Three Types of the Two-Phase Surface Tension of Molecules in Mesoporous Systems and Methods for Their Calculation

At temperatures T < T_c(H) (where T_c(H) is the critical temperature and H is the characteristic pore size), in all mesoporous systems sorbed adsorbate molecules are separated into two coexisting phases “vapor in a pore” and “liquid in a pore”. The conditions for such adsorbate separation depend on the pore width and adsorbent–adsorbate interaction energies. The distribution of an adsorbate over the pore volume in different materials plays an important role in the processes of substance transfer and the establishment of an equilibrium state in them. The separation of molecules is accompanied by the formation of menisci at the vapor–liquid interface. They largely determine the overall resistance to the process of mass transfer through porous materials. The most advanced results on the description of vapor–liquid interfaces are obtained on the basis of the so-called molecular lattice-gas model, which makes it possible to calculate the molecular distributions in heterogeneously distributed models of transition regions with equal accuracy. Nondeformable pore walls create an external field that affects the molecular distribution and forms adsorption films due to the adsorbate-adsorbent interaction potential. The surface tension of the discussed menisci, as well as at the boundaries between the vapor or liquid adsorbate and solid walls, is calculated from the excess free energy of the interface (according to Gibbs). The state of the coexisting phases “vapor in a pore” and “liquid in a pore” must satisfy the equality of chemical potentials, excluding the appearance of metastable states. Methods for calculating three types of two-phase surface tensions in a three-aggregate system and a method for localizing areas of three-phase contact, as well as a microscopic description of the molecular distributions and properties of these areas are outlined. The approach is demonstrated using the example of slit-like pores with smooth and rough walls, as well as cylindrical pores and their junctions between pores of different radii. The size effects of the contact angle are studied as a function of the geometry of the pore cross section and the potential of the pore walls. The results obtained are ahead of the level of existing published works.