Throughout the simulation, the Donnan potential ϕ D is automatically adjusted to drive the system to a charge neutral state. The pH in the above equation refers to that of the reservoir, however, knowledge of ϕ D , also allows us to simultaneously calculate the pH c inside an isolated canonical system using Eq.( ). We should also note that the presence of a neutralizing background requires a modification of the Bethe potential, φ B . We stress again that pH of the reservoir is not the same as of an isolated system of the same ionic content.