Theory of cyclic voltammetry in random arrays of cylindrical microelectrodes applied to carbon felt electrodes for vanadium redox flow batteries

In order to quantitatively investigate the kinetic performance and the pore size distribution of carbon felt electrodes for the application in vanadium redox flow batteries, the theory of cyclic voltammetry (CV) is derived for a random network of cylindrical microelectrodes on the base of convolutive modeling. In this context we present an algorithm based on the use of a modified Talbot contour for inverse Laplace transformation, providing the mass transfer functions required for the calculation of the CV responses in external cylindrical finite diffusion space. First-order homogenous chemical kinetics preceding and/or following the electrochemical reactions are implemented in this algorithm as well. The VO2+ oxidation is investigated as model reaction at pristine and electrochemically aged commercial carbon felt electrodes. A fit of simulated data to experimental data clearly shows that an electrochemical aging predominantly affects the kinetics of the electron transfer reaction and that internal electrode surfaces and pore size distributions remain constant. The estimated pore size distributions are in excellent agreement with porosimetry measurements, validating our theory and providing a new strategy to determine electrode porosities and electrode kinetics simultaneously via CV.