Concentration relationships of coefficients of self-diffusion and viscosity of the adsorbate in narrow slit-like pores

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.     

Self-diffusion,mass transfer,and viscosity coefficients for a binary mixture in narrow slit-like pores

The concentration dependences of the dynamic characteristics of a binary mixture in narrow slit-shaped pores of different widths are considered. The local and mean partial self-diffusion, label transfer, mass transfer (mutual diffusion), and shear viscosity coefficients for binary mixtures of various compositions were calculated. The calculation was based on the lattice-gas model in the quasichemical approximation for spherical components with approximately the same size. The calculation of dynamic characteristics took into account collisions between the molecules that determine the direction of their motion. All the kinetic coefficients depend substantially on the mixture density, the direction of motion, and the distance to the pore wall. The effect of the pore width on the calculated dynamic characteristics is considered. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1726—1735, August, 2005.     

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.     

Concentration dependences of heat conductivity coefficients of inert gases in narrow pores

Calculation of the transfer of molecules in porous systems requires self-consistent expressions describing the kinetic transfer coefficients for various concentrations and temperatures. The concentration dependences of heat conductivity and self-diffusion coefficients for fluids with different densities, ranging from rarefied gases to liquids, were considered in terms of a unified model. For monoatomic gases (argon), the model takes into account two energy transfer channels, namely, the vacancy mechanism and energy transfer through collisions of molecules. The former channel is characteristic of rarefied gases, while the latter is noted for condensed phases. The energy parameters of the model were determined on the basis of data on the heat conductivity coefficient in the bulk phase. The heat conductivity coefficient follows a linear temperature dependence for low density; in the medium and large density regions, these dependences follow a more complex pattern that changes depending on temperature. The influence of the interaction of atoms with the pore walls on the concentration dependences of the heat conductivity coefficients was investigated for different total amounts of the adsorbate. These coefficients depend appreciably on the distance to the pore wall and on the direction of heat transfer.     

Spherical particles in small porous sphero-cylindrical systems: phase diagrams and transfer coefficients

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.     

Calculation of the adsorption of rod-like molecules in narrow slit-shaped pores

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. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1476–1484, September, 2006.     

Calculation of the adsorption-desorption hysteresis curves in narrow-pore systems

The gas and liquid spinodal branches for an adsorbate located in narrow slit-shaped, cylindrical, and spherocylindrical pores were calculated. The adsorbate is modeled by Lennard-Jones spherical particles. The calculation was based on the lattice gas model taking into account the intermolecular interactions of nearest neighbors in the quasichemical approximation. The density-temperature diagrams for the gas and liquid spinodal branches in the pores are similar to the equilibrium vapor-liquid phase diagrams: they have a common critical point; the dense-phase branches are shifted to lower pore fillings, while the rarefied-phase branches are shifted toward higher pore fillings. The width of adsorption-desorption hysteresis loop in the adsorption isotherms for Lennard-Jones particles was analyzed as a function of the pore size and the interaction potential of the adsorbate with the pore walls. The effect of pore wall roughness and the accuracy of isotherm calculation on the width of the adsorption-desorption hysteresis loop in cylindrical pores is discussed Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 813–823, May, 2007.     

Principles of the theory of adsorption of large molecules in pores with nonuniform walls

Principles of the theory of adsorption of large molecules blocking more than one adsorption center on a surface in slit-like pores are proposed. The theory takes into account lateral adsorbate—adsorbate interactions and nonuniformity of the pore walls. The equations of adsorption isotherms are derived using the cluster approach. The lateral interactions are taken into account in the quasi-chemical approximation, preserving effects of direct correlations, and in the mean field approximation without effects of correlations. The following problems are discussed: 1) distinguishing of partial contributions of nonuniform adsorption centers on the pore walls; 2) exact solution for dimer adsorption in a two-layer pore with uniform walls; 3) basic types of adsorption isotherms, for which the differences are due to various orientations of the adsorbate in micropores with uniform walls; 4) estimates of the pressure responsible for volume filing of micropores; and 5) the effect of nonuniformity of the pore walls on the pressure values. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1467–1478, August, 1999.     

Calculations of the distribution of trace impurities in cylindrical pores

The equilibrium distribution of a trace impurity and the self-diffusion coefficients of molecules of the base component and the trace impurity in narrow cylindrical pores were calculated using the lattice-gas model. Two types of lattice structures with six and eight closest neighbors were considered. The sizes of the base component and impurity molecules were taken to be identical. Lateral interactions were taken into account in the quasi-chemical approximation. The equilibrium distributions of the trace impurity across a pore section in the gas and liquid phases of the base component and at the interface for the case of capillary condensation were considered. The probability of existence of isolated dimeric clusters was estimated and the self-diffusion coefficients of the base component and trace impurity for a single-phase distribution of the base component were calculated. The effects of the energy of interaction of impurities with the pore walls and the concentration of the base component on the diffusion mobility of the impurities were analyzed. The concentration dependences of the partition coefficient for the trace impurity between the pore center and the pore wall and the concentration dependences of the self-diffusion coefficients for the trace impurity molecules become nonmonotonic with an increase in the base component concentration. These effects are due to the displacement of the impurity from the near-surface area to the bulk of a pore following an increase in the pore coverage by the base component and to higher mobility of the impurity in the free bulk of the pore. Further filling of the pore bulk reduces the mobility of all molecules. The energetics of intermolecular interactions also plays a certain role. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 605–615, April, 2000.     

New method for calculating the adsorption of noble gases on amorphous surfaces

A new approach to calculating the equilibrium characteristics of the adsorption of noble gases on the amorphous surfaces of adsorbents was developed and applied to the Ar−TiO₂(rutile) system. Intermolecular adsorbate-adsorbate interactions are taken into account for the nearest neighbors in the quasi-chemical approximation. The lattice energy parameters of all interactions of the model are determined from the Lennard-Jones potential (12-6). The formation of amorphous TiO₂(rutile) surface includes completion of the surface layers and partial removal of the surface oxygen ions. The quality of the amorphization procedure was confirmed by the experimentally measured heats and isotherms of adsorption of the system under study. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1109–1118, June, 1997.