Phenomenological Interpretation of the Electrochromic Kinetics for Rutile TiO₂

Modeling the electrochromic (EC) kinetics explicitly for transition metal oxides is a tough, long-standing task since the analytical solution for Fick's law of diffusion is hardly unified considering the chemical diffusion coefficient is actually a variable during ion intercalation, as verified both theoretically and experimentally. Here, by defining the ratio of the first derivative of transmittance to the transmittance itself, i.e., $\frac{1}{T}·\frac{dT}{dt}$, an alternative phenomenological interpretation of the EC kinetics is proposed by formulating the linear correlation between the Ratio and the current. The linear relationship was successfully validated for a rutile TiO₂ nanowire electrode. The correlation not only probes fruitful information like color delay and structure evolution, but also unveils the physical significance of the molar extinction coefficient, an intrinsic parameter with the order of 10⁶ cm² mol^-1. These findings provide a fresh paradigm to understand the EC kinetics from the point of view of phenomenology.