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The continuum quasichemical approximation is used to improve the accuracy of describing molecular distributions in a vapor–liquid system. It considers displacements of the molecular center of mass from the center of a cell within the lattice gas model. It also allows for (as in its discrete variant) direct correlations of interacting molecules. The probability density of a molecule being inside the cell is used as a continuous function of its coordinate. An algorithm for solving a system of integral equations is developed with respect to the pair distribution function. The effect the continuum description of the particle distribution has on the concentration dependences of the main thermodynamic functions is investigated. The approach is shown to explain the concentration dependence of the parameter of effective lateral interaction.

The effect of adsorption on the characteristics of equilibrium rough surfaces of vapor–liquid and vapor–solid interfaces at a temperature close to the melting point is investigated. A discrete model of a dense phase—the lattice gas model, which includes direct correlations of all neighboring components of the system in a quasi-chemical approximation—is applied in the calculations. For simplicity, the model implies commensurability of the component size and the considered vibrations of particles through the effective contributions of the lateral interaction parameters for both adsorbent atoms and adsorbate molecules. The equilibrium profiles of adsorbent A and adsorbate B inside the transition area are calculated (provided that the adsorbent’s bulk phase remains unchanged) for physical adsorption and chemisorption. The effect of adsorption on the surface tension of the dense phase is examined. The probability of fluctuation processes of a new phase formation determined by the surface roughness of the pure adsorbent A, taking into account the adsorption of B particles on it, is estimated.

Expressions for calculating Gibbs vapor–liquid surface tension σ are generalized to allow for the interaction between comparable components of a mixture with an arbitrary radius of the interaction potential. Calculations are performed within a modified lattice gas model reflecting a discrete-continuous distribution of mixture components in space with allowance for direct correlations in a quasi-chemical approximation. The calculating of σ is associated with the rejection priority of mechanical characteristics over chemical potential, which is traditional in continuum mechanics. The chemical potential governs local equilibrium distributions of components in the transitional region of a boundary, resulting in the need to use microscopic Gibbs–Duhem equations in a deformed lattice structure of a substance to determine the average distance between molecules (as lattice structure parameters) and to consider effective one-particle motions of components in a dense phase that alter these parameters. Calculations of the surface tension of dense mixtures in models ignoring the existence of vacancies and structural deformation are discussed.

The fulfillment of the self-consistency condition in the description of adsorption and desorption the rates of dissociating vapor molecules on the rough surface of an adsorbent (equilibrium and tempered from an equilibrium state) is considered. The adsorption process causes the reconstruction of the equilibrium near-surface region of the adsorbent, but does not change the state of the tempered surface. The adsorption–desorption rates are calculated taking into account the interaction of the nearest neighbors in the quasi-chemical approximation. Four models are considered for the description of a nonuniform surface: the initial averaged multilayer model with different types of adsorption sites (and Henry constants), a model containing all the sites available for adsorption, and three types of its averaging. The first type of averaging is associated with the transition to a single-layer nonuniform surface containing different types of adsorption sites with different Henry constants, the second is associated with the transition to a set of effective uniform monolayers in the multilayer transition region, and the third is associated with the transition to a single-layer effective uniform surface. The condition of self-consistency is fulfilled in the last two types of averaging and is violated in the first type of averaging, as well as in the averaged model taking into account the differences between the types of sites. It is found that the state of a nonuniform surface (equilibrium or tempered) does not affect the self-consistency of the description of the rates of adsorption and desorption in the latter two types of models. The influence of taking into account the effects of correlation of the interaction of species on the condition of self-consistency is shown. The neglect of the effects of correlation of interacting species leads to the violation of the self-consistency condition in all models.

Ways of satisfying the condition for the self-consistent description of adsorption and desorption rates of non-dissociated molecules on a rough aerosol surface are considered. The rates are calculated with allowance for the interaction between nearest neighbors in the quasi-chemical approximation. Four types of models are analyzed. One describes the initial distributed heterogeneous surface, while the other three are variants averaged over the number of monolayers (with a transition to a single-layered heterogeneous surface) and different types of adsorption centers with different Henry constants (with a transition to an effective homogeneous monolayer in a multilayered transition region), or over the number of monolayers and types of adsorption centers (with a transition to the single-layered homogeneous surface) simultaneously. Types of models are distinguished for which the self-consistency condition is strictly satisfied and for which it is violated. Observed discrepancies are explained. The dependence of the degree of discrepancy (if there is one) on the density of the gas in the system, the energy of interaction of the activated complex, and the radius of adsorbent particles is established.

