Polarizable Surfaces: Weak and Strong Coupling Regimes

We study the ionic distribution near a charged surface. A new method for performing Monte Carlo simulations in this geometry is discussed. A theory is then presented that allows us to accurately reproduce the density profiles obtained in the simulations. In the weak-coupling regime, a theory accounts for the ion-image interactions, leading to a modified Poisson-Boltzmann equation. When the correlations between the ions are significant, a strong-coupling theory is used to calculate the density profiles near the surface and a Poisson-Boltzmann equation with a renormalized boundary condition to account for the counterion distribution in the far-field.