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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Lattice gas is considered in the framework of three-dimensional Ono-Kondo theory. It is shown that a nonlinear correction to the configurational energy results in significant improvement of phase behavior, especially near the critical point. [ABSTRACT FROM AUTHOR]

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 discussed in terms of the structural variety of self-assembled systems. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The absorption of molecules on a one -dimensional lattice is considered for repulsive interactions between adsorbate molecules are presented. 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.

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. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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.

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.

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.

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.

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.