An interacting spin–flip model for one-dimensional proton conduction

A discrete asymmetric exclusion process (ASEP) is developed to model proton conduction along one-dimensional water wires. Each lattice site represents a water molecule that can be in only one of three states; protonated, left-pointing and right-pointing. Only a right(left-) pointing water can accept a proton from its left (right). Results of asymptotic mean field analysis and Monte Carlo simulations for the three-species, open boundary exclusion model are presented and compared. The mean field results for the steady-state proton current suggest a number of regimes analogous to the low and maximal current phases found in the single-species ASEP (Derrida B 1998 Phys. Rep. 301 65– 83). We find that the mean field results are accurate (compared with lattice Monte Carlo simulations) only in certain regimes. Refinements and extensions including more elaborate forces and pore defects are also discussed. PACS numbers: 82.39.Jn, 02.50.Ey, 05.50.+q, 05.70.Ln