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

Abstract

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.

Kinetics and thermodynamics of enzymatic decarboxylation of α,β-unsaturated acid: a theoretical study

“….60 Â 10 À14 s À1 , whereas for the same reaction at 3 ¼ 1 (Int2b / TS3 / Int3), k S-Wig f ¼ 1.71 Â 10 8 s À1 , which indicates that acid catalyst (1) (III) is kinetically favorable in a low local dielectric environment. This is in accordance with our previous work, 11,14,24 in which the uctuation of the local dielectric environment was conrmed to govern the kinetics of proton transfer processes; based on this analysis, React / TS1 / Int1 (1,3-dipolar cycloaddition (I)) is kinetically more favorable than React 3 / TS1 3 / Int1 3 (k S-Wig f ¼ 3.44 Â 10 3 and k S-Wig,3 f ¼ 2.44 Â 10 3 s À1 , respectively). Attempt was made to correlate the rate constants obtained from the TST method with the experimental data.…”

“…Because the FDC1 enzyme is exceedingly large for high-level ab initio methods and because our previous studies showed that the mechanisms for proton transfer in heterocyclic aromatic systems can be studied reasonably well using the B3LYP method with the DZP basis set, [11][12][13] the B3LYP/DZP method was used in this study; our benchmark calculations on bifunctional proton transfers in poly(benzimidazole) (PBI) H-bond systems 14 conrmed that the B3LYP/DZP method yields approximately the same equilibrium and transition structures and relative interaction energies as the B3LYP/TZP method with reasonable computational resources. In this study, the model molecular clusters that were hypothesized in ref.…”

“…The model molecular clusters were constructed by substituting the carbon atoms of FDC1 Backbone that connect the residues with methyl (CH 3 ) groups (Table S2 †); for example, C R Glu277 is the carbon atom of the CH 3 group that substitutes the carbon atom of the FDC1 Backbone that connects the Glu277 residue (Scheme 1). Because our previous studies showed that the local dielectric environment (microenvironment) can affect the structures and energetics of elementary processes 11,13,14 and because enzymatic decarboxylation occurs in aqueous solution, the conductor-like screening model (COSMO) was used to simulate the effect of the aqueous environment. COSMO was used successfully in our previous studies on proton transfer processes in H-bond systems.…”

“…COSMO was used successfully in our previous studies on proton transfer processes in H-bond systems. 11,13,14 Previous theoretical studies used 3 ¼ 4 (ref. 5) and 5.7 (ref.…”

“…Because our previous studies showed that the local dielectric environment (microenvironment) can affect the structures and energetics of elementary processes 11,13,14 and because enzymatic decarboxylation occurs in aqueous solution, the conductor-like screening model (COSMO) was used to simulate the effect of the aqueous environment. COSMO was used successfully in our previous studies on proton transfer processes in H-bond systems.…”