A correct way of calculating the equilibrium surface tension of planar and curved vapor–liquid interfaces is formulated for the first time according to Gibbs (i.e., as the excess free energy in the region of immiscible phase transitions). Calculations are performed using a modified lattice gas model that reflects a discrete–continuous distribution in the space of mixture components. The discrete size scale is associated with regions of around the size of a molecule that form the cells of the lattice structure. The continuous scale corresponds to the intermolecular motion of components inside the cells. The intermolecular interactions of comparable components are considered in a quasi-chemical approximation that describes direct correlations. It is shown that considering only the discreteness of the molecular distribution on a rigid lattice does not provide simultaneous satisfaction of two special conditions of chemical and mechanical equilibria for any degrees of interface curvature, and that the conditions of phase partitioning are insufficient for unambiguous calculations of the surface tension. The condition for the complete equilibrium of two phases must be supplemented with the conditions of the local mechanical and chemical equilibria at each point of the boundary transition region, and the local pressure value must be adjusted to the local value of the chemical potential.

An approach to calculating the effects of density fluctuations is generalized with allowance for the movement of molecules in small condensed multicomponent heterogeneous systems (e.g., droplets, microcrystals, and adsorption on microcrystal faces). The collective character of statistical sums of vibrational, rotational, and translational motions of separate molecules in dense phases is expressed in dependences of these statistical sums on the local configurations of neighboring molecules. Using the quasi-chemical approximation with allowance for interparticle interactions reflecting the effects of direct short-range correlations, a relationship is derived between the statistical sum of a system consisting of a multicomponent mixture of molecules and the statistical sums of individual components. A structure is formulated for isotherm equations associating the density of mixture components and their chemical potentials in a thermostat, and for pair distribution functions.

An analysis is presented of one of the key concepts of physical chemistry of condensed phases: the theory self-consistency in describing the rates of elementary stages of reversible processes and the equilibrium distribution of components in a reaction mixture. It posits that by equating the rates of forward and backward reactions, we must obtain the same equation for the equilibrium distribution of reaction mixture components, which follows directly from deducing the equation in equilibrium theory. Ideal reaction systems always have this property, since the theory is of a one-particle character. Problems arise in considering interparticle interactions responsible for the nonideal behavior of real systems. The Eyring and Temkin approaches to describing nonideal reaction systems are compared. Conditions for the self-consistency of the theory for mono- and bimolecular processes in different types of interparticle potentials, the degree of deviation from the equilibrium state, allowing for the internal motions of molecules in condensed phases, and the electronic polarization of the reagent environment are considered within the lattice gas model. The inapplicability of the concept of an activated complex coefficient for reaching self-consistency is demonstrated. It is also shown that one-particle approximations for considering intermolecular interactions do not provide a theory of self-consistency for condensed phases. We must at a minimum consider short-range order correlations.

An approach to calculating the effects of fluctuations in density that considers the collective motions of molecules in small condensed phases (e.g., droplets, microcrystals, adsorption at microcrystal faces) is proposed. Statistical sums of the vibrational, rotational, and translational motions of molecules are of a collective character expressed in the dependences of these statistical sums on the local configurations of neighboring molecules. This changes their individual contributions to the free energy and modifies fluctuations in density in the inner homogeneous regions of small bodies. Interactions between nearest neighbors are considered in a quasi-chemical approximation that reflects the effects of short-range direct correlations. Expressions for isotherms relating the densities of mixture components to the chemical potentials in a thermostat are obtained, along with equations for pair distribution functions.

A procedure for calculating the surface tension of droplets consisting of two components in the vapor phase is considered. The calculations are performed using the lattice gas model in the quasi-chemical approximation with allowance for the correlation effects of the nearest interacting molecules. A layered model of the structure of a vapor–liquid interface is used. Ways of calculating the surface tension of droplets with different radii are considered. They are based on different thermodynamic definitions of reference surfaces. Typical dependences of the surface tension of metastable and equilibrium droplets on the droplets’ radii are analyzed for four types of phase diagram. It is found that if the energy of interaction between the components of one type exceeds by 150% the energies of interaction between components of another type and between particles of different types, and if the component with the highest energy of interaction predominates in a droplet, this results in a nonmonotonic profile of the component with the lowest energy of interaction in the region of transition. Mixture components are distributed in the region of transition such that the component with the highest energy of interaction is concentrated on the liquid side and the other component is concentrated on the vapor side. The surface tension of equilibrium droplets is less than that of metastable droplets.

