Lattice Boltzmann simulations for proton transport in 2-D model channels of Nafion

Proton conductance in a 2-D channel with a slab-like structure was studied to verify that the lattice Boltzmann method (LBM) can be used as a simulation tool for proton conduction in a Nafion membrane, which is a mesoscopic system with a highly disordered porous structure. Diffusion resulting from a concentration gradient and migration by an electrostatic force were considered as the origins of proton transport. The electrostatic force acting on a proton was computed by solving the Poisson equation. The proton concentration in the membrane is expressed as a continuous function and the sulfonic charge is placed discretely. The space-averaged conductance of protons in a nonequilibrium stationary state was evaluated as a function of the structural parameters: namely, channel width and distribution of the sulfonic groups. The resulting space-averaged conductance deviates from the bulk values, depending particularly on the sulfonic group distribution. Details of the simulation scheme are described and the applicability of the present scheme to real membranes is discussed.