Adsorption of Spherical Molecules in Probing the Surface Topography: 2. Model of Conditional Probabilities

Adsorption on a heterogeneous surface is considered within the framework of the lattice model taking into account a correlation in arrangement of nearest adsorption sites. The expression for an adsorption isotherm is derived in the mean field approximation. From an experimental isotherm, the proposed algorithm computes fractions of different adsorption sites, reduced adsorption energies, and a matrix expressing conditional probabilities of detection of different sites in a neighborhood of sites of a chosen kind. The elements of that matrix are supposed to be expressed via the fractions of the sites. In particular, in the case of the well-known model of patchwise heterogeneity, this matrix has diagonal form. In the latter case the algorithm allows one to estimate energies of lateral interactions for admolecules localized on different patches. The patchwise model is used for treatment of an isotherm of argon adsorption on muscovite. As established, the lateral interactions cannot be ignored even at very low degrees of surface coverage. Perhaps this fact is explained by grouping of the strongest adsorption sites into linear chains such as edges, growth steps, spiral dislocations, etc. However, the most reasonable explanation is accumulation of the adsorbate molecules around needle-shaped contacts between adsorbent particles. It follows from general considerations that adsorption sites in a neighborhood of such contacts must be the strongest ones and, hence, must be occupied first and foremost, i.e., at lowest pressures. In a vicinity of such contacts the adsorbate molecules can form rings that can be considered, in turn, as a one-dimensional lattice with coordination number 2. The next step of the theory should consist in determination of energies of lateral interactions by using standard systems with known crystallography.