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Abstract A way of deriving kinetic equations of physicochemical processes in dense phases is developed on the basis of the discrete–continuous description of the spatial distribution of components in the lattice gas model (LGM), with allowance for multi-particle effects. The emergence of multi-particle effects is associated with the simultaneous influence of all neighbors on the rate of the elementary stage with the participation of a given particle. They include multi-particle potentials of interaction, including quantum–chemical energy calculations, the effect the configurations of neighboring molecules have on the internal motion of the central particle, and the effects of the indirect correlation of interacting particles that occurs for any potential of pair interaction, assuming the internal motions of particles do not depend on the local configurations of neighbors. Multi-particle effects take models beyond the quasi-chemical approximation, which reflects direct correlations of interacting particles through pair distribution functions, and require the use of correlation functions for a larger number of particles in describing their kinetics. The rates of elementary one- and two-node stages are calculated within the theory of absolute rates of reactions in non-ideal reaction systems. Ways of calculating approximate rates of the elementary stages of mono- and bimolecular processes are discussed, along with the possibilities of generalizing the derived equations.

A study is performed of the accuracy of free energy F of a vapor–liquid system, calculated with modified fluid models in the quasi-chemical approximation (QCA) of the lattice gas model. Two ways of modifying the fluid model are discussed: (1) allowing for the softness of the lattice, which alters its weighted average parameter according to the density of the fluid and (2) jointly considering the translational and vibrational molecular motions in a rigid lattice. The effect the model of introducing the weighted average parameter of a soft lattice has on the calculated characteristics is analyzed. Calculations of the free energy using the analytical QCA formula (which contains no such modifications) are compared to thermodynamic relationships obtained with a chemical potential that considers them. It is found that both modifications of the fluid model result in distinctions between the two ways of calculating the free energy that grow along the density of the system. These distinctions are apparent at high densities and on the concentration dependence of pressure. The analytical QCA expression quantitatively estimates F values when there are small contributions from model modifications.

An approach is developed to describe the ordering of components in a regular structure of a binary А0.5В0.5 system within the lattice gas model with the combined application of the fragment method (FM) and the quasi-chemical approximation (QCA). FM enables an accurate calculation of statistical sums of configurational contributions of components on a small fragment, which includes indirect correlations. QCA contributions reflect direct correlations between interacting particles. The effect of components described in QCA on the occupancy states of fragment sites is taken into account through local external fields considered as a calibration function improving the accuracy of calculating thermodynamic functions with taking into account indirect correlations in the entire density and temperature ranges. The effect of indirect correlations on the temperature dependences of ordering and the ordering critical temperature as well as on its size dependence of cubic domains is analyzed. The domain boundary is set by an external field that changes the character of the distribution of system components in the near-surface region in comparison with their distribution in the phase volume, which makes the total system heterogeneous. The dependence of a decrease in the ordering critical temperature as the domain side decreases with taking into account indirect correlations is calculated for the first time. The role of domain sides in related situations, including ferroelectrics, is discussed along with the prospects of utilizing the new method.

The need to consider vibrational motions of molecules in bound states of a vapor–liquid system in order to calculate its thermodynamic functions (TFs) raises the question of possibly isolating them from the collective kinetic contribution and describing them. An attempt is made to do so using a molecular kinetic theory based on the cluster approach (CA) in the lattice gas model (LGM). The existence of physically bound groups of fluid particles forming associates, which is observed for rarefied vapor, is extended to the range of densities of a vapor–liquid system. An associative model of a fluid is proposed that reflects regions of rarefied and dense fluids, different types of molecular motions, and the effects of anharmonic vibrations of atoms in bound states. Starting from an isolated dimer to a dense phase, particle vibrations are calculated in a quasi-dimer model reflecting average local vibrational frequencies. In dense fluids, local density fluctuations characterize representations of associates. Under the effect of vibration anharmonism in bound associates, molecular pair interaction potentials are renormalized into many-particle potentials. The problem of calculating TFs according to correlation functions, which is done extensively in fluid theory and CA in the LGM, is discussed. The problem lies in two ways of calculating the free energy: using molecular distribution functions or thermodynamic relationships. An approach is formulated for strictly calculating TFs with the use of model free energies. A statistical sum is introduced into the theory of fluids and ensures a self-consistent description of equilibria and kinetics.