A procedure for analyzing the formation processes of two-dimensional droplets of an adsorbate on a rigid adsorbent support is considered. The molecular theory is based on data on the potential functions between adsorbent atoms and adsorbate molecules. Interactions between nearest neighbors are considered in the quasi-chemical approximation. The internal motions of adsorbent atoms and adsorbate molecules are ignored. Problems of describing the formation of droplets on heterogeneous adsorbents are associated with calculations for binodals (illustrated with the simplest example of two different homogeneous crystal faces) due to the choice of methods for calculating linear tension and the structural model of the region of the liquid–vapor transition. The dependence of the characteristics of droplets in the layered structural model on the method for determining the reference lines of the tension is shown for their metastable and equilibrium states. It is found that for a number of structural parameters, the thermodynamic determination of the line of tensions of metastable droplets can result in nonmonotonic dependences of the linear tension on their radii. The characteristics of two-dimensional liquid–vapor interfaces are compared for two structural models: coordination sphere and layered. It is found that the coordination sphere model allows the exclusion of the structural parameter of the layered model, but both models need refinement at small radii.

A molecular model developed earlier for a polar fluid within the lattice gas model is supplemented by considering the vibrational motions of molecules using water as an example. A combination of point dipole and Lennard-Jones potentials from SPC parametrization is chosen as the force field model for the molecule. The main thermodynamic properties of liquid water (density, internal energy, and entropy) are studied as functions of temperature. There is qualitative agreement between the calculation results and the experimental data. Ways of refining the molecular theory are discussed.

A molecular statistical theory for calculating the linear tension of small multicomponent droplets in two-dimensional adsorption systems is developed. The theory describes discrete distributions of molecules in space (on a scale comparable to molecular size) and continuous distributions of molecules (at short distances inside cells) in their translational and vibrational motions. Pair intermolecular interaction potentials (the Mie type potential) in several coordination spheres are considered. For simplicity, it is assumed that distinctions in the sizes of mixture components are slight and comparable to the sizes of adsorbent adsorption centers. Expressions for the pressure tensor components inside small droplets on the heterogeneous surface of an adsorbent are obtained, allowing calculations of the thermodynamic characteristics of a vapor–fluid interface, including linear tension. Problems in refining the molecular theory are discussed: describing the properties of small droplets using a coordination model of their structure, considering the effect an adsorbate has on the state of a near-surface adsorbent region, and the surface heterogeneity factor in the conditions for the formation of droplets.

Equations self-consistently describing chemical and mechanical equilibria in heterogeneous systems are derived. The equations are based on the lattice gas model using discrete distributions of molecules in space (on a scale comparable to molecular size) and continuum distributions of molecules (at short distances inside the cells) during their translational and vibrational motions. It is shown that the theory provides a unified description of the equilibrium distributions of molecules in three aggregate states and at their interfaces. Potential functions of intermolecular interactions (such as Mie pair potentials) in several coordination spheres that determine the compressibility of the lattice structure are considered. For simplicity, it is assumed that differences between the sizes of mixture components are small. Expressions for the local components of the pressure tensor inside multicomponent solid phases and heterogeneous systems (adsorptive, absorptive, and interfaces) are obtained. It is established that they can be used to calculate the lattice parameters of deforming phases and the thermodynamic characteristics of interfaces, including surface tension. The tensor nature of the chemical potential in heterogeneous systems is discussed.

The size dependence of the linear tension of round two-dimensional equilibrium drops in the vapor phase on a homogeneous surface of an adsorbent is studied at the pressure of saturated two-dimensional vapor. The calculations are based on the lattice gas model in a quasi-chemical approximation with allowance for the correlation effects of the nearest interacting molecules. Methods for calculating linear tension using the equimolecular reference line are considered. Temperature dependences of the linear tension are studied for metastable and equilibrium drops. It is found that the differences between the thermodynamic properties of two types of drops are slight over a wide range of variation in drop radii.

The effect of internal motions of an adsorbate on the local characteristics of adsorption and layering phase diagrams are studied for structurally heterogeneous surfaces of slit-like pores. A molecular model describing adsorbate distributions inside slit-like pores, which is based on discrete distribution functions (lattice gas model), is used for the calculation. Molecular distributions are calculated by the Lennard-Jones potential (12–6) in a quasi-chemical approximation reflecting the effects of direct correlations of interacting particles and for the combined interaction of an adsorbate with walls in the average potential approximation (9–3) and the short-range Lennard-Jones potential for structurally heterogeneous surface areas. The conclusion is made that internal motions reflect the vibrational motion of molecules within a modified quasi-dimer model and a displacement of the adsorbate during its translational motion inside cells. It was found that the taking into account of internal motions decreases the critical temperature of adsorbate layering in slit-like pores.

