A minimizing principle for the Poisson-Boltzmann equation
Lab. PCT, Gulliver CNRS-ESPCI UMR 7083 - 10 rue Vauquelin, 75231 Paris Cedex 05, France, EU
Accepted: 9 March 2012
The Poisson-Boltzmann equation is often presented via a variational formulation based on the electrostatic potential. However, the functional has the defect of being non-convex. It cannot be used as a local minimization principle while coupled to other dynamic degrees of freedom. We formulate a convex dual functional which is numerically equivalent at its minimum and which is more suited to local optimization.
PACS: 61.20.Qg – Structure of associated liquids: electrolytes, molten salts, etc. / 82.60.Lf – Thermodynamics of solutions / 05.20.Jj – Statistical mechanics of classical fluids
© EPLA, 2012