Modelling mobile species population changes in electroactive films under thermodynamically and kinetically controlled conditions

Modelling Mobile Species Dynamics within Electroactive Films under Mixed Thermodynamic and Kinetic Control

“…In our previous works, we explored individually the cases of ideal thermodynamic behavior [21] and of non-ideal thermodynamic behavior (non-linear film solvation with charge state) [21] from a theoretical perspective and identified experimentally the departure from thermodynamic control due to kinetic control by either coupled electron/ion or solvent transfers [22,23]. Under ideal thermodynamic control conditions, the film composition system obeys the Nernst equation, and the film solvent content is linearly related to its charge.…”

“…We consider this redox transformation in response to the most commonly employed electrochemical control function, a cyclic voltammetric sweep (scan rate v (V s À1 )). Figure 1 illustrates the concept [21] of the visual model. The instantaneous film composition is represented by the vector W(t), where:…”

“…The forward and reverse rate constants for Reaction 4 are denoted k f and k b , respectively, and their ratio is the solvation equilibrium constant K S . We have previously shown [21] that, under thermodynamically ideal conditions, the redox induced population change within the film of solvent, G s , can be expressed via:…”

“…Values of applied potential are referred to the standard electrode potential, E8/V. The effect of the solvation equilibrium constant, K S , is simply to scale the response on the G S axis [21]. Since this is essentially a thermodynamic effect we have described previously [21], we remove this straightforward effect by assigning an arbitrarily large value of 1000 to K S ; this corresponds to O and R states of very different solvation characteristics.…”

“…The effect of the solvation equilibrium constant, K S , is simply to scale the response on the G S axis [21]. Since this is essentially a thermodynamic effect we have described previously [21], we remove this straightforward effect by assigning an arbitrarily large value of 1000 to K S ; this corresponds to O and R states of very different solvation characteristics. In any given calculation (see below), we fixed the values of the normalized rate constants (k e and k s ) and of m, then calculated the response as the applied potential, E (V), was varied through a complete redox cycle, starting from an equilibrated fully reduced film.…”