesting clathrate structures and phase behaviors may be accessed in suitably designed microporous materials, with potentially useful applications in gas storage or separations.

Computational Study of Uniaxial Deformations in Silica Aerogel Using a Coarse-Grained Model

Simulations of a flexible coarse-grained model are used to study silica aerogels. This model, introduced in a previous study (J. Phys. Chem. C 2007, 111, 15792), consists of spherical particles which interact through weak nonbonded forces and strong interparticle bonds that may form and break during the simulations. Small-deformation simulations are used to determine the elastic moduli of a wide range of material models, and large-deformation simulations are used to probe structural evolution and plastic deformation. Uniaxial deformation at constant transverse pressure is simulated using two methods: a hybrid Monte Carlo approach combining molecular dynamics for the motion of individual particles and stochastic moves for transverse stress equilibration, and isothermal molecular dynamics simulations at fixed Poisson ratio. Reasonable agreement on elastic moduli is obtained except at very low densities. The model aerogels exhibit Poisson ratios between 0.17 and 0.24, with higher-density gels clustered around 0.20, and Youngs moduli that vary with aerogel density according to a power-law dependence with an exponent near 3.0. These results are in agreement with reported experimental values. The models are shown to satisfy the expected homogeneous isotropic linear-elastic relationship between bulk and Youngs moduli at higher densities, but there are systematic deviations at the lowest densities. Simulations of large compressive and tensile strains indicate that these materials display a ductile-to-brittle transition as the density is increased, and that the tensile strength varies with density according to a power law, with an exponent in reasonable agreement with experiment. Auxetic behavior is observed at large tensile strains in some models. Finally, at maximum tensile stress very few broken bonds are found in the materials, in accord with the theory that only a small fraction of the material structure is actually load-bearing.

An investigation of the effects of the structure of gel materials on their adsorptive properties using a simple lattice–gas model

We have used a simple lattice–gas model solved in the mean-field approximation to study the effects of material structure on adsorption and desorption isotherms in simple models of silica aerogels and xerogels. We have varied independently the gel particle radius, the density, the surface wettability and the degree of long-range structural correlation in the gel, and in each case obtained adsorption and desorption data at a series of temperatures. These data are discussed in the context of standard adsorption theories and classifications. Kelvin-like behaviour is observed over the entire range of models studied, for both randomly generated gel structures and diffusion-limited aggregates. The shape of the hysteresis loops in these systems appears to vary smoothly with gel structure and is principally determined by the gel density and gel particle size. We have also measured the structure factor at each pressure along each isotherm, for which we discuss data in developing a microscopic understanding of adsorption in these systems. The relative merits of small-angle scattering data and geometrically defined pore size distributions for understanding adsorptive behaviour are discussed. For the material models considered here, a geometric measure of pore size distribution appears to be the best predictor of adsorptive behaviour.

Structural and Transport Properties of Tertiary Ammonium Triflate Ionic Liquids: A Molecular Dynamics Study

Ammonium-based protic ionic liquids (PILs) have shown promising physicochemical properties as proton conductors in polymer membrane fuel cells. In this work, molecular dynamics simulations are used to study the structural, dynamic, and transport properties of a series of tertiary ammonium triflate PILs. Nonpolarizable all-atom force fields were used, including two different models for the triflate anion. Previous simulation studies of these PILs have yielded poor results for transport properties due to unrealistically slow dynamics. To improve performance, polarization and charge-transfer effects were approximately accounted for by scaling all atomic partial charges by a uniform factor, γ. The optimum scaling factor γ = 0.69 was determined by comparing simulation results with available experimental data and found to be transferable between different ammonium cations and insensitive to both the temperature and choice of experimental data used for comparison. Simulations performed using optimized charge scaling showed that the transport properties significantly improved over previous studies. Both the self-diffusion coefficients and viscosity were in good agreement with experiment over the whole range of systems and temperatures studied. Simulated PIL densities were also in good agreement with experiment, although the thermal expansivity was underestimated. Structural analysis revealed a strong directionality in interionic interactions. Triflate anions preferentially approach the ammonium cation so as to form strong hydrogen bonds between sulfonate oxygen atoms and the acidic ammonium hydrogen. The ionic conductivity was somewhat underestimated, especially at lower temperatures. Analysis of conductivity data suggests that there is significant correlated motion of oppositely charged ions in these PILs, especially at short times. These results overall indicate that the transport properties of this class of PILs are accurately modeled by these force fields if charge scaling is used and properly calibrated against selected experimental data.

Nested sampling of isobaric phase space for the direct evaluation of the isothermal-isobaric partition function of atomic systems

Nested Sampling (NS) is a powerful athermal statistical mechanical sampling technique that directly calculates the partition function, and hence gives access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. NS has been used predominately to compute the canonical (NVT) partition function. Although NS has recently been used to obtain the isothermal-isobaric (NPT) partition function of the hard sphere model, a general approach to the computation of the NPT partition function has yet to be developed. Here, we describe an isobaric NS (IBNS) method which allows for the computation of the NPT partition function of any atomic system. We demonstrate IBNS on two finite Lennard-Jones systems and confirm the results through comparison to parallel tempering Monte Carlo. Temperature-entropy plots are constructed as well as a simple pressure-temperature phase diagram for each system. We further demonstrate IBNS by computing part of the pressure-temperature phase diagram of a Lennard-Jones system under periodic boundary conditions.

Thermodynamic and structural properties of finely discretized on-lattice hard-sphere fluids: Virial coefficients, free energies, and direct correlation functions.

Using both molecular simulation and theory, we examine fluid-phase thermodynamic and structural properties of on-lattice hard-sphere fluids. Our purpose in this work is to provide reference data for on-lattice density functional theories [D. W. Siderius and L. D. Gelb, Langmuir 25, 1296 (2009)] and related perturbation theories. In this model, hard spheres are located at sites on a finely discretized cubic lattice where the spacing between lattice sites is between one-tenth and one-third the hard-sphere diameter. We calculate exactly the second, third, and fourth virial coefficients as functions of the lattice spacing. Via Monte Carlo simulation, we measure the excess chemical potential as a function of density for several lattice spacings. These results are then parametrized with a convenient functional form and can immediately be used in on-lattice density functional theories. Of particular interest is to identify those lattice spacings that yield properties similar to those of the off-lattice fluid. We find that the properties of the on-lattice fluid are strongly dependent on lattice spacing, generally approaching those of the off-lattice fluid with increasing lattice resolution, but not smoothly. These observations are consistent with results for larger lattice spacings [A. Z. Panagiotopoulos, J. Chem. Phys. 123, 104504 (2005)]. Certain lattice spacings are found to yield fluid properties in particularly good agreement with the off-lattice fluid. We also find that the agreement of many different on- and off-lattice hard-sphere fluid properties is predicted quite well by that of the virial coefficients, suggesting that they may be used to identify favorable lattice spacings. The direct correlation function at a few lattice spacings and a single density is obtained from simulation. The on-lattice fluid is structurally anisotropic, exhibiting spherical asymmetry in correlation functions. Interestingly, the anisotropies are properly captured in the Percus-Yevick-based calculation of the direct correlation function. Lastly, we speculate on the possibility of obtaining a theoretical equation of state of the on-lattice hard-sphere fluid computed in the Percus-Yevick approximation.