Electrochemical Impedance Spectroscopic Analysis of Diffusion-Layer Thickness Distribution Associated with Flagellar Motion of <i>Volvox carteri</i> (Supporting Information)

<p dir="ltr">Although electrochemical methods have been used to relate microbial motility with ionic or redox signals, the evaluation of diffusion-layer variations induced by such motility using electrochemical impedance spectroscopy (EIS) remains limited. Thus, in this study, EIS is used to investigate how the flagellar activity of <i>Volvox carteri</i> modulates the diffusion layer above an electrode. Finite-element simulations and distributed equivalent-circuit modeling are performed for both uniform and non-uniform diffusion-layer thicknesses. Simulations predict that phototactic flagellar convection results in impedance spectra with a slope lower than 45° in the mid-frequency region and a pronounced finite-diffusion bend at low frequencies. These features are validated through experiments involving <i>Volvox</i>-immobilized electrodes under dark and illuminated conditions. Light irradiation reduces the effective diffusion-layer thickness from 2.4 × 10⁻² cm to 6.6 × 10⁻³ cm and introduces a distributed thickness ranging from 4.5 × 10⁻⁴ to 9.0 × 10⁻³ cm, as extracted by transmission-line fitting. These results provide quantitative insights into bio-induced mass-transport modulation and demonstrate the applicability of distributed diffusion models in bioelectrochemical systems.</p>