G. L. Aranovich

Adsorption isotherms for microporous adsorbents

Adsorption equilibria in slit pores are calculated using an analytic solution of the classical Ono-Kondo equation with modified boundary conditions. A new equation is developed for isotherms of gas adsorption on microporous adsorbents. This equation describes isotherms of Type I in the IUPAC classification scheme for temperatures below the critical point and also describes the unusual adsorption of supercritical fluids. This new equation predicts an isotherm that follows the behavior of the Dubinin-Radushkevich (DR) isotherm for relative pressures pps, between 10−1 and 10−5. However, while the DR equation does not give correct behavior either for very low pressures or for moderate to high pressures, this new equation is valid over the whole range of relative pressures. Results obtained are compared with experimental data for adsorption of nitrogen, carbon dioxide, hydrogen sulfide, propane, carbon tetrachloride, ethanol, benzene, iso-octane, n-butane, and methane on activated carbon.

A new model for lattice systems

A new model is derived for lattice systems (lattice gas and binary mixtures of monomers). This model is based on a generalization to three dimensions of the Ono–Kondo equations for the density profile near a flat surface. The internal energy is calculated and compared with previous models. Unlike many previous theories, this new model has the correct limiting behavior at infinite dilution, at high densities, when the interchange energy goes to zero and for the lattice gas. In addition, it displays the correct behavior for systems with very strong interactions (such as hydrogen bonds) in that it predicts that the energy saturates to a constant value at a low density. For one‐component, monomer systems, the new theory also describes simulation data for square‐well (off‐lattice) molecules better than previous theories.

Vapor adsorption on microporous adsorbents

Abstract A new equation describing the adsorption of vapors on microporous adsorbents is presented. This equation is based on the Ono–Kondo model for adsorption in slit-like pores. Results are compared with experimental data for nitrogen on activated carbon over the range of pressures from 0.3 Pa to 0.133 MPa. It is shown that this new equation has several advantages over the widely used Dubinin–Radushkevich (DR) isotherm. In particular, this new equation gives the correct limit of Henry’s law at low concentrations and is more general than the DR equation because it is applicable to gases at supercritical conditions.

A lattice model for fluids with directional interactions

Here we analyze a lattice model for fluids with directional interactions in the framework of the Ono–Kondo theory. The free energy of the system is represented as an explicit function of the temperature and bulk density. It is shown that the model predicts both order–disorder and vapor–liquid phase transitions. This theory predicts a tricritical point where the vapor–liquid and order–disorder phase transitions both disappear. Also, it predicts retrograde condensation where the boundary of phase stability becomes a multivalued function of concentration. In addition, predictions of the theory are compared with Monte Carlo simulation data. It is shown that the partition function cannot be factored to predict separately the contributions of, for example, dispersion and hydrogen bonding interactions.

Nonrandom behavior in multicomponent lattice mixtures: Effects of solute size and shape

A new lattice theory is proposed to describe nonrandom behavior for multicomponent mixtures of monomers, for mixtures of monomers interacting with a polymer, and for mixtures of monomers at a surface. Based on concepts first proposed by Ono and Kondo, this new approach allows one to derive local densities around each species taking into account molecular interactions as well as molecular geometry and lattice structure. This approach can be used to describe a number of very different systems in the framework of a single model. The generalizations presented here are rigorous in that no assumptions beyond those of the original (binary) theory are needed in order to treat multicomponent mixtures of molecules of different sizes and shapes.

Adsorption on surfaces with molecular‐scale heterogeneities

The Ono–Kondo lattice model for the density gradient near a surface is applied to surfaces where the adsorbate–adsorbent interactions are not homogeneous. While solving the general equations would be quite complex, relatively simple solutions can be obtained for periodic surfaces such as a checkerboard. It is shown that the adsorption behavior on surfaces with molecular‐scale heterogeneities is very different from adsorption on surfaces where the surface heterogeneities are much larger than the size of the adsorbent molecules.

Lattice density functional theory predictions of order–disorder phase transitions

Calculations of lattice density-functional theory (DFT) are performed for systems that have both attractive and repulsive forces. Order–disorder phase transitions are observed.

Lattice gas 2D/3D equilibria: Chemical potentials and adsorption isotherms with correct critical points

A priori information is used to derive the chemical potential as a function of density and temperature for 2D and 3D lattice systems. The functional form of this equation of state is general in terms of lattice type and dimensionality, though it contains critical temperature and critical density as parameters which depend on lattice type and dimensionality. The adsorption isotherm is derived from equilibrium between two-dimensional and three-dimensional phases. Theoretical predictions are in excellent agreement with grand canonical Monte Carlo simulations.

Modeling self-assembly in molecular fluids

Equilibrium self-assembly in fluids is studied in the framework of the lattice density-functional theory (DFT). In particular, DFT is used to model the phase behavior of anisotropic monomers. Though anisotropic monomers are a highly idealized model system, the analysis presented here demonstrates a formalism that can be used to describe a wide variety of phase transitions, including processes referred to as self-assembly. In DFT, the free energy is represented as a functional of order parameters. Minimization of this functional allows modeling spontaneous nano-scale phase transitions and self-assembly of supramolecular structures. In particular, this theory predicts micellization, lamellization, fluid–glass phase transitions, crystallization, and more. A classification of phase transitions based on general differences in self-assembled structures is proposed. The roles of dimensionality and intermolecular interactions in different types of phase transitions are analyzed. The concept of primordial codes is...

Monte Carlo simulations on the effect of substrate geometry on adsorption and compression

Canonical Monte Carlo simulations were used to study the adsorption and compression of fluid layers on model substrates with cubic, (111) fcc, and graphite geometries. The effect of the relative size of the fluid and substrate molecules on adsorption was considered for strong molecule-surface interactions. In the case of monolayer formation, it was found that the surface geometry and the size of the adsorbate molecules had a significant effect on the structure of the adsorbed layer. These structures varied from well-ordered, commensurate layers to liquid-like structures. Lateral compression was observed for certain fluid to substrate molecule sizes. For the interactions studied in this work, it was found that maximum lateral compression occurred on the cubic surface when adsorbate molecules had a diameter approximately 15% larger than the substrate diameter. In the case of multilayer formation, it was found that second and higher adsorbed layers could compress into the adsorbed layers below them. For cubic substrates, the interlayer compression was predicted analytically with reasonable accuracy, with maximum interlayer compression found for fluid diameters approximately 90% the size of substrate molecule diameters.