Molecular simulation of mass transport in phosphoric acid doped poly(2,5-benzimidazole) polymer electrolyte membranes

•Mass transfer in ab-PBI membrane is simulated by MD.•Two kinds of proton transfer mechanisms in the ab-PBI membrane are evaluated.•The first transfer mechanism is the main proton transfer mechanism in ab-PBI.•The diffusion of H2PO4− controls the mass transfer in ab-PBI membrane.

In this paper, a molecular model based on quantum mechanics and molecular dynamics (MD) is developed to study the transfer mechanisms of proton, phosphoric acid (PA) molecule and dihydrogen phosphate anion (H2PO4−) in PA-doped poly(2,5-benzimidazole) (ab-PBI) membrane. This model couples with intermolecular potential energy, interaction force between two particles, linear momentum conservation equation, angular momentum conservation equation, total energy conservation equation, the radial distribution function and Einstein's law of diffusion. The simulated molecular system consisting of ab-PBI macromolecules doped with PA is optimized to obtain an optimal structure of the amorphous cell unit system. The effects of PA doping level, temperature and electric field intensity on the mass transfer in the ab-PBI membrane are studied. A comparison between this simulation results and experimental data gotten from literatures shows this model and its simulation are reliable. Two kinds of proton transfer mechanisms are evaluated, and the first transfer mechanism, in which H2PO4− takes as a carrier and [−C=N−][−C=N−] takes as a stronghold, is considered as the main proton transfer mechanism in an ab-PBI membrane at the studied doping levels. The diffusion coefficient of PA is about 2.5 times of that of H2PO4−, which indicates the diffusion of H2PO4− controls the mass transfer in the ab-PBI membrane.

Graphical abstractThere are proton transfer, phosphoric acid (H3PO4H3PO4, PA) molecule transfer and dihydrogen phosphate anion (H2PO4−) transfer in PA-doped poly(2,5-benzimidazole) (ab-PBI) membrane. The diffusion coefficient of H3PO4H3PO4 is about 2.5 times of that of H2PO4−, which indicates the diffusion of H2PO4− controls the mass transfer in the ab-PBI membrane.Figure optionsDownload full-size imageDownload as PowerPoint slide