Counterions at disordered charged planar surfaces

Using field-theoretic and numerical methods, we study counterion density profiles at planar surfaces with disordered surface-charge distributions. Experimental examples include mixed lipid bilayers and weakly charged surfaces where pH-controlled charge regulation takes place. Quenched as well as annealed disordered surface charge distributions exhibit markedly enhanced counterion densities close to the surface even for weak coupling parameter, in contrast to ordered dilute substrates where the counterion surface enhancement is relatively weak.