The phase state of adsorbate in porous systems is considered, in which the walls are characterized by interaction potential with adsorbate: from strong attraction to absence of attraction. The equations are based on discrete distribution functions (the lattice gas model) taking into account the contribution of the vibration motions of adsorbate. The vibration motion of molecules is taken into account in the modified quasi-dimer Mie model. Molecular distributions are calculated in the quasi-chemical approximation reflecting the effects of direct correlations of interacting particles using the Lennard-Jones potential. Conditions of express estimates of vibration frequencies are discussed in which vibration frequencies weakly affect molecular distributions in the case of strong adsorption. It is found that consideration of vibrations results in a shift in adsorption isotherms in the coordinates of chemical potential-density to higher values of vapor pressure in the range of high fillings. This is related to the necessity of additional vapor “compression” for its transition into the adsorbed state characterized by higher kinetic energy.

A molecular model of adsorbate melting in slit-like pores [1] is used to calculate adsorption isotherms with regard to the contribution from vibrational motions of the adsorbate. The equations are based on discrete distribution functions (the lattice gas model). Molecular distributions are calculated in a quasi-chemical approximation reflecting the effects of direct correlations of interacting particles using the Lennard-Jones potential. The vibrational motion of molecules is taken into account using a modified quasi-dimer Mie model. It is shown that considering vibrations shifts the adsorption isotherms in the chemical potential-density coordinates to higher vapor pressures in the region of high filling. This is due to the need for additional compression of the vapor to transfer it into the adsorbed state with increased kinetic energy.

The numerical implementation of a crystallization/melting theory that has two branches of isotherms for liquids and solids as in Landau’s theory within the general self-consistent theory of condensed states is discussed. Equations are based on discrete distribution functions (the lattice gas model). Molecular distributions are calculated to a quasi-chemical approximation reflecting the effects of direct correlations between interacting particles. the interaction between particles is described by the Lennard-Jones potential, while the vibrational motion of molecules is included using a modified quasi-dimer Mie model. The effect of the vibrations of atoms on lateral interactions between nearest and next nearest neighbors is considered, along with a scheme for considering the displacement of particles in a liquid that modify such lateral interactions. Examples of calculations describing a defective crystal and vapor-liquid system are given.

The role of local environment relaxation is studied in calculating the rates of elementary processes in vapor-liquid systems consisting of dipole molecules. It is accepted that the intermolecular interaction potential of reaction system components includes dipole-dipole and Lennard-Jones terms. Two limiting cases of short and long characteristic times of an elementary reaction are considered relative to the thermal progressive and rotational motions of neighboring dipole molecules. It is shown that the condition of long characteristic times for elementary reactions that correspond to the concept of activated complex activity distorts the properties of a system. Good correspondence is obtained for the temperature dependence of the water self-diffusion coefficient.

We investigate the effect of restricting the area of planes of microcrystals and equilibrium density fluctuations in components of binary mixtures on partial isotherms of the adsorption of binary mixtures of molecules and the rate of a surface reaction of the Langmuir-Hinshelwood type. Adsorption of components of mixture is considered in a large canonical assembly, and the rate of an elementary step is calculated in kinetic regime. The value of a section of the surface on a plane contains a number of adsorption centers in the range of 10 to 105. The effect of the structure of a heterogeneous surface on the rate of the considered reaction is studied. The effect of the density fluctuations of adsorbed molecules on partial adsorption isotherms and fluctuations in the rate of reaction on heterogeneous surfaces is discussed. It is shown that the greatest effect of density fluctuations on the rate of a step is observed at low fillings of each plane of a particle and at the almost complete filling of a plane.

A molecular dynamic theory based on the lattice-gas model for the local reorganization of multi-component systems containing charged species is considered. Expressions for the mono- and bimolecular stages of the elementary processes that describe chemical reactions and displacements and rotations of molecules in dense gases and liquids are derived, with consideration given to direct and indirect effects of the initiation of electron and proton transfer. The proposed kinetic equations describe small-scale restructuring of solutions containing components of different sizes under the influence of changes in the external parameters of the molecular system at the kinetic stage of evolution of the system. The theory retains the effects of direct spatial correlations in the distribution of all the components of the mixture with the help of pair distribution functions in the quasi-chemical approximation. The dynamics of the local reorganization of molecules includes the kinetic equations for the local densities and pair distribution functions. The equations derived are intended to describe liquid-phase reactions, ion charge exchange, mutual diffusion of components of different sizes in multicomponent solutions, extraction processes at liquid phase boundaries, and photochemical processes in condensed phases.

Equations for the isotherms of adsorption of pure substances on small inhomogeneous crystalline particles with taking into account density fluctuations and intermolecular interactions in the quasi-chemical approximation were obtained for the first time.

