Modification of classical approximations for diffusion in fluids with density gradients.

An analysis of classical approximations is performed for diffusion in fluids with density gradients. This approach gives a new diffusion equation taking into account the asymmetry of molecular mean-free paths and the velocity distribution in the flux term. It is shown that new model is consistent with Einstein's evolution equation for an asymmetric distribution of spatial displacements and with molecular dynamic simulations for hard spheres.

Resolving the inconsistency between classical diffusion and adsorption.

The inconsistency between density profiles of fluids near surfaces and predictions of classical diffusion model is analyzed. A new diffusion equation and its solutions are proposed to reconcile adsorption behavior with predictions of the diffusion equation at the equilibrium limit. The classical phenomenological model of diffusion in fluids is based on the concepts of the mean-free-path, lambda, and diffusion coefficient, D = (1/3)lambdaV, where Vis the characteristic velocity. Using the limit of lambda --> 0 in the flux term gives classical diffusion equation, that is, Fick's law. However, imposing the limit of lambda --> 0 reduces two independent parameters, V and lambda, to one parameter, D = (1/3)lambdaV. This is equivalent to reducing two independent length scales, lambda and Vt, to only one length scale, (Dt)1/2, where t is time. Since the lambda length scale determines density profiles near surfaces, the classical diffusion model "loses" adsorption phenomena after applying the limit of lambda --> 0 and classical solutions are in conflict with adsorption at surfaces. Here, we show that relaxing the requirement of lambda --> 0 by using an exact (finite-difference) functional for the flux term fixes the problem. Solution of the finite-difference diffusion equation is analyzed. This solution allows boundary conditions consistent with density profiles in fluids near surfaces.

Configurational probabilities for monomers, dimers and trimers in fluids.

A new analytical approach is proposed to model aggregation of molecules with isotropic, nearest-neighbor, attractive interactions. By treating the clustering process as a chain reaction, equations with the exact high temperature limit are derived by evaluating the occupation probabilities of nearest neighbors based on the Ono-Kondo approach for a hexagonal lattice to calculate the configurational probabilities of i-mers (i = 1, 2, 3). Equilibrium constants for dimers and trimers are calculated based on the configurational probability data. The proposed model agrees well with Monte Carlo simulations at medium and high temperatures. At low temperatures, the model can be improved by considering the full set of site densities in the first shell of a central trimer. Approximate analytical solutions derived from exact calculations of the grand partition function for monomer adsorption on a 4 x N hexagonal lattice with cylindrical boundary conditions also are presented.

Monte Carlo simulations of phase transitions and adsorption isotherm discontinuities on surface compression.

Low temperature, Grand Canonical Monte Carlo simulations were used to study the adsorption of fluid layers on cubic, hexagonal, and atomically smooth substrates to determine the effects of registry and surface compression on the system. The size of the fluid molecules was fixed to be 20% larger than the substrate molecules in order to observe the transition from an expanded to commensurate and finally to an incommensurate monolayer. For relatively weak fluid-substrate interactions, the cubic system underwent a first-order phase transition. As the strength of the fluid-substrate interactions increased, the molecules became fixed at commensurate locations and the transition from low density to commensurate packing became continuous. The strong fluid-substrate interactions lead to the development of a kink in the adsorption isotherm that showed the increased stability of the commensurate phase. This kink became more pronounced as the system temperature was decreased. The hexagonal system showed less dramatic results due to a decrease in the substrate well depth of the relative to the cubic system. The system did experience a first-order phase transition for a weak fluid-substrate interactions and the transition became much more gradual as the fluid-substrate interaction increased. The molecules became fixed to commensurate substrate locations, but the surface was not corrugated sufficiently to have a stable commensurate phase. The atomically smooth substrate showed the first-order phase transition expected of a low temperature system with no effects of registry.

Configurational probabilities for symmetric dimers on a lattice: an analytical approximation with exact limits at low and high densities.