Using the lattice gas model, we consider a unified description of three types of two-phase interfaces (vapor–liquid, solid–vapor, and solid–liquid) in the vapor–liquid meniscus system inside a size-limited pore in the form of a rectangular parallelepiped. Pore walls are considered to be undeformable. They form the external field for a stratifying fluid. The state of coexisting “vapor in a pore” and “fluid in a pore” phases satisfy the equality of chemical potentials, which excludes the appearance of metastable states. We present a calculation procedure for molecular distributions and shapes of menisci in the isolated pore considered, which enables the equally accurate calculation of molecular distributions in heterogeneous distributed models of transition regions of three interfaces. The calculation procedure of the surface tension (ST) on three types of two-phase interfaces of the liquid–vapor–solid wall system is elaborated. The procedure of introducing a contact angle in the liquid–vapor–solid pore wall system is described using adsorbate molecular distributions in the considered pore. It is obtained that, as the system decreases, the critical temperature lowers, while the pressure, chemical potential, and ST values of a fluid with a solid increase. Liquid–vapor ST decreases with decreasing area of pore bases (i.e., with pore narrowing), and when the pore height increases, liquid–vapor ST increases. The dependences of the liquid–vapor transition region width and the contact angle of the vapor–liquid meniscus are derived as functions on the pore width and the pore wall potential.

A numerical investigation is performed of the effect indirect correlations of nearest interacting particles have on the characteristics of stratification curves calculated within the lattice gas model. A combination of the fragment method (FM) and the quasi-chemical approximation (QCA) is used. The FM allows precise calculation of the statistical sums of configurational contributions from molecules on a small fragment with indirect correlations. The effect particles have on the state of site occupancy in a fragment as described in the QCA is considered through local external fields. A combined FM + QCA approach is used that considers external fields a calibration function for improving the accuracy of calculating thermodynamic functions with regard to indirect correlations throughout the ranges of density and temperature. It is found that allowing for indirect correlations changes the probabilities of small associates forming and lowers the critical temperature of the stratification phase transition. Calculations are made for both a square planar lattice (for which we can compare the critical and Onsager temperatures) and a cubic lattice. The calculated results are compared to similar curves in the QCA, which considers only direct correlations.

It is that the proposed that the fragment method (FM), which accurately describes configuration states of small systems, and the quasi-chemical approximation (QCA), which considers only direct correlations between interacting particles, be combined to calculate thermodynamic functions in the lattice gas model (LGM). The FM forms a full spectrum of configurations on a small number of sites; but because of the small size of the system, it does not allow for the emergence of phases. Neighboring sites whose local density is calculated in the QCA create an external field for a fragment site, changing their occupancy states and stratifying the whole system. This approach improves the accuracy of the LGM, in which the particle distribution is described with regard to effects of indirect correlations. Formal delocalization of a QCA site ensures the same local densities at all fragment sites, so it may be considered an analog of a calibration function whose parameters can be found from the known value of the critical temperature. Possible versions of using the combined FN + QCA technique are discussed for different situations on heterogeneous surfaces, in bulk phases, and at the boundaries of stratifying phases.

The relationship between the second law of thermodynamics and Gibbs’ thermodynamics is discussed. The second law of thermodynamics is formulated more generally than Gibbs’ thermodynamics, which considers only strictly equilibrium values of thermodynamic functions. Gibbs’ approach generalizes the statistical mechanical theory of equilibrium for thermodynamic variables, except for the difference between the periods of relaxation of all thermodynamic parameters. For small systems, this approach consists of replacing the real physical nature of systems with the stratification of coexisting phases using a model with an interface of mobile phases in contact with a foreign (nonequilibrium) body. For solids, this results in confusion of concepts of the complete phase equilibrium of a system and the mechanical equilibrium of a deformed solid. These two problems are revealed using the molecular kinetic theory of condensed phases, ensuring a self-consistent description of three aggregate states and their interfaces. This theory allows the concepts of the times of the onset and completion of forming entropy in the considered system to be introduced. Allowing for experimental data on the ratios between the measured periods of relaxation for momentum, energy, and mass transfer processes in considering real processes not only ensures a solution to the two problems noted above; it also testifies to the redundancy of the Caratheodory mathematical theory to substantiate the introduction of entropy into multicomponent mixtures. A microscopic interpretation of the formation of entropy in closed systems is given that illustrates the essence of processes preceding the emergence of the reaction completeness parameter in de Donder and Prigogine approaches. Systems in which allowing for periods of relaxation alters existing theories are discussed.

