Surface Characterization by Adsorption Measurements: Competition between Heterogeneous Adsorption Potential and Adsorbate–Adsorbate Lateral Interactions

We address the problem of surface characterization via inversion of the adsorption isotherm equation for particles with repulsive nearest-neighbor interactions adsorbed on square lattices, combining theoretical analysis with Monte Carlo simulations. At low temperature (or strong lateral interaction), adsorption isotherms display a pronounced plateau at coverage θ = 0.5, separating two regimes. From θ = 0 to 0.5, adsorption occurs on isolated sites until a c (2 × 2) structure forms, with no particle–particle interaction. From θ = 0.5 to 1.0, adsorption fills the vacant sites of this structure, each new particle interacting with four neighbors. The isotherms for different coupling strengths w are well described by a two-local-isotherm model, with adsorption energies ϵ S and ϵ D corresponding to the two regimes. Thus, repulsive adsorption on a homogeneous surface can be mapped onto noninteracting adsorption on a heterogeneous bivariate surface, with ϵ S – ϵ D ∝ w . This duality highlights an intrinsic ambiguity in surface characterization based only on isotherms. We show that additional measurements, such as adsorption heats or fluctuation-sensitive observables, resolve this ambiguity. These thermodynamic arguments are reinforced by information-theoretic tools, providing insights into accurate surface topography characterization.