A new approach is developed for lattice density functional theory of interacting symmetric dimers at high temperatures. Equations of equilibrium for two-dimensional square and three-dimensional cubic lattices are derived for the complete set of configurations in the first three shells around the central dimer, and rules of truncation for higher shells are based on exact results from the mathematical theory of domino tilings. This provides exact limits for both low and high densities. The new model predicts contributions of particular configurations which are in agreement with Monte Carlo simulations over the whole range of densities, including agreement with pocket Monte Carlo simulations at high densities.

Equilibrium limit of diffusion equation for interacting particles: are bifurcations and multiplicity of correlation functions an artifact or real?

The structure of a fluid is analyzed by taking the equilibrium limit of a diffusion equation including the Giacomin-Lebowitz term for intermolecular interactions. This equation represents the differential mass balance in fluids with the Metropolis algorithm for fluxes; it allows a new qualitative yet analytical approximation for the direct correlation function over the entire range of fluid densities and temperatures. This approximation is analogous to a classical Ono-Kondo model for adsorption if the distribution of molecules around a central molecule is viewed as the adsorption of molecules on a central molecule. While this model qualitatively predicts known behavior for both gas and liquid phases, approaching a phase transition (e.g., condensation of gas into liquid) results in a bifurcation and multiplicity of the direct correlation function. The model predicts a sequence in the transformation of correlation functions from that of a gas to that of a liquid. This sequence starts with the appearance of an isolated loop in the direct correlation function, indicating states that are stable but cannot be achieved without perturbation of the system. However, the system seems to sense its proximity to a phase transition and reflects the distance to the phase boundary by the size and shape of this isolated loop in the direct correlation function. At lower temperatures, this loop merges with the gas-phase peak, indicating that clusters can form spontaneously. Then, these clusters grow into a high-density (liquid) phase. The notion of bifurcations and multiplicity in correlation functions is an unusual and controversial concept. Certainly, it is unexpected and raises important questions: (a) if such a behavior is not real, why does the diffusion equation predict such behavior, i.e., is it a mathematical artifact or is it due to conflicting physical assumptions? (b) if this behavior is real, how does one interpret it at a molecular level? Here, we present some interpretations, but they are open for discussion.

Liquid-vapor density profiles from equilibrium limit of diffusion equation for interacting particles.

Liquid-vapor density profiles are derived from the equilibrium limit of diffusion equation for interacting particles. These profiles are in good agreement with classical hyperbolic tangent relation. For simple Lennard-Jones fluids, predicted density distributions agree with computer simulation data, but have a slightly sharper transition zone. For alkali metals with Lennard-Jones-like potentials, the new equations predict a very good average distribution with quite satisfactory agreement with Monte Carlo simulation results. For liquid metals and water surfaces, accurate interfacial profile predictions also can be achieved by using effective two-body potential data instead of Lennard-Jones parameters.

Thermodynamics of symmetric dimers: lattice density functional theory predictions and simulations.

A new lattice density functional theory (DFT) approach is proposed for symmetric dimers taking into account all possible configurations for molecules adjacent to a central dimer. Comparison with Monte Carlo simulations shows significant improvement of the proposed model compared to previously developed version of lattice DFT for dimers. It is shown that the new model gives accurate analytical solutions over a wide range of densities and temperatures. Phase transitions in dimers are analyzed and fundamental differences between dimers and monomers are discussed.

Generalization of Kelvin's equation for compressible liquids in nanoconfinement.

The Kelvin equation for a compressible liquid in nanoconfinement is written in a form that takes into account not only Laplace's pressure, but also the oscillatory compression pressure. This leads to a simple analytical equation for pressure in nanocapillaries. The corrected equation is used to analyze properties of aqueous systems, including the oscillatory structural forces between attractive surfaces and inert surfaces, repulsive "hydration" forces between hydrophilic surfaces, and attractive "hydrophobic" forces between hydrophobic surfaces. Relative vapor pressure in a nanocapillary also is discussed.

