Charge regulation and ionic screening of patchy surfaces

The properties of surfaces with charge-regulated patches are studied using nonlinear Poisson-Boltzmann theory. Using a mode expansion to solve the nonlinear problem efficiently, we reveal the charging behavior of Debye-length sized patches. We find that the patches charge up to higher charge densities if their size is relatively small and if they are well separated. The numerical results are used to construct a basic analytical model which predicts the average surface charge density on surfaces with patchy chargeable groups.