Theoretical calculation of proton mobility for collective surface proton transport

We present a theoretical study of surface proton mobility at a minimally hydrated array of protogenic surface groups. At dense packing, the array assembles into a 2D bicomponent lattice that is formed by sulfonate anions, which are only allowed to fluctuate about fixed equilibrium positions, and mobile hydronium ions. Proton transport on the lattice proceeds by collective translocations of hydronium ions. This type of motion is described within the framework of soliton theory. Our main objective in this article is to establish the relation between microscopic surface structure and effective proton mobility. To this end, we present an approach to calculate microscopic interaction parameters that determine hydronium ion motion. The developed formalism enables us to theoretically derive an expression for soliton mobility at a given surface structure and compare it with experimentally measured mobilities.