3 years ago

Dual free energies in Poisson-Boltzmann theory.

R. Blossey, A.C. Maggs

Poisson-Boltzmann theory is the underpinning to essentially all soft matter and biophysics problems involving point-like charges of low valencies, in the form of counter-ions or dissolved salts. Going beyond the mean-field approach typically requires the application of loop expansions around a mean-field solution for the electrostatic potential $\phi({\bf r})$, or sophisticated variational approaches. Recently, Poisson-Boltzmann theory has been recast, via a suitably defined Legendre transform, as a theory involving the dielectric displacement field ${\bf D}({\bf r})$. In this paper we consider the path integral formulation of the dual theory. Exploiting the transformation between $\phi$ and ${\bf D}$, we formulate a fluctuation-corrected dual theory in terms of the displacement field and provide a strategy to compute free energies beyond the leading order.

Publisher URL: http://arxiv.org/abs/1801.10404

DOI: arXiv:1801.10404v1

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