About the choice of the protogenic group in polymer electrolyte membranes: Ab initio modelling of sulfonic acid, phosphonic acid, and imidazole functionalized alkanes

The possible use of sulfonic acid, phosphonic acid, or imidazole as the protogenic group in polymer electrolyte membranes for fuel cells operating at intermediate temperature (T > 100 degrees C) and very low humidity conditions is examined by comparing specific molecular properties obtained with first principles based electronic structure calculations. Potential energy profiles determined at the B3LYP/6-311G** level for rotation of imidazole, phosphonic acid and sulfonic acid functional groups on saturated heptyl chains revealed that the torsional barriers are 3.9, 10.0, and 15.9 kJ mol(-1), respectively; indicating that the imidazole is clearly the most labile when tethered to an alkyl chain. Minimum energy conformations (B3LYP/6-311G**) of methyl dimers of each of the acids indicated that the binding of the pairs of the acids is greatest in the phosphonic acids and lowest for the imidazoles. Comparison of the ZPE corrected total energies of the methyl acid dimers with corresponding pairs consisting of the conjugate acid and conjugate base revealed that the energy penalty in transferring the proton (from acid to acid) was greatest for imidazole (120.1 kJ mol(-1)) and least for the phosphonic acid (37.2 kJ mol(-1)). This result is in agreement with experimentally measured proton conductivities of acid-functionalized heptyl compounds under dry conditions and further underpins the observation that phosphonic acid possesses the best amphoteric character critical in achieving proton conductivity when no solvent (i.e. water) is present. Finally, BSSE corrected binding energies were computed for the methyl acids with a single water molecule and indicated that while the magnitude of the interaction of the sulfonic and phosphonic acids with water are similar (47.3 and 44.4 kJ mol(-1), respectively), the binding is much weaker to the imidazole (28.8 kJ mol(-1)). This result suggests that the oxo-acids will probably retain water better under very low humidity conditions and that the dynamics of the hydrogen bonding of the first hydration water molecules will be more constrained with -SO3H and -PO3H2 than imidazole