Modified Ewald Summation Method for Slab Geometries: Application to Donnan Potentials, Confinement Electrostatics, and Titration Simulations

Abstract

Simulating electrochemical systems confined within nanoscale slab geometries is a major challenge due to long-range electrostatic interactions and the breakdown of global charge neutrality when the domain exchanges ions with an external bulk electrolyte reservoir. In this work, we present a grand-canonical simulation framework designed for slab geometries that utilizes a regularized 3D periodic Ewald summation technique to systematically converge to the true 2D periodic Green’s function without unphysical cell-width (Lz) dependencies. Unlike traditional grand canonical methods that rely on neutral-pair insertions to maintain a zero net charge, our framework allows the net cell charge to fluctuate by implementing decoupled, single-ion trial moves. This approach bypasses the cooperative sampling bottlenecks that plague neutral-pair insertions inside dense, strongly charged nanopores. Crucially, the method allows us to calculate the Donnan potential (φD) inside the cell, which cannot be accessed directly by any other available simulation method. The Donnan potential acts as a direct microscopic analog to the electromotive force (emf) of a nanoscale electrochemical cell, making the method uniquely suited for iontronic and nanofluidic applications where nonideal ion–ion correlations and strong inhomogeneities modify device potentials. The methodology is validated against exact solutions of the nonlinear Poisson–Boltzmann equation, demonstrating excellent agreement for both local ionic density profiles and self-consistent potentials. Finally, we demonstrate the utility of this framework by simulating charge regulation and surface titration of weak acidic groups at the pore wall.