Topological control of local electroneutrality in confined electrolytes.

Topology governs finite-size violations of local electroneutrality in confined electrolytes. Within Poisson-Boltzmann theory, we show that this topological control gives rise to a universal hierarchy of deviations in spherical, cylindrical, and planar confinement. We quantify this effect through an electroneutrality deviation ratio that captures the global electrostatic constraints associated with compactness and boundary multiplicity in Ωsph ≃ S2 × [0, δ], Ωcyl≃S1×R×[0,δ], and Ωslit≃R2×[0,δ]. Although local electroneutrality is asymptotically restored in the limit of infinite cavity size, finite-size deviations follow a robust topological hierarchy, being strongest in spherical cavities, weaker in cylindrical confinement, and weakest in planar slits. These results prove that topology is the organizing principle underlying confinement-induced charge redistribution and violations of local electroneutrality constitute a general electrostatic constraint governing overcharging, charge reversal, and long-range charge correlations. More fundamentally, they demonstrate that changing the topology modifies the global electrostatic constraints without altering the local Poisson-Boltzmann equations. As a counterintuitive manifestation of nonlinear confinement in a point-ion model, we report the existence of inside confinement charge reversal in charged hollow cylindrical and spherical nanoparticles. Since physically consistent, more general electrolyte theories must recover the Poisson-Boltzmann description in the appropriate limiting case, the present results establish a benchmark against which topological effects should be assessed beyond the Poisson-Boltzmann description.