Effective states approximation (ESA) for adsorption on homogeneous and heterogeneous surfaces

A simple approximation for the local and overall adsorption isotherms of monoatomic species on heterogeneous surfaces with different topographies is presented. The model relies on the lattice-gas approach where the site adsorption energies generated by the gas–solid potential, split into a set of independent energy substates because of the ads–ads interactions. The distinctive feature of the approximation is that it preserves in a simple manner the energy states for single particles by making more crude assumptions in counting the total number of configurations compared to standard approaches (mean-field, quasi-chemical) in which the energetics of single particles are oversimplified while the counting of lattice configurations is carried out as accurately as possible. At a comparable degree of approximation this approach, which is denoted as ESA leads to appreciably better results than mean-field. ESA can also be applied to adsorption on heterogeneous surfaces with distinct energy topographies. The effect of lateral interactions and surface topography on the local isotherm at fixed overall coverage and temperature (the so-called energetic structure of the adsorbate) is analyzed and the results are compared with Monte Carlo simulations, the Bragg–Williams and the quasi-chemical approximations. The assumption of an intermediate energy topography characterized by nearest-neighbor site energy correlation, rather than random or patch-wise distributions, is shown to have a significant effect on the distribution of molecules over adsorption sites.