Showing papers by "Lev D. Gelb published in 2009"

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

Abstract: 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.

Modeling Amorphous Porous Materials and Confined Fluids

Abstract: Many of the porous materials used in laboratory and industrial processes do not have simple regular or crystalline structures This greatly complicates efforts to characterize them and to understand and optimize their performance for particular applications This review surveys recent efforts to use simulation and modeling to better understand the structure and performance of several classes of materials, including phase-separated glasses, sol-gel-derived materials, templated silica materials, and activated carbons Approaches to modeling these materials fall generally into two classes: reconstructions, which generate models based on experimental measurements, and mimetic simulations, which attempt to model the preparation of the materials While significant progress has been made in many respects, both reconstructive and mimetic transferred currently available are often computationally intensive and not easily transferable between different classes of materials Finally, since gas adsorption is used widely as a characterization tool for amorphous porous materials and is often the focus of the materials' application, recent developments in simulation and theory appropriate to the study of capillary phenomena in amorphous porous materials are reviewed

Structure, thermodynamics, and solubility in tetromino fluids.

Abstract: To better understand the self-assembly of small molecules and nanoparticles adsorbed at interfaces, we have performed extensive Monte Carlo simulations of a simple lattice model based on the seven hard "tetrominoes", connected shapes that occupy four lattice sites. The equations of state of the pure fluids and all of the binary mixtures are determined over a wide range of density, and a large selection of multicomponent mixtures are also studied at selected conditions. Calculations are performed in the grand canonical ensemble and are analogous to real systems in which molecules or nanoparticles reversibly adsorb to a surface or interface from a bulk reservoir. The model studied is athermal; objects in these simulations avoid overlap but otherwise do not interact. As a result, all of the behavior observed is entropically driven. The one-component fluids all exhibit marked self-ordering tendencies at higher densities, with quite complex structures formed in some cases. Significant clustering of objects with the same rotational state (orientation) is also observed in some of the pure fluids. In all of the binary mixtures, the two species are fully miscible at large scales, but exhibit strong species-specific clustering (segregation) at small scales. This behavior persists in multicomponent mixtures; even in seven-component mixtures of all the shapes there is significant association between objects of the same shape. To better understand these phenomena, we calculate the second virial coefficients of the tetrominoes and related quantities, extract thermodynamic volume of mixing data from the simulations of binary mixtures, and determine Henry's law solubilities for each shape in a variety of solvents. The overall picture obtained is one in which complementarity of both the shapes of individual objects and the characteristic structures of different fluids are important in determining the overall behavior of a fluid of a given composition, with sometimes counterintuitive results. Finally, we note that no sharp phase transitions are observed but that this appears to be due to the small size of the objects considered. It is likely that complex phase behavior may be found in systems of larger polyominoes.

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

Abstract: 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.