Calculating the Electrostatic Potential Profiles of Double Layers from Simulation Ion Density Profiles

Computer simulations of the planar double layer geometry provide the charge profile with statistical noise. To compute the mean electrostatic potential profile from the charge profile, one must solve Poisson’s equation with appropriate boundary conditions (BC). In this work, we show that it is advantageous to use the Neumann or Dirichlet BCs at the boundaries of the simulation domain with an integrated version of Poisson’s equation. This minimises errors from the simulation’s noisy density profiles, in contrast to traditional convolution integrals that amplify the noise. The Neumann BC, where the electric field is prescribed, can be used in both the constant surface charge and constant electrode voltage ensembles. In the constant voltage ensemble, where the potential difference between the confining electrodes is prescribed, one can also use the Dirichlet BC, where the potentials at the boundaries are set. We show that the new methods provide converged results for the potential profile faster than the convolution integral does.