Molecular Simulation of Phosphoric Acid-Doped Polybenzimidazoles as High- Temperature Proton Exchange Membranes

Proton transfer (PT) in fuel cell membranes consists of proton hopping along the hydrogen bond network (structural diffusion, occurs in the time scale of picoseconds) and the diffusion of the proton carrier between hops (vehicular diffusion, occurs in the time scale of nanoseconds). In this study, multiscale modeling using quantum mechanics (QM), classical molecular dynamics (MD), and Atom-centered Density Matrix Propagation (ADMP) ab initio molecular dynamics (AIMD) using ONIOM hybrid calculations have been employed to investigate PT and the structure of the hydrogen bond network in phosphoric acid (PA)-doped polybenzimidazole membranes.;QM calculations at the B3LYP/6-31++G(d,p) level of theory were performed to calculate gas-phase proton affinity, interaction energy, and energy barriers for different PT pathways between benzimidazole, PA, water molecules, and their corresponding ions. Results of energy barriers indicate a general trend that PT is prone to occur between the same molecules or between a molecule and its corresponding ion.;Classical MD simulations using the Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) forcefield were performed to study the hydrogen bond network structures and vehicular diffusion properties in neat, hydrated, and PA-doped polybenzimidazoles. The influences of different polybenzimidazole structures, PA-doping levels, temperatures, and water contents were evaluated. Results indicate the strength of hydrogen bond is mainly determined by the donor with the donor strength decreases in the order PA > water > polybenzimidazole. The number of PA-involved hydrogen bonds increases with PA-doping level, decreases with increasing temperature, and increases with decreasing water content. The vehicular diffusion coefficient in PA-doped polybenzimidazoles decreases in the order water > PA > polybenzimidazole. Specifically, the vehicular diffusion of PA increases with PA-doping level, temperature, and water content.;The proton diffusion coefficient obtained from ADMP calculation of a cluster of three PA molecules at the B3LYP/6-31++G(d,p) level of theory compared favorably with the experimental value for PA. ADMP/ONIOM calculations were also performed on the PA-doped polybenzimidazole model to study the initial steps during PT and the interfacial properties between polybenzimidazole and PA. Results indicate that the protonation of the "=N-" atom on the imidazole ring of polybenzimidazole occurs when there are two or more PA molecules surrounding each imidazole ring, which agrees with the model that Ma et al. [1] proposed based on experimental conductivity results measured at different PA doping levels. Simulation results also indicate when there are two PA molecules per imidazole ring in the system, protonation occurs only when two hydrogen bonds exist between the two PA molecules that are hydrogen-bonded to the imidazole ring. When there are three PA molecules per imidazole ring in the system, the two PA molecules that are hydrogen-bonded to the imidazole ring can have one hydrogen bond or even no hydrogen bond, but a third PA molecule has to form hydrogen bonds with both of the two PA molecules in order to protonate the "=N-" atom.