An approach to consideration of non-integer ratios between linear molecule sizes having shapes close to linear chains, plates, and rectangular parallelepipeds was suggested for the lattice gas model. A statistical description of molecule orientation states retains spatial discretization as for molecules with multiple ratios between linear molecule sides, but the general balance of filled nodes and, which is most important, the influence of interparticle potentials reflects real molecule sizes through the nonideality function.

The effect of the finiteness of face areas and equilibrium fluctuations on the adsorption isotherms of binary molecular mixtures and the rate of surface processes occurring on nanosized particles is studied. The adsorption process is considered in the grand canonical ensemble; the rates of elementary stages are calculated in the kinetic mode. The surface region on the face is found to contain a number of adsorption centers ranging from 10 to 105. The effect of density fluctuations of adsorbed molecules on the partial adsorption isotherms and rate fluctuations is discussed. A calculation procedure for density fluctuations in heterogeneous microparticles with different faces and different binding energies of molecules with the surface is considered. It is shown that the greatest effect of density fluctuations is manifested at a low occupancy of each face of the particle.

The molecular theory of curved vapor-liquid interfaces within the lattice gas model is applied to analyze supersaturated vapor states in dependence on the new phase size and system temperature. The molecular interaction is considered in the quasi-chemical approximation which describes effects of direct correlations of the nearest molecules. Two methods for determining the surface tension are discussed: equimolecular and according to the surface tension minimum in the intermediate region, i.e., on the tension surface. It is shown that a tension surface exists for metastable drops in supersaturated vapor over the temperature range, but its use leads to multivaluedness of solutions for its position; the minimum range of the existence of metastable drops is close to the previously determined lower limit for equilibrium.

A dynamic theory of the local rearrangement of multicomponent molecular systems based on the lattice-gas model is constructed. Kinetic equations describing the small-scale restructuring of solutions containing components of different sizes under the influence of the external parameters of the system are derived. The intermolecular interactions between the reactants and the solvent specified in the form of an atom-atom potentials are described in the quasi-chemical approximation. This approach reflects the direct effects of spatial correlations in the distribution of all components of the mixture by means of pair distribution functions. The dynamics of the local rearrangement of the molecules is described by the equations for local density and pair distribution function. The theory is also capable of describing the mutual diffusion of components of different sizes in multicomponent solutions and the processes of swelling of polymers under the action of low-molecular substances dissolved in them. The problems of detailed description of the rates of elementary stages in dense gases and liquids by taking into account the direct dynamic effects of colliding molecules and the cooperative movement of polymer units during the relaxation of amorphous polymer matrices are examined.

Principles of the fluctuation theory of microheterogeneous systems are considered based on the example of adsorption on a heterogeneous surface of microcrystals and spherical liquid droplets in the vapor phase. Equations that describe the equilibrium distributions of molecules are derived within the lattice gas model with allowance for lateral interactions in the mean-field approximation. This approximation does not take into account the correlation effects of interacting particles. We discuss the structure of entropy and energy contributions in the derived equations and the relationship between the molecular chemical potential and the expansion pressure, which is analogous to the equation of the state, as well as the molecular interpretation of the concept of pressure in an ensemble of small particles and its relation to the mechanical interpretation of the surface tension.

The structure of a closed system of kinetic equations based on the lattice gas model is discussed for multistage processes in condensed phases including the electron transfer stage. The transition from the traditional energy description of the state of a system to the coordinate description is related to the necessity of the inclusion of the spatial correlation of mixture components. An arbitrary type of interaction potentials between solution components is considered possible. Electron transfer is limited by the reorganization of surrounding molecules. Local distributions of mixture components form a local potential barrier to electron transfer. The system of equations was constructed for an arbitrary electron transfer mechanism. The distributions of all solution components are calculated in the quasi-chemical approximation for taking into account the spatial correlation of interacting particles. The evolution of reagent and solvent molecule local distributions determines the influence of solution component concentrations on both the local and overall rate of liquid-phase reactions.

A lattice gas model is used to describe the vapor-liquid state of water molecules. The orientationally directed interaction of the water molecules via their tetrahedral structure and dipole-dipole interaction are considered in the theory, along with the Lennard-Jones contributions to the potential of molecular interaction, which stabilize the system with dipole interaction. We studied how the radius of the molecular interaction potential affects the equilibrium characteristics of the system (the phase separation curves of the vapor-liquid system, and the relationship between the fluid density and the chemical potential value).

