Mapping the dynamics of reversible and irreversible heterogeneous electron transfers under steady-state conditions by the phase-space method

We describe in this work how the phase-space approach provides information about the dynamics of an electrochemical reaction occurring under steady-state conditions. Mapping the trajectories in the phase-space is proposed as a new tool for following the progress of a heterogeneous electron transfer. For a simple electron transfer reaction, the analytical expressions of the features of phase-space are given. Moreover, the progress of the reaction can be expressed in terms of a probability distribution function of the charge transmission. The probabilistic approach allows us to characterise the non-equilibrium thermodynamic properties of the heterogeneous electron transfer. New methods for the determination of the degree of the reversibility, the transfer coefficient, and the formal potential are given. The notions of chemical distance and chemical velocity are introduced to characterise the system dynamics. Thus, the electrochemical conductance of the system can be determined. Experimental data on ferrocene and ferric ions obtained in rotating disc electrode experiments are given to illustrate the proposed methodology.