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 pre-exponential 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 the electrode overpotential speeds the 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 on 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 the 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. This result applies to reaction times faster than microseconds and is currently limited by the available dielectric relaxation data.

Electron Transfer Kinetics in a Deep Eutectic Solvent

“…the analysis, it is useful to use the Marcus formalism as done in several studies related to electron transfers in molecular solvents but also in ionic liquids. (See for example 7,8,31,32 ) Table 1. Calculated parameters and comparison of k s measured in different media.…”

Equilibrium Solvation, Electron-Transfer Reactions, and Stokes-Shift Dynamics in Ionic Liquids

“…This is the only parameter accessible to measurements; calculations of ϵ L (k) require numerical simulations or liquid-state theories. 3,20 The longitudinal susceptibility χ L (k) and the charge−charge structure factor S Z (k) are related by the following equation 3,21…”

“…In turn, the memory function is related to the longitudinal conductivity σ L (k, ω) of the ionic liquid 3,21 M k k ( , ) 4 ( , )…”

“…The longitudinal susceptibility χ L ( k ) and the charge–charge structure factor S Z ( k ) are related by the following equation , …”

“…The correlation function Φ̃( k ,ω) can be alternatively written in terms of the memory function , In turn, the memory function is related to the longitudinal conductivity σ L ( k , ω) of the ionic liquid , One, therefore, can rewrite eq as …”