The molecular model of a polar liquid based on the lattice gas theory was used to study the liquid—gas phase equilibrium. In this theory, the key unknown variables are the probabilities of various mutual pair positions of the molecules. The molecules are considered as non-polarizable point dipoles. The intermolecular interaction potential includes a dipole—dipole component depending on the molecular orientation and the Lennard-Jones contribution stabilizing the system with dipole interactions. The theory provides qualitative agreement with experimental data on the water—vapor equilibrium.

Fundamentals of the equilibrium fluctuation theory of adsorption of molecules on microcrystalline particles taking into account the atomic structure of nonuniform surfaces were developed. The importance of taking into account the discrete character of adsorption centers in constructing adsorption isotherm equations was demonstrated. This changes the type of the mathematical apparatus in the search for a maximum distribution function term in a grand canonical ensemble: instead of differential derivatives, symmetrized difference derivatives should be used. The fluctuation theory of adsorption was generalized to ideal multicomponent mixtures of molecules. Adsorption isotherm equations for multicomponent mixtures on uniform and nonuniform surfaces taking into account limited sizes of the surface of various microcrystal faces and fluctuation contributions were obtained. The equations describe the influence of equilibrium fluctuations on adsorption isotherms for adsorbent particles of all sizes, from nanometric to macroscopic. An analysis of the equations showed that the influence of fluctuations was strongest at low coverages for each microcrystal face. The simplest case of taking fluctuations into account in the presence of contributions of lateral interactions in the mean field approximation was discussed.

The molecular theory of adsorption is used to estimate the upper bound of the validity of the Kelvin equation for calculating the saturated vapor pressure in meso- and macroporous adsorbents. The values of saturated vapor pressure are compared according to the theoretical adsorption isotherms obtained in terms of the lattice gas model and the Kelvin equation for atoms of argon and molecules of nitrogen and tetrachloride carbon. As the temperature increases, the agreement between the two methods improves. It is shown that the validity of the results obtained using the Kelvin equation for problems of absorption porometry is even limited for pores as small as 50 nm.

In this work, a microhydrodynamic approach is used to investigate the motion of the meniscus on a vapor—liquid interface in narrow slitlike pores. Calculations are performed on the basis of Navier—Stokes—type equations, in which the transport coefficients and equation of state for a compound are calculated within the simplest molecular model of a gas lattice that takes into account the inherent volume of molecules and their interaction with each other and the pore wall. The dynamic modes of the flow of a liquid monatomic gas (argon) bearing a vapor bubble through nanosized pores at a given pressure difference across the pore are studied. The differences in the average rates of the liquid and vapor-bubble motion in a quasi-stationary regime caused by the intensive nonequilibrium processes of molecule exchange on the liquid—vapor and vapor—liquid boundaries, i.e., by the phase transitions on both boundaries of a bubble, are revealed.

The modified lattice-gas model is used to construct the model and the concentration profiles of the liquid—vapor for spherical drops of different size. A monotonic character of the temperature dependence of the width of the transition layer between the liquid and the vapor is demonstrated. The dependence of the surface tension on the drop size was studied. The calculation was carried out in the quasichemical approximation, which takes into account the correlation effects of the neighboring interacting molecules. The results are in qualitative agreement with earlier density functional theory calculations and calculations by the van der Waals theory of capillarity. The numerical analysis of the molecular model of the spherical drop gives two types of solution, which correspond to equilibrium and metastasble states of the drop.

The properties of the van der Waals loops for isotherms of the adsorbate located in the slit-shaped and cylindrical pores of different width were analyzed. The adsorbate molecules are modeled by spherical Lennard-Jones type particles. The calculation was based on the latticegas model in the quasichemical approximation for intermolecular interactions. The accuracy of calculations of the adsorption hysteresis loops increases due to the use of distributed models, which reflect the spatial inhomogeneity of the distribution of molecules along the normal to the pore wall. The effect of the adsorbate-adsorbent interaction potential and pore width on the pattern of adsorption isotherms is considered. Taking into account the inhomogeneity of the spatial distribution of molecules changes the course of the spinodal sections of the adsorption isotherms.

Stratification of molecules in inhomogeneous systems can cause the appearance of multiplicity of critical points on vapor-liquid stratification curves. Such systems are open inhomogeneous surfaces and porous solids. The adsorption of molecules on them is determined by the joint action of the surface potential and intermolecular interactions. The joint influence of these potentials forms subregions of the system as a whole in which first-order phase transitions occur. The number and parameters of critical points depend on the composition and structure of inhomogeneous systems. The largest possible number of critical points is related to the presence of macroscopic regions of various types. If regions comprising adsorption centers of various types have locally ordered structures, the system contains one critical point with modified critical parameters, similarly to homogeneous systems. If the influence of the surface potential prevails over intermolecular interaction, the system does not contain critical points.

