Beyond Poisson-Boltzmann: fluctuations and fluid structure in a self-consistent theory

Poisson-Boltzmann (PB) theory is the classic approach to soft matter electrostatics which has been applied to numerous problems of physical chemistry and biophysics. Its essential limitations are the neglect of correlation effects and of fluid structure. Recently, several theoretical insights have allowed the formulation of approaches that go beyond PB theory in a systematic way. In this topical review we provide an update on the developments achieved in self-consistent formulations of correlation-corrected Poisson-Boltzmann theory. We introduce the corresponding system of coupled nonlinear equations for both continuum electrostatics with a uniform dielectric constant and a structured solvent, a dipolar Coulomb fluid, including nonlocal effects. While the approach is only approximate and also limited to corrections in the so-called weak fluctuation regime, it allows to include physically relevant effects, as we show for a range of applications of these equations.