Dipolar Poisson models in a dual view

Hélène Berthoumieux (1) , Geoffrey Monet (1) , Ralf Blossey (2)

1 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
2 UGSF - Unité de Glycobiologie Structurale et Fonctionnelle - UMR 8576

In this work we study the continuum theories of Dipolar-Poisson models. Both the standard Dipolar-Poisson model as well as the Dipolar-Poisson-Langevin model, which keeps the dipolar density fixed, are non-convex functionals of the scalar electrostatic potential φ. Applying the Legendre transform approach introduced by A.C. Maggs [A.C. Maggs, Europhys. Lett. 98, 16012 (2012)], the dual functionals of these models are derived and are given by convex vectorfield functionals of the dielectric displacement D and the polarization field, P. We compare the convex functionals in P-space to the non-convex functionals in electric field E-space and apply them to the classic problem of the solvation of point-like ions. Since the Dipolar-Poisson model does not properly describe polarization saturation, we argue that only the Dipolar-Poisson-Langevin functional can be used to provide a nonlinear generalization of the harmonic polarization functional used in the theory of Marcus for electron transfer rate to nonlinear regimes. We show that the model can be quantitatively parametrized by molecular dynamics simulations.

Domaines: Physique [physics]

Hélène Berthoumieux, Geoffrey Monet, Ralf Blossey. Dipolar Poisson models in a dual view. Journal of Chemical Physics, 2021, ⟨10.1063/5.0056430⟩. ⟨hal-03312399⟩