Determination of the energetic topography of bivariate heterogeneous surfaces from adsorption isotherms

Abstract

The reversible adsorption process occurring on patchwise heterogeneous bivariate surfaces is studied by Monte Carlo simulation and mean-field approximation. These surfaces are characterized by a collection of deep and shallow adsorbing patches with a typical length scale l. Patches can be either arranged in a deterministic chessboard structure or in a random way. Previous studies showed that the topography of a given surface can be obtained from the knowledge of the corresponding adsorption isotherm and a reference curve. In the present work, we discuss the advantages and disadvantages of using different reference curves. One of the main consequences of this analysis is to provide an improved method for the determination of the energetic topography of the surface from adsorption measurements.

Adsorption isotherm predicted from a lattice gas with general lateral interactions in a single-phase regime

“…The density functional theory yields similar results [26], while the quasi-chemical approximation yields a more complex isotherm equation [14]. For heterogeneous surfaces an average of Langmuir isotherms was obtained [17,18]. An intriguing case that is still not well understood is the region of subcritical temperatures where first-order phase transitions can occur.…”

“…where µ is the chemical potential and λ j = 0, 1 is the site occupancy. Nevertheless, heterogeneous surfaces have also been investigated [15][16][17][18].…”

Effects of surface topography on the collective diffusion of interacting adsorbed particles

“…In this context, simple heterogeneous surfaces, characterized by two kinds of nonequivalent sites, have also been intensively used in modeling adsorption [29][30][31][32][33] and surface diffusion phenomena [34][35][36][37][38][39][40][41][42][43][44]. In the first case, adsorption on bivariate surfaces with square patches and strip topographies has been studied through Monte Carlo simulations for adparticles with nearest-neighbor interaction energy, at a fixed temperature [29,30].…”

“…Later, the study was extended to include the effects of temperature on the adsorption process [31]. It was found that both the adsorption isotherms and the differential heat of adsorption follow scaling laws involving the patch size l with a universal exponent, and that this characteristic length defining the topography could, in principle, be obtained from the analysis of experimental results [32,33].…”

Computer simulation and detailed mean-field approximation applied to adsorption on nanoparticles

“…where now θ (T ,μ) not only depends on the adsorptive energy at a given point on the surface but also on the adsorptive energy at (in general)"m" neighboring points, and f (ε 1 ,...ε m ) is a multivariate probability distribution which specifies how adsorptive energies are spatially distributed, or in other words, the energetic topography of the surface. In this context, Bulnes et al [30,31] analyzed the case of bivariate surfaces, with particles interacting through a repulsive interaction by Monte Carlo (MC) simulations. Despite the complexity of the surface, different quantities were identified which scale obeying power laws as a function of the patch length and the difference of adsorptive energy between strong and weak adsorption sites.…”