Effective adsorption energy and generalization of the Frumkin-Fowler-Guggenheim isotherm

The adsorption phenomenon is often described by means of a kinetic equation, in the form proposed by Langmuir. From the statistical point of view, the analysis is done in terms of adsorption sites, in the framework of Boltzmann or Fermi-like statistics. We show that a more simple description can be done in terms of an effective adsorption energy, taking into account its dependence on the density of adsorbed particles. Some elementary lateral interaction potentials are analyzed to illustrate this dependence. We show that the effective adhesion energy may be written as a power law of the surface coverage ratio. Eventually, we propose a generalization of the Frumkin-Fowler-Guggenheim model as a self-consistent non-linear relation determining the actual equilibrium distribution of surface particles.