Kinetics of Radical Dimerization. Simple Evaluation of Rate from Convolution Voltammetry and Faradaic Phase Angle Data.

Electrochemically generated organic radicals often undergo a fast dimerization. This deactivation of radicals was recently considered as a possible mode of storing binary information and is called 'reversible dimer switching'. Joint collaboration with several synthetic groups (F. Teplý and I. Starý from Prague, M.J. Fuchter from London) yielded several examples of redox dimer formation: pyridiniums, dodecylpyridinium, quinolinium, azoniahelicene and benzimidazolinium cations [1-4]. Reversible dimer switching can be monitored by UV-vis spectra or electronic circular dichroism [5]. Figure shows reversible switching of ECD signal of (P)-azoniahelicene at two wavelengths by application of potential pulses of 100 s duration between the full reduction and reoxidation. Estimation of the rate of dimerization is therefore an issue. Data analysis of the second order kinetics is hampered by non-existence of the inverse Laplace transformation of partial differential equations containing a quadratic term. In the past this was circumvented by digital simulations of series of voltammograms at different concentrations and scan rates using the finite difference methods. Alternative evaluation of kinetic parameters from faradaic phase angle ? leads to a problem to include the surface concentration c(0,t) at a given potential. Shapes of theoretical cot? as a function of the square root of frequency for values of dimerization rate constants in the range 104 to 107 M 1os 1 are shown in the middle figure. All previous communications using the phase angle approach suggested the estimation of c(0,t) by the finite difference technique as in the case of voltammetry. This duplicates the evaluation and offers no special advantage. We will demonstrate a substantial simplification by combining the convolution voltammetry and the electrochemical impedance spectroscopy. Our procedure works with convolution of a single cyclic voltammogram, yielding c(0,t), and a single set of impedance spectrum at the same bulk concentration. Typical example of experimental and simulated cot? data with the dimerization rate constant kD = 6.6?107 M-1.s-1 for benzimidazolinium is shown in the bottom figure. From the same set of data the linear high frequency asymptote yields the value of the heterogeneous electron transfer rate constant k0 = 0.63 cmos 1. Programs for simulations were written in software Mathematica.