A new phase-field approach to variational implicit solvation of charged molecules with the Coulomb-field approximation. (English) Zbl 1407.65234
Summary: We construct a new phase-field model for the solvation of charged molecules with a variational implicit solvent. Our phase-field free-energy functional includes the surface energy, solute-solvent van der Waals dispersion energy, and electrostatic interaction energy that is described by the Coulomb-field approximation, all coupled together self-consistently through a phase field. By introducing a new phase-field term in the description of the solute-solvent van der Waals and electrostatic interactions, we can keep the phase-field values closer to those describing the solute and solvent regions, respectively, making it more accurate in the free-energy estimate. We first prove that our phase-field functionals \(\Gamma\)-converge to the corresponding sharp-interface limit. We then develop and implement an efficient and stable numerical method to solve the resulting gradient-flow equation to obtain equilibrium conformations and their associated free energies of the underlying charged molecular system. Our numerical method combines a linear splitting scheme, spectral discretization, and exponential time differencing Runge-Kutta approximations. Applications to the solvation of single ions and a two-plate system demonstrate that our new phase-field implementation improves the previous ones by achieving the localization of the system forces near the solute-solvent interface and maintaining more robustly the desirable hyperbolic tangent profile for even larger interfacial width. This work provides a scheme to resolve the possible unphysical feature of negative values in the phase-field function found in the previous phase-field modeling (cf. [H. Sun et al., “A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson-Boltzmann electrostatics”, J. Chem. Phys. 143, 243110 (2015)]) of charged molecules with the Poisson-Boltzmann equation for the electrostatic interaction.
MSC:
65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
65K10 | Numerical optimization and variational techniques |
65Z05 | Applications to the sciences |
65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
35Q35 | PDEs in connection with fluid mechanics |
78A30 | Electro- and magnetostatics |
76T20 | Suspensions |
35Q20 | Boltzmann equations |