The micro-optical ring electrode Part 2: Theory for the transport limited, steady-state photocurrent

The micro-optical ring electrode (MORE) is a photoelectrochemical device based on a ring microelectrode that uses the insulating material interior to the ring electrode as a light guide. In this paper, we derive asymptotic analytical expressions for the steady-state, transport limited photocurrent generated at MOREs with thin microrings ((ring inner radius)/(ring outer radius) values > 0.99) for two general types of photoelectrochemical system (a) the PE (photophysical–electrochemical) system, wherein the photoexcited species itself is directly detected on the ring; and (b) the PCE (photophysical–chemical–electrochemical) system, wherein the photoexcited species undergoes a homogeneous electron transfer reaction prior to electrochemical detection. The expressions are generated by exploiting the properties of discontinuous integrals of Bessel functions to solve the diffusion equation for the photogenerated electroactive species both inside and outside the beam. The resultant solutions are then matched at the beam surface. The expressions themselves are used to design experimental protocols that allow for the complete characterization of the photoelectrochemical kinetics of a system and are tested by using them to interpret the results of a MORE study of the photoelectrochemical behaviour of the Ru ( bipy ) 3 2 + / Fe 3 + photosensitiser/quenching agent system. The value of the Stern–Volmer constant for the quenching of photoexcited Ru ( bipy ) 3 2 + by Fe3+ so obtained (0.36 m3 mol−1) compares favourably with the value obtained from fluorescence measurements (0.9 m3 mol−1).