Entropic barriers in the kinetics of aqueous proton transfer

Aqueous proton transport is uniquely rapid among aqueous processes, mediated by fluctuating hydrogen bond reorganization in liquid water. In a process known as Grotthuss diffusion, the excess charge diffuses primarily by sequential proton transfers between water molecules rather than standard Brownian motion, which explains the anomalously high electrical conductivity of acidic solutions. Employing ultrafast IR spectroscopy, we use the orientational anisotropy decay of the bending vibrations of the hydrated proton complex to study the picosecond aqueous proton transfer kinetics as a function of temperature, concentration, and counterion. We find that the orientational anisotropy decay exhibits Arrhenius behavior, with an apparent activation energy of 2.4 kcal/mol in 1M and 2M HCl. Interestingly, acidic solutions at high concentration with longer proton transfer time scales display corresponding decreases in activation energy. We interpret this counterintuitive trend by considering the entropic and enthalpic contributions to the activation free energy for proton transfer. Halide counteranions at high concentrations impose entropic barriers to proton transfer in the form of constraints on the solution's collective H-bond fluctuations and obstruction of potential proton transfer pathways. The corresponding proton transfer barrier decreases due to weaker water-halide H-bonds in close proximity to the excess proton, but the entropic effects dominate and result in a net reduction in the proton transfer rate. We estimate the activation free energy for proton transfer as ∼1.0 kcal/mol at 280 K.