Photoelectrochemistry with the optical rotating disc electrode. Part 3. The theoretical analysis for photophysical–chemical–electrochemical (PCE) processes

Abstract

Exact and asymptotic analytical expressions are obtained for the diffusion-controlled light-on transient photocurrents exhibited at an optical disc electrode (ODE) by two types of photoelectrochemical systems: (i) the photophysical-reversible–chemical–electrochemical (PrCE) system wherein the decay of the photogenerated excited species, S*, and the reversible chemical reaction of S* with a solution phase charge scavenger, A, obey pseudo-first-order kinetics with rate parameters k₀, k₁ (forward chemical) and k₂ (reverse chemical) respectively; and (ii) the photophysical-irreversible–chemical–electrochemical (PiCE) system wherein the chemical reaction between S* and A is considered to be irreversible i.e. k₂=0. Exact descriptions of [S*] as a function of distance from the electrode surface at t→∞ are given for both systems for a range of values of k₀, k₁ and, where appropriate, k₂. The photoelectrochemical collection efficiency of the ODE is also presented as a function of t and the rate parameters. Pre-existing approximate expressions for the rotation-speed dependence of the diffusion-controlled steady-state photocurrent recorded at an optical rotating disc electrode (ORDE) are extended and applied to the PiCE process allowing ORDE diffusion layer profiles for [S*] to be calculated for the first time. The asymptotic expressions for the transient and steady-state photocurrent behaviour at stationary and rotating electrodes are combined, producing fourteen composite cases that completely describe the behaviour of PrCE and PiCE systems at ODEs. Each case is discussed and procedures are given for extracting values of k₀, k₁, k₂ and ϕ (the quantum efficiency for the photogeneration of S*) from experimental data. The relationship between the cases is illustrated by a series of case diagrams. A case assignment flow diagram is also presented. For the purposes of illustration, the colloidal CdS/Fe(CN)₆³⁻ system is case-assigned and its associated rate parameter values are calculated.