On the Repulsive Interaction Between Strongly Overlapping Double Layers of Charge-regulated Surfaces

The Donnan equilibrium is employed to evaluate the entropic repulsion between two charged plates that feature charge regulation and are in equilibrium with a reservoir solution of monovalent salt. This approach represents the zero-field limit of the Poisson–Boltzmann equation, valid for strongly overlapping electrical double layers. We show that this scenario features an intrinsic length scale, which serves as the unscreened pendant of the Debye length for strongly overlapping double layers. In general, the scaling of the disjoining pressure with inter-plate distance is dependent on the boundary conditions (constant charge, constant potential, or charge regulation). Surprisingly, here we find for sufficiently low potentials the same inverse-square decay as for constant charge surfaces. We test the validity of the zero-field limit by comparison with self-consistent field lattice computations that invoke the full Poisson equation for finitely sized ions between two charge-regulated plates.