n this talk, i will first recall a mean field approximation of electrostatic free energy for an ionic solution, and discuss two issues: (1) rigorous mathematical justification of the existence of equilibrium concentrations and their boltzmann relations; (2) the effect of inhomogeneous dirichlet boundary condition to the solution of the related poisson-boltzmann equation for the electrostatic potential. i will then consider a class of variational implicit solvent models for the solvation of biomolecules, and present a formal derivation of the first variation of the electrostatic free energy with respect to the location change of the dielectric boundary. this result is needed for level-set relaxation and force calculations of biomolecular structures and dynamics. //www.ladysinger.com/~bli/research/mbbseminar/