A Charge-Transfer-Resistance Model for Proton Transmission through CVD Single-Layer Graphene in Proton-Exchange-Membrane Cells

Abstract

High-rate proton transmission through single-layer graphene has been reported by several research groups but the mechanism by which it occurs is still not clear. Low activation energies for proton transmission have been experimentally obtained but are difficult to reconcile with computational modeling studies that predict high activation energies and low transmission rates for protons passing through pristine single-layer graphene at ambient temperatures. It seems likely that a reaction coordinate with an activated complex structure involving proton passage through graphene is involved, though the structural details of such a complex are still not clear. This lecture will review some of our recent experimental results on proton transmission rates through CVD single-layer graphene at variable temperature, with special attention to a kinetics model whereby experimentally-obtained proton-transfer resistances are interpreted as proton-transfer resistances that are linked to heterogeneous proton—transfer rate constants, in a manner that is formally similar to the Butler-Volmer model used to treat electron-transfer rate data in the low overpotential limit. The heterogeneous proton-transfer rate constants are then interpreted using a pre-equilibrium model for protons approaching graphene, coupled to a first-order rate constant for proton transmission through graphene from the pre-equilibrium complex. This first-order proton-transmission rate constant has fundamental significance and may be interpreted in terms of an activation energy and frequency factor for proton transmission. In applying such an analysis to our proton transmission rate data, we obtain a proton-transmission frequency factor that is within a factor of two of the vibrational frequency of the O-H bond in water, suggesting that O-H bond vibration is involved in the rate-determining step of proton transmission.