Convergence of PhaseField Free Energy and Boundary Force for Molecular Solvation
Abstract
We study a phasefield variational model for the solvation of charged molecules with an implicit solvent. The solvation freeenergy functional of all phase fields consists of the surface energy, solute excluded volume and solutesolvent van der Waals dispersion energy, and electrostatic free energy. The surface energy is defined by the van der WaalsCahnHilliard functional with squared gradient and a doublewell potential. The electrostatic part of free energy is defined through the electrostatic potential governed by the PoissonBoltzmann equation in which the dielectric coefficient is defined through the underlying phase field. We prove the continuity of the electrostatics—its potential, free energy, and dielectric boundary force—with respect to the perturbation of the dielectric boundary. We also prove the {Γ}convergence of the phasefield freeenergy functionals to their sharpinterface limit, and the equivalence of the convergence of total free energies to that of all individual parts of free energy. We finally prove the convergence of phasefield forces to their sharpinterface limit. Such forces are defined as the negative first variations of the freeenergy functional; and arise from stress tensors. In particular, we obtain the force convergence for the van der WaalsCahnHilliard functionals with minimal assumptions.
 Publication:

Archive for Rational Mechanics and Analysis
 Pub Date:
 January 2018
 DOI:
 10.1007/s0020501711584
 arXiv:
 arXiv:1606.04620
 Bibcode:
 2018ArRMA.227..105D
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 40 pages