Transmission Line Model to Study the Redox Adsorption-Dependent Impedance of Porous Electrode
Abstract
Abstract The present study theoretically investigates the impedance of an electrochemical system with strong redox adsorption kinetics, paired with a porous electrode surface. In contrast to a diffusion-controlled redox system with the classical two-channel transmission line circuit representation, the pore impedance of a redox adsorption system is expected to rely on a third conduction channel: the adsorbate film, in addition to the solution and electrode channels. With this motivation, a three-channel transmission line model is proposed, with solution-, adsorbate film-, and electrode- channels connected crosswise with charged double layer and adsorption-associated faradaic circuit components. Furthermore, based on the interaction of the solution and film channels, two distinct circuits are designed, pertaining to decoupled vs coupled charge transfer. General expressions are obtained for small signal ac potential and current profiles. The ac impedance is derived for general and limiting conditions, and the distribution of relaxation time is analysed. Predictive trends in impedance response with variation of channel resistances is discussed. Impedance characteristics is theoretically evaluated and graphically represented with Nyquist, Cole-Cole and DRT plots. This study aims to develop a comprehensive theoretical understanding of adsorption electrokinetics in porous electrodes, which can ultimately aid analysis, and render tunability to relevant electrochemical systems.