A calculation procedure of the surface tension (ST) of vapor–liquid menisci in porous bodies based on the microscopic lattice gas model (LGM) is presented. Ideas of this model are used to describe a two-level structural model of mesoporous bodies and to calculate adsorbate distributions in a given structure of an adsorbent. The supramolecular level of the model is presented as a granule/grain of a porous material with the set distribution function of connected pores of different sizes and types. At the molecular level, a LGM ensures an equally accurate description of adsorbate molecular distributions in the coexisting vapor and liquid phases and at their interface. ST is calculated through a local excess of the free energy that is generated by vapor–liquid interfaces inside the pores. Calculated STs characterize the spatial distribution of mobile phases in porous systems. The capability to obtain local information about ST, which reflects the size and energy features of porous systems, significantly exceeds the capabilities of the thermodynamic approach.

Three types of two-phase interfaces (vapor–liquid, solid–vapor, and solid–liquid) are considered in the “vapor and liquid meniscus” system inside a slitlike pore with rough walls. A unified description of these interface surfaces is given based on the lattice gas model that enables an equally accurate calculation of molecular distributions in heterogeneous distributed models of transition regions of interfaces. Undeformable pore walls generate an external field affecting the molecular distribution and forming adsorption films due to the adsorbate–adsorbent interaction potential. Surface tensions (STs) are calculated from the excess of the free energy of the interface (according to Gibbs) for each three types of two-phase interfaces. The ST for the solid–liquid interface corresponds to the surface passing through the contacting phases, i.e., via bonds between the adsorbate and the adsorbent. The state of coexisting “vapor in a pore” and “liquid in a pore” phases must satisfy the equality of chemical potentials, excluding the appearance of metastable states. Distinctions introduced by the wall roughness are mainly observed for narrow pores and they decrease as the pore width increases. The wall roughness changes the critical parameters of fluid stratification into liquid and vapor phases. The calculated ST values are compared with similar values for smooth walls of a slitlike pore. It is found that solid–liquid and solid–vapor STs are close to each other (their difference is smaller on a rough surface than on the smooth one) and are larger (in their absolute value) than the liquid–vapor ST in the center of the pore by approximately an order of magnitude. Local vapor–liquid ST values nonmonotonically change when removed from the wall.

Current possibilities of modeling the kinetics of supercritical processes are considered, based on the theory of an absolute rate of the reaction for non-ideal reaction systems, which considers intermolecular interactions that change the effective energy of activation of elementary stages. This allows the theory to describe the rates of elementary stages for arbitrary temperatures and densities of the reagent in different phases. Application of this theory in a wide range of state parameters (pressure and temperature) is examined while calculating elementary bimolecular reactions and dissipative coefficients under supercritical conditions. Generalized dependences within the law of corresponding states are calculated for the compressibility, viscosity, and thermal conductivity coefficients of pure substances and those of the compressibility, self- and mutual diffusion, and viscosity of binary mixtures. The effect density and temperature have on the rates of elementary stages under supercritical conditions is demonstrated for a reaction’s effective energies of activation, diffusion and share coefficients, and equilibrium constants of adsorption. Differences between models with effective parameters and the prospects for developing them by allowing for differences in size and contributions from the vibrational motions of components are described, along with ways of improving the accuracy of describing correlation effects.

An adsorbate can simultaneously affect the external and internal surfaces of an adsorbent, changing the volume of a sample with a fixed amount of the adsorbent. This process is discussed from the standpoints of mechanics of continuous media, thermodynamics, and molecular models. The microscopic theory of solids distinguishes between external and internal deformations, which makes it possible to associate mechanical characteristics with adsorption ones. Based on the lattice gas model, the principles of two-level structural models are formulated for deformable porous bodies. They enable the self-consistent description of changes in their volumes and adsorption isotherms as a function of the adsorbate external pressure at a fixed temperature. For the simple presentation of the calculation scheme, it is accepted that the atomic sizes of a solid and components of the adsorbate mobile phase are comparable. The molecular level reflects the volume of molecules and their lateral interaction in the quasi-chemical approximation. The supramolecular level of the model is presented as a granule/grain of a porous material with the set distribution function of different (in size and type) pores connected with each other. A relationship between internal deformations and the nonequilibrium state of a solid is shown. A calculation procedure for local mechanical modules with regard to internal and external deformations characterizing the mechanical properties of solids is exemplified by the compression modulus. The procedure takes into account the effect of the nonequilibrium of an adsorbent on adsorbent isotherms and its volume. The approach proposed can be also applied to related systems in which the adsorption of active mobile solutions by highly dispersed compounds changes their volume.

