A fluctuation-corrected functional of convex Poisson–Boltzmann theory

R. Blossey (1) , A C Maggs

1 UGSF - Unité de Glycobiologie Structurale et Fonctionnelle - UMR 8576

Poisson-Boltzmann theory allows to study soft matter and biophysical systems involving point-like charges of low valencies. The inclusion of fluctuation corrections beyond the mean-field approach typically requires the application of loop expansions around a mean-field solution for the electrostatic potential φ(r), or sophisticated variational approaches. Recently, Poisson-Boltzmann theory has been recast, via a Legendre transform, as a mean-field theory involving the dielectric displacement field D(r). In this paper we consider the path integral formulation of this dual theory. Exploiting the transformation between φ and D, we formulate a dual Sine-Gordon field theory in terms of the displacement field and provide a strategy for precise numerical computations of free energies beyond the leading order.

Domaines: Matière Molle [cond-mat.soft]

R. Blossey, A C Maggs. A fluctuation-corrected functional of convex Poisson–Boltzmann theory. Journal of Physics A: Mathematical and Theoretical, 2018, 51 (38), pp.385001. ⟨10.1088/1751-8121/aad352⟩. ⟨hal-02344717⟩