Application of optically transparent electrodes: Part II. Analytical solution of illumination step chronoamperometry for first-order kinetics with the lambert-beer concentration profile

Abstract

A theoretical study of transient photocurrent-time curves caused by a step functional illumination through an optically transparent electrode, i.e. “illumination step chronoamperometry” is presented for first-order kinetics of the dark back reaction of photochemically generated species with the Lambert-Beer concentration profile. Characteristics of the present method for the study of photo-redox systems consisting of two redox couples A, B and Y, Z which react according to the following scheme: ▪ Electrode B→A±e are discussed in comparison with those of flash electrolysis. The simple cases, whose differential equations can be solved exactly without the aid of digital simulation, are considered and some of the analytical solutions are compared with the previous results by the digital simulation in Part I for the cases of no dark back reaction. Using lower case letters a, b, y, and z for the concentrations of A, B, Y. and Z, the assumptions made can be written as: (1) thermal reaction of A+Z can be ignored and b ∡ a (i.e. a = a 0) in the dark, (2) intensity of illuminated light is not so strong and b ∡ b ∡ a (i.e. a = a 0) even under the illumination, (3) b ∡ y (i.e. y = y 0) for the first order kinetics, (4) to keep the quantum efficiency for the generation of B constant during illumination, b ∡ z (i.e. z = z 0). The effect of double layer charging effect, which cannot be neglected in the photocurrent transient measurements in a short period comparable to the cell time constant, is also discussed, and observable transient photocurrent-time curves taking the effect into account are derived.