Scaling behavior of adsorption on patchwise bivariate surfaces revisited

The adsorption of gases on patchwise heterogeneous bivariate surfaces is studied. These surfaces are characterized by a collection of strong and weak adsorbing patches with a typical length scale l. Different forms and spatial arrangements of these patches determine different topographies characterized by an effective length, l(eff) = sigmal, where sigma takes values from 1 to 4 for the different topographies considered here. Previous studies showed that the mean square deviation between isotherms corresponding to different values of l(eff) scaled as a power law with exponent alpha, without providing any physical interpretation of such behavior. In the present work, we introduce a different scaling function, chi(l), which is shown to be twice the difference in free energy per site between a reference isotherm and the given isotherm, at half coverage. With this function the scaling behavior and the value of the scaling exponent alpha are determined over the whole range of interparticles interaction energy and adsorptive energy, and for different temperatures, through Monte Carlo simulations. The results are similar to those obtained in previous studies, with a value of alpha which is half the one obtained before due to the different definition of the scaling function, but the present analysis provides a full understanding of the scaling behavior based on the physical significance of the scaling function and the scaling exponent.