  While important for many industrial applications, chemical reactions
responsible for charging of solids in water are often poorly understood. We
theoretically investigate the charging kinetics of solid-liquid interfaces, and
find that the time-dependent equilibration of surface charge contains key
information not only on the reaction mechanism, but also on the valency of the
reacting ions. We construct a non-linear differential equation describing
surface charging by combining chemical Langmuir kinetics and electrostatic
Poisson-Boltzmann theory. Our results reveal a clear distinction between
late-time (near-equilibrium) and short-time (far-from-equilibrium) relaxation
rates, the ratio of which contains information on the charge valency and ad- or
desorption mechanism of the charging process. Similarly, we find that
single-ion reactions can be distinguished from two-ion reactions as the latter
show an inflection point during equilibration. Interestingly, such inflection
points are characteristic of autocatalytic reactions, and we conclude that the
Coulombic ion-surface interaction is an autocatalytic feedback mechanism.
