Two overall neutral surfaces with positive and negative charged domains("patches") have been shown in recent experiments to exhibit long-rangeattraction when immersed in an ionic solution. Motivated by the experiments, wecalculate analytically the osmotic pressure between such surfaces within thePoisson-Boltzmann framework, using a variational principle for thesurface-averaged free energy. The electrostatic potential, calculated beyondthe linear Debye-H\"uckel theory, yields an {\it overall attraction} at largeinter-surface separations, over a wide range of the system's controlled lengthscales. In particular, the attraction is stronger and occurs at smallerseparations for surface patches of larger size and charge density. In thislarge patch limit, we find that the attraction-repulsion crossover separationis inversely proportional to the square of the patch charge-density and to theDebye screening length.
展开▼
