Title: Electrode Reactions in Slowly Relaxing Media,
Abstract: Standard models of reaction kinetics in condensed materials rely on the
Boltzmann-Gibbs distribution for the population of reactants at the top of the
free energy barrier separating them from the products. While energy dissipation
and quantum effects at the barrier top can potentially affect the transmission
coefficient entering the rate preexponential factor, much stronger dynamical
effects on the reaction barrier are caused by the breakdown of ergodicity for
populating the reaction barrier (violation of the Boltzmann-Gibbs statistics).
When the spectrum of medium modes coupled to the reaction coordinate includes
fluctuations slower than the reaction rate, such nuclear motions dynamically
freeze on the reaction time-scale and do not contribute to the activation
barrier. Here we consider the consequences of this scenario for electrode
reactions in slowly relaxing media. Changing electrode overpotential speeds
electrode electron transfer up, potentially cutting through the spectrum of
nuclear modes coupled to the reaction coordinate. The reorganization energy of
electrochemical electron transfer becomes a function of the electrode
overpotential, switching between the thermodynamic value at low rates to the
nonergodic limit at higher rates. The sharpness of this transition depends of
the relaxation spectrum of the medium. The reorganization energy experiences a
sudden drop with increasing overpotential for a medium with a Debye relaxation,
but becomes a much shallower function of the overpotential for media with
stretched exponential dynamics. The latter scenario characterizes electron
transfer in ionic liquids. The analysis of electrode reactions in
room-temperature ionic liquids shows that the magnitude of the free energy of
nuclear solvation is significantly below its thermodynamic limit.