Symmetry breaking of interacting charge-regulated planar macroions at low salt concentration

The charge of macroions such as colloids and membranes can often be regulated by reversible ion adsorption or dissociation reactions. When two chemically identical macroions interact across an electrolyte, charge regulation will typically lead to the same charge density on both macroion surfaces. However, it was recently demonstrated that a non-ideal, Frumkin-like adsorption behavior of the ions can lead to a spontaneous symmetry breaking, where the coupling of charge regulation leads to different surface charge densities on both macroions in thermal equilibrium. While previous modeling was carried out numerically in the presence of salt for selected systems, we argue that the no-salt limit captures experimentally relevant situations at low salt concentration. We therefore focus on macroions with dissociable surface groups in the absence of salt, where the Poisson-Boltzmann equation can be solved analytically and the spontaneous emergence of uniform but different degrees of dissociation on both macroions signifies a symmetry breaking. Using a perturbation approach we derive analytic results for the local stability of the symmetric state. This not only provides a complete thermodynamic characterization of the symmetry breaking as function of all parameters, it also uncovers previously unrecognized features. First, depending on the degree of non-ideality, the symmetry breaking transition can be continuous or discontinuous. Second, metastable states do exist far away from critical points but not in their vicinity. And third, electrostatic interactions generally act toward weakening or suppressing the occurrence of symmetry breaking.