Mean-field beyond mean-field: the single particle view for moderately to strongly coupled charged fluids

In a counter-ion only charged fluid, Coulomb coupling is quantified by a single dimensionless parameter. Yet, the theoretical treatment of moderately to strongly coupled charged fluids is a difficult task, central to the understanding of a wealth of soft matter problems, including biological systems. We show that the corresponding coupling regime can be remarkably well described by a single particle treatment, which, at variance with previous works, takes due account of inter-ionic interactions. To this end, the prototypical problem of a planar charged dielectric interface is worked out. Testing our predictions against Monte Carlo simulation data reveals an excellent agreement.