Three types of two-phase interfaces (vapor–liquid, solid–vapor, and solid–liquid) are considered in a liquid–vapor meniscus system inside a slit-like pore. A unified description of these interface surfaces is given on the basis of the lattice gas model, ensuring a uniformly accurate calculation of molecular distributions in heterogeneous distributed models of the transitional regions of interfaces. It is shown that undeformable pore walls generate an external field, affecting the molecular distribution and forming adsorption films due to the potential of adsorbate–adsorbent interaction. Ways of calculating surface tension (ST) via the excess free energy of the interface (according to Gibbs) on the three given two-phase interfaces are discussed, along with means that consider specific features of the nonequilibrium state of a solid. It is established that the state of coexisting vapor-in-a-pore and fluid-in-a-pore phases must satisfy the equality of the chemical potential that excludes the emergence of metastable states. Vapor–solid and liquid–solid STs outside the region of three-phase contact are calculated for the first time, along with local values of a vapor–liquid ST as a function of the removal of a local part of the boundary from the pore walls. It is found that in the center of a pore, the solid–liquid ST is an order of magnitude greater than the liquid–vapor ST, and the solid–vapor ST is two orders of magnitude greater than this value. Local values of a vapor–liquid ST change nonmonotonically as they move away from a wall.

An analysis is performed of the state of a molecular theory oriented toward describing three-aggregate systems from a single viewpoint that includes their three bulk phases and three types of interfaces (vapor–liquid, solid–vapor, and solid–liquid). It is established that the theory, which is based on the lattice gas model (LGM), provides a common structure to express the pressure of not only three different bulk aggregate states but in their transitional regions of interface boundaries. The existence of vacancies in the LGM allows it to be used for all concentrations of the components of a multicomponent mixture from zero (which is characteristic of rarefied gas) to unity (in mole fractions) (which is characteristic of solids). Mechanical characteristics are calculated for heterogeneous systems using equations of local partial isotherms with the same structure in different regions of a common heterogeneous system. General expressions are derived for the pressure in different aggregate phases and the local pressure in the transitional regions of the three interfaces, through which local pressures the surface tensions of diverse interfaces are determined.

A unified description of three types of two-phase interfaces (vapor–liquid, solid–vapor, and solid–liquid) at a vapor–liquid meniscus inside a slit-like pore are considered on the basis of the lattice gas model. This approach allows equally accurate calculations of molecular distributions in heterogeneous distributed models of transitional regions at all interfaces. It is assumed that pore walls cannot be deformed, and they create an external field for a stratifying fluid. Adsorption films form at solid–mobile phase interfaces due to the potential of adsorbate–adsorbent interaction. The state of the coexisting vapor-in-a-pore and liquid-in-a-pore phases satisfy the equality of the chemical potential that excludes the appearance of metastable states. Conditions for distinguishing regions of the system that lie beyond solid–liquid–vapor three-phase contact are discussed. A procedure is discussed for introducing a contact angle into a liquid–vapor–solid pore wall system through molecular distributions of the adsorbate in a slit-like pore. Dependences of the width of the considered interfaces and the contact angle as a function of the pore width and pore wall potential are found.

The effect the vibrational motion of inert gas atoms in the bound states at an arbitrary density of a vapor–liquid system has on the equilibrium concentration dependence of the chemical potential on density is considered for the first time. Both the potential energy of interaction between atoms and their vibrations in the bound states, starting from an isolated dimer to a dense phase, are considered. Calculations are made using the lattice gas model (LGM) for a one-dimensional fluid. Spatial atomic distributions are described in a quasi-chemical approximation. Local frequencies of atoms are calculated in a quasi-dimer model of vibrational motion. At the same time, the translational motion of atoms when they move to neighboring vacant cells are considered. The calculations are made in two versions of the theory: discrete and continuum. The latter reflects the motion of the center of mass inside the cells into which the entire volume is partitioned in the LGM. It is found that allowing for the vibrations of atoms in the bound states at a fixed density of the system shifts the chemical potential to lower values.

