Nonlocal, nonlinear electrostatics: like-charge attraction and asymmetric solvation
We study an equilibrium system, where linear molecules with a rigid charge distribution interact via the mean-field generated by the Coulomb coupling. We focus on the nonlinear regime, which is valid close to external charges immersed in the system. The finite molecular size in this regime leads to a nonlocal response at short distances. First, we show that the mean-field potential is non-monotonic, i.e., like charges can attract each other. Second, we show that the polarization induced by an external charge (and hence its solvation structure) depends on the sign of this charge, violating the effective C-symmetry of the macroscopic electrodynamics. We identify several scenarios of this effect, characterize it with the free energy and entropy differences, and compare it with analogous effects in asymmetric electrolytes described by nonlinear Poisson-Boltzmann equations.