The Grotthuss mechanism for bifunctional proton transfer in poly(benzimidazole)

Poly(benzimidazole) (PBI) has received considerable attention as an effective high-temperature polymer electrolyte membrane for fuel cells. In this work, the Grotthuss mechanism for bifunctional proton transfer in PBI membranes was studied using density functional theory and transition state theory. This study focused on the reaction paths and kinetics for bifunctional proton transfer scenarios in neutral ([PBI](2)), single (H(+)[PBI](2)) and double-protonated (H(2+)[PBI](2)) dimers. The theoretical results showed that the energy barriers and strength for H-bonds are sensitive to the local dielectric environment. For [PBI](2) with ε = 1, the uphill potential energy curve is attributed to extraordinarily strong ion-pair H-bonds in the transition structure, regarded as a ‘dipolar energy trap’. For ε = 23, the ion-pair charges are partially neutralized, leading to a reduction in the electrostatic attraction in the transition structure. The dipolar energy trap appears to prohibit interconversion between the precursor, transition and proton-transferred structures, which rules out the possibility for [PBI](2) to be involved in the Grotthuss mechanism. For H(+)[PBI](2) and H(2+)[PBI](2) with ε = 1, the interconversion involves a low energy barrier, and the increase in the energy barrier for ε = 23 can be attributed to an increase in the strength of the protonated H-bonds in the transition structure: the local dielectric environment enhances the donor–acceptor interaction of the protonated H-bonds. Analysis of the rate constants confirmed that the quantum effect is not negligible for the N–H(+) … N H-bond especially at low temperatures. Agreement between the theoretical and experimental data leads to the conclusion that the concerted bifunctional proton transfer in H(2+)[PBI](2) in a high local dielectric environment is ‘the rate-determining scenario’. Therefore, a low local dielectric environment can be one of the required conditions for effective proton conduction in acid-doped PBI membranes. These theoretical results provide insights into the Grotthuss mechanism, which can be used as guidelines for understanding the fundamentals of proton transfers in other bifunctional H-bond systems.