Interaction between two overall neutral charged microscopically patterned surfaces

We study the interaction between heterogeneously charged surfaces in an electrolyte solution by employing classical Density Functional Theory (cDFT) and Monte Carlo simulations. We observe a consistent behavior between cDFT and Monte Carlo simulations regarding force curves and two-dimensional density profiles. Armed with the validated cDFT, we explore the system's behavior under parameters that are challenging to simulate directly. Our findings include the impacts of domain size, domain charge, domain charge configuration, and bulk electrolyte concentration on the osmotic pressure. Remarkably, the force curve is more sensitive to the domain size for an asymmetric configuration than a symmetry configuration; the bulk concentration weakly influences the force curve independent of the system configurations.