Yu. K. Tovbin

Lower size boundary for the applicability of thermodynamics

The problem of the lower boundary of the intrinsic linear size of the range in which the thermodynamic approach is applicable is considered. It is established that a natural constraint of any thermodynamic approach is the discrete structure of a substance at the atomic-molecular level. It is shown that with a reduction in the size of a substance, the fraction of surface particles compared to their total amount grows and spontaneous density fluctuations increase. The molecular theory of density fluctuation in small systems is discussed. Drop radii below which thermodynamic approaches cannot be used, and for which thermodynamic approaches can be used when both the discreteness of a substance and the contributions from spontaneous fluctuations can be ignored, are estimated. The consequences of the molecular theory of curved vapor-liquid interfaces are examined within the lattice gas model for spherical drops in the vapor phase. The limitations and conditions for considering corrections for density fluctuations in macrophases are discussed.

Molecular theory of spherical drops in the vapor phase

The molecular theory of the distorted vapor-liquid interface in the context of the lattice gas model was used to study the surface tension of spherical drops at different drop sizes and system temperatures. The molecular interactions were taken into account in a quasichemical approximation that describes the direct correlation effects of neighboring molecules. Two types of solution corresponding to the metastable and equilibrium states of the system were found for the concentration profile of molecules in the transition region. The notion of equilibrium drops was introduced for the first time. The thermodynamic properties of metastable and equilibrium drops were found to be similar. Various methods for determining the surface tension were discussed. The surface of tension was shown to be nonexistent at low temperatures and small radii of metastable and equilibrium drops. Three characteristic sizes of drops were revealed: (1) the critical size at the start of phase formation at which the surface tension of a dense phase appears, (2) the critical radius above which a thermodynamic description of the surface tension of a drop is justified, when both the discrete character of the substance and the spontaneous fluctuations can be neglected, and (3) the radius of large drops above which the surface tension is close to the bulk value. The correspondence between the metastable states, described by the Kelvin equation, and the equilibrium phase diagram were discussed.

The problem of a self-consistent description of the equilibrium distribution of particles in three states of aggregation

The possibility of unified self-consistent calculations of equilibrium distributions of molecules in three states of aggregation within the framework of the lattice gas model is considered. The corresponding approach was generalized to arbitrary pressures with including the compressibility of lattice structures. Closed equations were obtained for calculating thermodynamic functions (including an equation for the chemical potential of mixture components) in the continuum quasi-chemical approximation. Their use ensures equally accurate calculations of interphase equilibria in gas-liquid-solid systems and the determination of the triple and critical points. Possibilities for simplifying the equations by passing to the effective pair interaction potential, which takes into account averaged vibrations and volume accessible to the translational motion of molecules of commensurate sizes, are considered.

Fundamentals of the theory of melting of simple substances with consideration of their defects

Molecular principles of the theory of melting of simple substances are considered with regard to defects caused by vacancies. Equations are derived for the chemical potential of atoms in a defective crystal with allowance for their vibrational motion, enabling the determination of coexisting phases (solid-vapor or solid-liquid) from the condition of the equality of chemical potentials. All three aggregate states of matter are described within a unified molecular approach: a lattice gas model. This makes it possible to combine a description of a cell filling with liquid, or vapor and a solid with phase differences in these states during the cell filling. N.N. Bogolyubov’s concept of quasi-averages, from which the degeneration of the density distribution function in space is removed, is applied to describe the crystals. Questions as to the minimum size of the phase corresponding to the concept of quasi-averages and the criteria for the transition of a defective crystal to the frozen state are discussed.

A theory of a curved vapor-liquid separation boundary: The lattice gas model

Molecular theory of curved vapor-liquid interphase boundaries was considered in terms of the lattice gas model. The theory uses the quasi-thermodynamic concept of curved layers of a separation boundary with a large radius. The transition from a rectangular lattice to such layers is performed by the introduction of a variable number of the nearest neighbors. The problems (1) of the transition from distributed molecular models to layer models reflecting macroscopic symmetry of the interphase boundary and (2) of a minimum linear size of the surface region to which thermodynamic approaches are applicable were considered. Equations for the quasi-equilibrium distribution of molecules at the vapor-liquid boundary in a metastable system were constructed in the quasi-chemical approximation taking into account direct correlations between the nearest interacting molecules. A metastable state is maintained by a pressure jump described by the macro-scopic Laplace equation on a separation surface inside the interphase region. Equations for local mean pressure values and normal and tangential pressure tensor components inside the interphase region were constructed. These equations were used to obtain microscopic difference mechanical equilibrium equations for curved boundaries of spherical and cylindrical drops in the metastable state. The relation between the micro-scopic difference mechanical equilibrium equations and similar differential equations and the macroscopic Laplace equation, which described pressure jump in a metastable system, was considered. Various definitions of surface tension are discussed.

THE VOLUME OF MICROPORES AND THE DUBININ-RADUSHKEVICH EQUATION

The substantiation and the area of applicability of the Dubinin—Radushkevich equation for determination of the micropore volume in microporous systems from experimental data on adsorption isotherms were examined. It was shown that the micropore volumes found using the standard procedure are overestimated. A more accurate method for determining the mircopore volumes based on the pressure of filling of micropores was proposed.

Generalizing the molecular theory of adsorbate melting in slit pores to structurally heterogeneous walls

The molecular theory of adsorbate melting in slit pores or near planar open surfaces is generalized to the case of arbitrary pores with a random character of the spatial distribution of adsorption centers (a fully distributed model). The states of liquid and crystalline adsorbates with regard to the contributions from vibrational motions are described using a unified molecular approach based on discrete distribution functions (the lattice gas model). Equations for the chemical potential of the adsorbate in a defect crystal and a vapor-liquid system are derived with allowance for their vibrational motion within the modified quasi-dimeric model. The concentration profile of a substance at the planar interface between two solid phases or a solid-liquid interface and inside a slit pore is calculated. Molecular distributions are calculated in a quasi-chemical approximation reflecting the effects of direct correlations of interacting particles via the Lennard–Jones potential. The transition to the averaged interaction potential of an adsorbate with structurally heterogeneous walls of slit pores, the transition to an averaged description of the lattice parameter of the system, and the problem of estimating the vibrational spectrum of the adsorption system are discussed.

A theory of adsorbate melting near the surfaces of adsorbents and in slit-shaped pores

Molecular principles of a theory of adsorbate melting near the open surfaces of adsorbents in the frozen state or in slit-shaped pores are discussed. The states of liquid and crystalline adsorbates are described in terms of a single molecular approach (the lattice gas model). The crystalline state is described using the concept of quasi-average distributions, for which the degeneracy of the density distribution function in the plane of the adsorbent is eliminated. Equations for the chemical potential of the adsorbate in defective crystals and vapor-liquid systems are derived with allowance for their vibrational motion, making it possible to calculate the concentration profile of the substance at the planar interface between two solid phases, between a solid and a liquid, and inside a slit-shaped pore.

Equilibrium fluctuations in the theory of surface processes on microparticles

The question of the role of equilibrium fluctuations in the adsorption theory and kinetics of surface processes occurring on the particles of the nanometer size range is discussed. Differences are put forward that need to be introduced to the fluctuation theory of surface processes on microparticles and that generalize Hill’s approach to describing the thermodynamic properties of small systems. We show the importance of allowing for the discrete character of adsorption centers on the surfaces and their heterogeneity when describing adsorption isotherms and the rates of adsorption processes.

The fundamentals of adsorption theory for a mixture of bulky molecules in slit-shaped pores with heterogeneous wall surfaces

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.