An approach to calculating the surface energy and the surface tension in solid–vapor systems of binary solid solutions with different degrees of ordering is developed based on the lattice gas model (LGM). The LGM is the only procedure allowing a uniformly accurate description of the properties of phases and transition regions between the coexisting equilibrium phases. The model is targeted at mixture components with comparable sizes. It is adapted for the simplest type of ordering in a bulk phase, which reflects the structure of two interpenetrating sublattices in a simple cubic lattice or a body-centered cubic lattice of β-brass type. The transition region between a solution and vapor is presented as a multilayered region with a variable density of components. Interatomic interaction potentials are taken into account in the approximation of pair contributions with maintaining direct correlation effects. To reduce the system of equations for the distribution of components, a change of variables is applied, which makes it possible to bring the problem to the dimensionality of concentration profiles of components in the transition region. The procedure that has been developed allows the evaluation of the interface roughness state, the specific surface of the rough surface, and the segregation of solution components, as well as an analysis of the effect of their surface segregation on the degree of ordering of solution components in the transition region.

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.

An approach is formulated that allows calculation of three types of surface and linear tensions in the region of contact angles of a three-aggregate system. A molecular theory for three-aggregate systems based on the lattice gas model (LGM) is used to calculate surface tension (ST) and linear tension (LT). It provides a uniform description of molecular distributions of mixture components inside three bulk phases in different aggregate states and three types of their interfaces. The calculations are based on the Gibbs definition of STs and LTs, derived by calculating the excess free energy determined from interfaces of the mentioned phases, and experimental data on the relaxation times of mass and momentum transfer processes. For simplicity of description, a general approach is formulated for interfaces with ideal geometry: planar and spherical. Under real conditions, solid phases are typically nonequilibrium because of hindered redistribution of components. Non-equilibrium analogs of equilibrium potentials must be developed to describe these. Diffusion-type kinetic equations for unary and pair distribution functions must be used to calculate their evolution. Distributions of components of mobile vapor and liquid phases adapt to the distribution of components in solid phases. Problems in calculating STs and LTs are discussed using the example of vapor–liquid phases in a solid-phase porous matrix.

An approach for calculating the surface thermodynamic characteristics of solid solutions (alloys, salts, oxides, ferroelectrics, and nonstoichiometric compounds) with different degrees of ordering at the vapor–solid interface is formulated on the basis of the lattice gas model. This approach is the only one that makes it possible to describe the properties of phases and transition regions between equilibrium coexisting phases with equal accuracy. The model is constructed for the mixture components having comparable (but different) sizes with an arbitrary type of ordered structures in the bulk phase. The type of ordering is determined by some pattern formed by different sublattices periodically repeated in space. The transition region between the solid solution and vapor is a multilayered region with a variable density of components. Interatomic interaction potentials are taken into account in the approximation of pair contributions with preservation of direct correlation effects for several coordination spheres. A change of variables was used to reduce the equilibrium set of equations to component distributions, which allows one to reduce the problem to the dimensionality of the concentration profiles of components in the transition region. The case of nonequilibrium states of a solid solution and description of its evolution by kinetic equations are discussed. Finding the concentration profile of a solid solution allows one to evaluate the state of the interface roughness, the specific area of the rough surface, and the surface segregation of the solution components, and to analyze the effect of the surface segregation on the degree of ordering of the solution components in the transition region.

The effect a limited cubic volume has on the critical temperature of ordering corresponding to the regular structure of a binary А0.5В0.5 system is considered. A molecular theory based on the lattice gas model, which is traditionally used to describe the ordered state of alloy components and adsorbates, is applied. It is assumed there is an external field near the cube boundary, changing the distribution of system components relative to the one in the phase volume and making the entire system heterogeneous. The dependence is obtained for a drop in the critical temperature of ordering when the cube side shrinks and the contribution from near-border areas of the domain to the entire heterogeneous system grows. The role of domain walls in related situations (magnetics and ferroelectrics) is discussed.

