Molecular dynamics simulation to investigate anhydrous phosphoric acid-doped polybenzimidazole

The study conducted a molecular dynamics simulation based on a condensed-phase optimised molecular potentials for atomistic simulation studies force field model to investigate an anhydrous system of phosphoric acid-doped polybenzimidazole (poly[2,2′-(m-phenylene)-5,5′-bibenzimidazole], PBI). Intermolecular pair correlation functions and corresponding coordination numbers were calculated to research the strengths for various types of hydrogen bonding. The results display that the strengths of the hydrogen bonding interactions are in the order of o1–h pair > o2–h pair > n2a–h pair > n3a–h pair, and most protons are located around the neighbourhood of H2PO4– rather than that of PBI. The proton conductivities are 3.86 × 10−3 S cm−1 at 298 K and 8.50 × 10−3 S cm−1 at 413 K. Moreover, the value obtained from our simulation system at 413 K is within the same order of magnitude as the experimentally measured value 0.012 S cm−1 at 420% doping level. The distribution of proton displacement exhibits that the displacement of most protons is about 1.25–2.5 Å. The displacement is over 3.0 Å only for a fraction of protons. In addition, the greatest displacement can approach 4.595 Å. The trajectory analyses of protons show that the most possible mechanisms of proton transfer come from three ways: (a) between two H2PO4– anions, (b) between H2PO4– anions and benzimidazole moieties and (c) between two benzimidazole moieties. The dynamics of polymer motion was studied by the trajectory analyses of ring flips. The large amplitude flips of rings in the polymer chains were found in the system. The flips between benzene and benzimidazole are more frequent than that between benzimidazole moieties.