Simulation of Charged Systems in Heterogeneous Dielectric Media via a True Energy Functional

For charged systems in heterogeneous dielectric media, a key obstacle for molecular dynamics (MD) simulations is the need to solve the Poisson equation in the media. This obstacle can be bypassed using MD methods that treat the local polarization charge density as a dynamic variable, but such approaches require access to a true free energy functional, one that evaluates to the equilibrium electrostatic energy at its minimum. In this Letter, we derive the needed functional. As an application, we develop a Car-Parrinello MD method for the simulation of free charges present near a spherical emulsion droplet separating two immiscible liquids with different dielectric constants. Our results show the presence of nonmonotonic ionic profiles in the dielectric with a lower dielectric constant.

Figure 1

Ionic density profiles for different concentrations of monovalent electrolyte inside the dielectric sphere. The outside salt concentration is held fixed at 0.3 M for all curves. The inset shows the accumulation of ions near the interface on the lower permittivity side. The dashed line in the middle shows the position of the interface. On the left side we sketch our model for the liquid-liquid emulsion droplet in the presence of a monovalent electrolyte (not to scale).