Electrostatic interactions between double layers: influence of surface roughness, regulation, and chemical...

Electrostatic interactions between two surfaces as measured by atomic force microscopy (AFM) are usually analyzed in terms of DLVO theory. The discrepancies often observed between the experimental and theoretical behavior are usually ascribed to the occurrence of chemical regulation processes and/or to the presence of surface chemical or morphological heterogeneities (roughness). In this paper, a two-gradient mean-field lattice analysis is elaborated to quantifying double layer interactions between nonplanar surfaces. It allows for the implementation of the aforementioned sources of deviation from DLVO predictions. Two types of ion-surface interaction ensure the adjustment of charges and potentials upon double layer overlap, i.e., specific ionic adsorption at the surfaces and/or the presence of charge-determining ions for the surfaces considered. Upon double layer overlap, charges and potentials are adjusted via reequilibrium of the different ion adsorption processes. Roughness is modeled by grafting asperities on supporting planar surfaces, with their respective positions, shapes, and chemical properties being assigned at will. Local potential and charge distributions are derived by numerically solving the nonlinear Poisson-Boltzmann equation under the boundary conditions imposed by the surface profiles and regulation mechanism chosen. Finite size of the ions is taken into account. A number of characteristic situations are briefly discussed. It is shown how the surface irregularities are reflected in the Gibbs energy of interaction.