The suitability of mechanics models for calculating interface surface tension (ST) is analyzed from the viewpoint of molecular kinetic theory. A theory based on the lattice gas model is shown to consider the intermolecular interactions of comparable components and a change in the average bond lengths between dense phase particles in a quasi-chemical approximation that describes direct correlations. It can be applied to three aggregate states and their interfaces, allowing comparison of mechanics and thermodynamics models if the concept of ST is introduced. It is found that the Laplace equation is incompatible with the conditions of the equilibrium of coexisting phases on distorted vapor–liquid interfaces, but it can be used to describe the mechanical equilibrium in systems with an intermediate film between the neighboring phases (if there is no chemical equilibrium between them). Mechanical and thermodynamic definitions of ST under different conditions are discussed. It is shown that to calculate equilibrium ST, we must use the Gibbs definition as the excess free energy at the interface. A procedure for calculating nonequilibrium analogs of surface characteristics (free Helmholtz energy, chemical potential, ST) of solid solutions is formulated that considers internal deformations of solid boundaries and the effect of external loads.

The description of deformed solids in thermodynamics is analyzed from the viewpoint of the concept of phase separation based on Gibbs’s familiar result of the total equilibrium of a system representing the mandatory simultaneous attainment of three partial equilibria (mechanical, thermal, and chemical). It is therefore necessary to examine the relaxation times of establishing these partial equilibria. It is shown that the main postulates of equilibrium thermodynamics and continuum mechanics are mutually exclusive. The microscopic theory of describing the internal and external deformations of defective one- and multicomponent systems is considered. It is found that the existence of internal deformations of solids is due to the slowing of component mixing over a system’s space. The concept of interface equilibrium and allowing for relaxation times are shown to ensure distinctions in the interpretations of major principles for deformed and undeformed solids, based only on the character of mass distribution without using certain model/microscopic representations of solids.

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.

A procedure to calculate the surface tension is developed based on a modified lattice gas model (MLGM) for the vapor–liquid system in a strict correspondence to the thermodynamic Gibbs definition for any curvature of the boundary. It is shown that MLGM enables a calculation of molecular distributions in a layered model of the transition region of the interface with regard to the softness of a lattice structure. The state of coexisting phases must satisfy the Yang–Lee theory of condensation, and additional conditions for chemical, thermal, and mechanical equilibria are imposed on the properties of the transition region of an equilibrium droplet with any curvature in each layer. The new calculation procedure for the surface tension is compared with the existing calculation procedures for equilibrium and metastable droplets. A difference in size dependences of the surface tension σ(R) for equilibrium and metastable droplets with a radius R in vicinity of the line σ/σbulk = 1, where σbulk is the bulk surface tension, allows us to formulate the accuracy and reliability criterion for different modeling methods: if the mentioned line exceeds the calculation accuracy σ(R), then it indicates that the method does not correspond to the Gibbs definition.

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.

This article considers pioneering works by M.I. Temkin in the field of adsorption, the theory of elementary stages of surface processes and general questions describing condensed phases using as examples the processes on surfaces in dense monolayers and in the volume phase. A brief review of the subsequent development of his ideas in these areas is given. The questions of the correct way to take into account the cooperative behavior of adsorbed species in equilibrium and surface reactions and the principle of self-consistent description of the rates of stages and the equilibrium state of the reactants for heterogeneous surfaces and nonideal reaction systems are discussed.

The work analyzes the energy characteristics of rough interfaces with and without taking into account adsorption. For simplicity, the theory of the lattice gas model is exemplified by taking into account a lateral interaction between the nearest components of the system. The behavior of the surface free and internal energies of the interface between the rough solid and the adsorbed gas is considered. The effect of the non-equilibrium states of interfaces on the energy characteristics of the surface are analyzed depending on the formation temperature of a flat rough surface. The difference between the excess surface energy at the solid–mobile phase interface and the non-equilibrium analogue of the surface tension of the same system, which transforms into the surface tension in the complete equilibrium state, is discussed. The effect of adsorption on the energy characteristics of the flat rough surface and the position of the equimolar surface is explored, depending on the gas pressure during physical adsorption and chemisorption. The means of calculating the fluctuation estimates of the formation probability of a rough solid boundary from the metastable state with a flat boundary is formulated. The size dependences of the formation probability of a circular region with a rough solid boundary on its curvature radius are obtained.

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.

