Résumé
Can we avoid molecular dynamics simulations to estimate the electrostatic interaction between charged objects separated by a nanometric distance in water? To answer this question, we develop a continuous model for the dielectric properties of water based on a functional of the polarisation. A phenomenological Landau–Ginzburg Hamiltonian for the electrostatic energy of water is parameterised to capture the dipolar correlations in the fluid at the nanometric scale. We show that in this framework, the effective interactions of simple objects such as point charges are analytically tractable. In particular, the derivation of the interaction energy between a solvated charge and a surface can be reduced to a system of linear equations of electrostatic potentials and analytically solved. This approach could thus give access in few calculation lines to data that necessitate long and costly simulations.