The molecular theory of the transport of pure substances and mixtures of molecules of different shapes in narrow slit-like pores, in which the potential of surface forces creates a strongly anisotropic distribution of molecules across pores and thereby makes the hydrodynamics equation inapplicable, is considered. The new microhydrodynamic approach is based on the lattice gas model, which takes into account the intrinsic volume of molecules and intermolecular interactions in the quasi-chemical approximation. Self-consistent calculations of dissipative coefficients taking nonlocal fluid properties into account were performed on the basis of the transition state model including information about equilibrium adsorbate distribution. Changes in fluid concentrations from the gaseous to liquid state and a broad temperature range, including the critical region, are analyzed. This allows vapor, liquid, and vapor-liquid fluid flows to be considered in the presence of capillary condensation. An increase in the size of pores transforms the equations of the theory into hydrodynamic transfer equations for gas or liquid flows, while preserving the relation of transfer coefficients to intermolecular potentials. The use of microhydrodynamic approach equations in numerical calculations and the possibility of applying this approach are discussed.

The molecular-kinetic theory of transfer of the components of the gaseous and liquid mixtures of inert gases is generalized to the case of narrow pores of complex structure. The theory is based on the latticegas model, which provides a self-consistent method for calculating the equilibrium and transport characteristics of noble gases and liquids. This model is used to describe the supramolecular structure of finely dispersed bodies and to calculate the distributions of the mixture components within the pore space. The supramolecular structure is composed of slitlike, cylindrical, spherical, and globular model elements and their joints. An analysis of the effect of the molecular properties of the mixture components, physicochemical properties of the pore walls and the width of the cylindrical and complex sections of variable diameter of spherocylindrical pores on the concentration dependences of the local label transfer coefficients and viscosity coefficients for mixtures of spherical molecules at supercritical temperatures range is performed. Correlations between the partial degrees of filling of pores with mixture components and the local dynamic characteristics of the mixture in the spherocylindrical systems are considered. It is shown that an increase in the binding energy increases the local flow viscosity and reduces the diffusion coefficients of the labeled mixture components.

The adsorption of rod-like molecules in slit-shaped pores was considered within the frame-work of the lattice-gas model. This model is applicable over a broad range of fluid concentrations (from the gaseous to the liquid state) and temperatures (including the critical region). In the calculation of the local distributions of mixture components in the equilibrium states, lateral interactions are taken into account. The equations of the model reflect the strong anisotropy of the distribution of mixture components along the normal to the pore wall surface and ordering of the rods along various directions.

The concentration dependences of the label transport and shear viscosity coefficients for rod-like molecules in slit-shaped pores were studied. The calculations were carried out using the lattice gas model, which describes a broad range of fluid concentrations (from the gaseous to the liquid state) and temperatures (including the critical region). In the calculation of the local distributions of mixture components in the equilibrium states, lateral interactions were taken into account. The translational and rotational motions of molecules were described in terms of the transition state theory for nonideal reaction systems, which took into account the influence of neighboring molecules on the height of the activation barrier. The model equations reflect the pronounced anisotropy of the distribution of system components along the normal to the pore wall surface and ordering effects of molecules along various directions.

Expressions for calculating the thermal velocities of the motion of rodlike molecules in slitlike pores were obtained within the framework of a lattice gas model valid over a wide range of fluid densities (from rarefied gases to liquids) and temperatures, including the critical region. The translational and rotational motion of molecules was described using the transition-state theory for nonideal reaction systems, which takes into account the effect of the neighboring molecules on the activation barrier height. The local distributions of the components of the mixture under equilibrium conditions were calculated by describing lateral interactions in the approximation of isolated contacts. The equations of the model reflect the fact that the distributions of the components in the direction perpendicular to the pore walls (due to the effect of adsorption forces) and along the pore axis (if capillary condensation occurs) exhibit a strong anisotropy.

The concentration dependences of the shear-viscosity coefficient of a fluid, representing a binary mixture of components with molecules of approximately equal sizes, in narrow slot-like pores filled to a different degree (from a rarefied gas to a liquid) have been theoretically investigated with the use of a lattice-gas model accounting for the characteristic volume of atoms and interactions between them in the quasichemical approximation. This model allows one to determine the self-consistent equilibrium characteristics of a vapor-liquid system and the shear-viscosity coefficients of molecules with the use of a unique set of energy parameters. The influence of the activation energy of the surface migration of molecules on the local coefficients of viscosity has been considered. A molecular interpretation of the sliding friction of a fluid near the walls of pores has been given; this effect was explained by the surface migration of the mixture components.