The role of adsorption compression in nanocapillarity.

Influence of adsorption compression on nanocapillarity is discussed. Kelvin's equation for a compressible liquid is written in a form that takes into account not only Laplace's pressure, but also adsorption compression. This leads to a simple analytical equation for pressure in nanocapillaries. It is shown that the ratio of Laplace's pressure to the adsorption compression pressure determines different types of nanocapillary behavior. When the Laplace pressure dominates, it results in classical capillarity that is well studied and understood. There is an intermediate range where Laplace's pressure is partially or fully compensated by adsorption compression, and the resulting pressure in a capillary is an interplay between attraction to walls and repulsions from neighboring molecules in compressed adsorbed fluid. If the adsorption compression pressure dominates, it results in inversion of capillary pressure and the fluid adsorbed in the nanocapillary presses on walls from inside. This phenomenon has been observed experimentally for fluids in nanoporous solids; in particular, high-precision measurements have shown significant expansion of nanoporous adsorbents loaded with various fluids. It is also shown that oscillatory adhesion forces and internal forces in nanoporous adsorbents have a common thermodynamic origin and can be discussed in the framework of adsorption compression mechanisms.

Adsorption behavior of repulsive molecules.

Recently, it has been shown that adsorption of gases on solid surfaces often leads to repulsive forces between adsorbate molecules. In this paper, adsorption of molecules on a one-dimensional lattice is considered for repulsive interactions between adsorbate molecules. Exact adsorption isotherms are calculated and analyzed for finite and infinite chains of active sites (i.e., a one-dimensional lattice). Although the mathematical solution for the one-dimensional lattice is known for attractive and repulsive systems, the effects of intermolecular repulsions on adsorption behavior have not been studied in detail previously. Similarly, though the mathematics for the one-dimensional lattice has been solved for any arbitrary lattice length, the effect of finite size on adsorption isotherms for repulsive adsorbate interactions has never been examined. This paper shows that spatial confinement and strong attraction to active sites can cause compression of an adsorbed phase and that repulsive interactions between adsorbed molecules result in steps in the adsorption isotherms. For higher chemical potentials, the density increases until saturating at the lattice capacity. These steps in the adsorption isotherm have not been observed in previous studies of lattice systems. For small lattices, the adsorption behavior was found to be fundamentally different for even and odd values of lattice length. Lattices with an even number of lattice sites can have two steps in the adsorption isotherm, whereas systems with an odd number of sites only have a single step occurring at a coverage slightly greater than half the lattice capacity.

Diffusion equation for interacting particles.

A new approach to molecular diffusion is developed using density functionals for fluxes and the Metropolis algorithm in the mass balance equation. This procedure results in a new equation for diffusion of interacting particles which has multiple solutions and gives density distributions for coexisting and metastable phases. It is shown that the diffusion of interacting molecules is driven by two variables: the density gradient of molecules and the density of molecule-vacancy pairs ("pseudoparticles").

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.

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.

Phase loops in density-functional-theory calculations of adsorption in nanoscale pores.

Phase loops with multiple solutions are observed in calculations of lattice density-functional theory. It is shown that the standard numerical methods for solving such problems distort the solution. A technique is proposed to obtain multiple solutions for phase equilibria in confined fluids. This method gives the entire phase equilibrium curve, including hidden points which determine wetting transitions and capillary condensation. A synergetic effect of walls on adsorption in nanoscale pores is analyzed.

[Characteristics of Debye potentials in cell structures]. / Osobennosti potentsialov Debaia v kletochnykh strukturakh

The activity of the cellular system is accompanied by the changes of substrate concentrations and excreted substances in the medium. This event brings about essential changes of the medium electrical properties. For the accomplishment of stationary metabolism the following condition should be fulfilled B=--2nsquare rootA, where n=1,2...., A and B are some functions depending on the diffusion coefficient of the substrate and excrement, their molecular weights, dissociation coefficients, membrane permeabilities and other parameters of the cellular structure.