Finite element modelling of surface-bound quinone proton coupled electron transfer voltammetry

A numerical (finite element) model has been developed to simulate the proton coupled electron transfer (PCET) reaction for surface bound quinone species. It is easily adaptable to a wide range of PCET systems. Employing a user-friendly interface we show how factors such as scan rate, pH, buffer capacity, quinone pK_a and surface coverage, along with protonation and electron transfer rate constant(s) can impact simulated voltammograms. It is further demonstrated how the model can be used to assess the validity of Laviron plots when applied to PCET reactions for the determination of apparent electron transfer (ET) rate constants. The extracted ET rate constants from simulated voltammograms of peak potential versus log scan rate are compared against those obtained from analytical expressions derived for use with PCET reactions. For the (1-electron, 1-proton) 1e^-1H⁺ system, when a fast rate of proton transfer is employed, typical of aqueous systems, there is very good agreement between the ET rate constants extracted using the two methods. In contrast, for the case of 2e^-2H⁺ PCET, good agreement is not seen and highlights for the more complex system that even when the rate of protonation is high, slower rates of deprotonation can result (and vice versa), moving the system away from being ET rate-limited. Hence Laviron analysis should not be applied quantitatively to 2e^-2H⁺ PCET systems. The simulation model is also employed to offer practical solutions for use of quinone functionalised electrodes in the voltammetric sensing of solution pH. Experimentally, deviations from 2e^-2H⁺ PCET Nernstian behaviour are typically seen in unbuffered solutions with monolayer coverage electrodes due to local depletion (or accumulation) of protons during voltammetry. By simulating the interfacial proton concentrations at the electrode surface as a function of quinone surface coverage, it is possible to determine the required reduction in surface coverage (ca. two orders of magnitude) to negate such effects.