A modification of the elementary kinetic theory of a gas mixture in terms of the lattice gas model is proposed. It is assumed that molecules of components of the mixture are spherical and close in size. In calculating the diffusion flux of molecules through a selected plane, instead of the mean thermal velocity of molecules, the mean relative velocity of molecules of components of different types is used. In this case, the flux explicitly depends on the type of component with which a molecule collided last before intersecting the selected plane. The proposed modification allows one to derive an expression for the mutual diffusion coefficient of components of a binary mixture that at low densities of the mixture (as in a rarefied gas phase), is consistent with the expression obtained in the rigorous kinetic theory of gases.

The characteristics of a vapor-liquid interface are calculated using the lattice gas model applied to the analysis of the states of metastable supersaturated vapor, depending on the size of a liquid drop and the system temperature. The interaction of molecules is considered in a quasi-chemical approximation describing the effects of direct correlations of nearby molecules. It is found that considering the density fluctuation increases the drop radius, corresponding to the condition of the generation of a new phase.

The equilibrium and transport characteristics of spherical particles in sphero-cylindrical porous systems were studied in terms of the lattice-gas model. The supramolecular structure of these systems is modeled by segments with a simple regular geometry (cylindrical and spherical) with additional inclusion of the interconnecting areas between different pore segments. Thus, one can model various types of porous systems ranging from zeolite cavities to stackings of long cylindrical sections in new mesoporous materials such as MCM-41 and MCM-49. The distribution of molecules is described in the quasichemical approximation with allowance for intermolecular interactions. The concentration dependences for local self-diffusion and shear viscosity coefficients were calculated. The contributions of the near-wall regions caused by the molecule—wall potential to the general pattern of phase diagrams, the effect of the pore size on the capillary condensation conditions, and the role of the molecular mobility on pore walls were discussed.

The concentration dependences of the coefficients of shear viscosity of molecules in a wide range of pore fillings (from a rarefied gas to a liquid state) for different potentials of molecule–surface interactions have been theoretically investigated with the use of the lattice‐gas model allowing for the volume occupied by atoms and the interaction between the atoms in the quasichemical approximation. This model allows one to find the self‐consistent equilibrium characteristics of a vapor‐liquid system and the coefficients of shear viscosity of molecules with the use of a single set of energy parameters. Molecular interpretation of the coefficient of sliding friction of the fluid near the pore walls is discussed.

A self-consistent approach to the calculation of equilibrium and transport characteristics of inert gases and liquids in complex narrow-pore systems based on the lattice-gas model is proposed. A supramolecular structure for fine-grained solids was constructed and the adsorbate distribution within the pore volume is described. The supramolecular structure is simulated using slit-shaped, cylindrical, spherical, and globular segments. Additionally, junctions of pore systems with different structures are included, and the heterogeneity of their walls and the presence of structural defects in the pore segments are taken into account. The distributions of molecules are described in the quasi-chemical approximation to take into account intermolecular interactions using calibration functions to correct this approximation in the near-critical area. Expressions for local and integrated flow transfer coefficients are constructed, in particular, self-diffusion, shear viscosity and heat conductivity. The contributions of the near-wall areas and the core parts of pores to the general form of phase diagrams, the effect of the pore size on the conditions of capillary condensation, and the role of surface mobility of molecules are discussed.

Concentration relationships of dynamic characteristics of the adsorbate (coefficients of self-diffusion and shear viscosity) in narrow slit-like pores with different widths were considered. These coefficients were calculated using the simplest molecular model (lattice-gas model), which takes into account the intrinsic volume of molecules and their interactions in the quasi-chemical approximation. The values of coefficients of self-diffusion and shear viscosity of the adsorbate depend strongly on the distance to the pore wall.

The fundamentals of the adsorption theory for a mixture of bulky molecules blocking more than one adsorption site on the surface in slit-shaped pores with heterogeneous wall surfaces are outlined. The adsorbate—adsorbate lateral interactions are taken into account in the quasi-chemical approximation and in the mean-field approximation. The expressions for the partial adsorption isotherms and for the binary coefficients of mixture separation and the way of isolation of the partial contributions of molecules on heterogeneous adsorption sites on pore walls are discussed. A simplified variant of adsorption theory for a binary mixture of molecules of different sizes in two-layer pores with the assumption of complete coverage of the pores is considered. The influence of the energy of binding of molecules to pore walls, lateral interactions, and the ratio of the component sizes on the shape of adsorption isotherms is analyzed. The results of calculations are compared with the experimental data for the benzene—CCl4—microporous AC carbon adsorbent system.