Ways of calculating interatomic vibrations in a fluid are considered using the example of an inert gas. Discrete continuum theory in the lattice gas model is used. An approach is proposed for deriving expressions for the statistical sums of the vibrational motion of atoms in a fluid that are always in the bound state. Equations of the bulk equilibrium molecular distribution for concentrations and pair distribution functions in the quasi-chemical approximation are obtained, allowing for effects of direct correlations. Two approaches are used to describe local relative displacements of bound molecules with different amplitudes, provided that the local momentum equilibrium is preliminarily established and compared to the local mass equilibrium. The resulting equations are compared to approaches proposed earlier.

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.

A molecular theory based on the lattice gas model is employed to describe the surface tension of the vapor–liquid interfaces of one- and two-component metal melts. The surface tension of the melts are calculated in the quasi-chemical approximation of taking into account intermolecular interactions of the nearest neighbors. Parameters of the model are found from the experimental data for the bulk surface tension of the melts, which enables the calculation of the surface tensions of vapor–liquid interfaces of one- and two-component droplets with different sizes as a function of their radii. Estimates for the minimum size of small droplets of melts having the properties of a homogeneous phase inside them, which correspond to their thermodynamic stability, are obtained.

The position of the inflection point in polylayer adsorption isotherms, which has been traditionally used to determine the specific surface of many disperse systems, is analyzed. The inflection point positions versus the molecular parameters of the adsorption system and the degree of surface nonuniformity are considered. The surface heterogeneity is exemplified by the droplet roughness formed on rapid cooling. The vapor–liquid-droplet interface creates the thermal heterogeneity of the surface on which gas-phase molecules are adsorbed after cooling. Conditions for using the inflection point to estimate the specific surface of silica samples during argon and nitrogen adsorption are discussed, along with distinctions between the monolayer capacity found from the isotherm and complete filling of the monolayer itself determined by the degree of filling surface centers.

A microscopic analysis is presented of the existing definitions of equilibrium surface tension, which can be divided into two types: mechanical and thermodynamic. Each type of definition can be studied from the presentation below according to thermodynamic hypotheses or molecular calculations. An analysis of the planar interface is given and its generalization for curved (spherical) interfaces is considered. The distinction between approaches describing the surface tension of metastable and equilibrium droplets is discussed. Based on nonequilibrium thermodynamics, it is shown that the introduction of metastable droplets is due to a violation of the relationship between the times of impulse and chemical potential relaxation in condensed phases. Problems of calculating the surface tension in nonequilibrium situations are created.

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.

To describe the surface tension of vapor–liquid interfaces of one- and two-component simple fluids, a molecular theory based on the lattice gas model is applied. The surface tension of mixtures of simple fluids are calculated in a quasi-chemical approximation of an accounting of the intermolecular interactions of the nearest neighbors. The model parameters previously found from experimental data on bulk surface tensions enable calculation of the surface tension of vapor–liquid interfaces of one- and two-component droplets with different sizes as the function of their radius. The minimum size of thermodynamically stable small droplets with the properties of a homogeneous phase inside is estimated.

An approach is developed for studying polymolecular adsorption on the modeled rough surface of a small aerosol obtained from a liquid droplet on its rapid cooling. A way of estimating the specific surface of adsorbent droplets with rough surfaces is proposed, and the temperature and size dependences of the specific surface are established. Isotherms of N2 and Ar polymolecular adsorption on a heterogeneous surface of small spherical particles of SiO2 are derived. The possibility of using this approach to describe an experiment is demonstrated. Comparison to the experimental isotherms reveals agreement with isotherms of argon and nitrogen on silica surfaces, with an error of up to 4.5%.

An approach is formulated that theoretically describes the structure of a rough surface of small aerosol particles obtained from a liquid droplet upon its rapid cooling. The problem consists of two stages. In the first stage, a concentration profile of the droplet–vapor transition region is calculated. In the second stage, local fractions of vacant sites and their pairs are found on the basis of this profile, and the rough structure of a frozen droplet surface transitioning to the solid state is calculated. Model parameters are the temperature of the initial droplet and those of the lateral interaction between droplet atoms. Information on vacant sites inside the region of transition allows us to identify adsorption centers and estimate the monolayer capacity, compared to that of the total space of the region of transition. The approach is oriented toward calculating adsorption isotherms on real surfaces.