Diffusion impedance modeling for interdigitated array electrodes by conformal mapping and cylindrical finite length approximation

Impedimetric sensing using interdigitated array (IDA) electrodes usually encounters an analytical problem. Finite diffusion of redox species dominates at low frequencies and confuses researchers, making incorrect understanding of underlying phenomena possible. In this work, an integral equation for calculating the diffusion impedance of IDA electrodes is derived using conformal mapping and cylindrical finite length approximation. Electrodes of different bandwidths and gap widths are fabricated, and their heights and symmetric electrochemical characteristics are verified. Simulations are performed to verify the predicted constant concentration contours. The calculated zero-frequency impedance showed high correlation with the reciprocal of limiting current calculated from literature study (R2 = 0.992) and from chronoamperometry experiments (R2 = 0.970). Further evidence for the correctness of theory is established due to the fact that experimental EIS data and calculated impedances are highly consistent (R2 ≥ 0.948 for real and imaginary part). This sheds some light on explaining the diffusion phenomenon of impedance using IDA electrodes in the low frequency spectrum. An equivalent circuit fitting program is further designed for fitting several elements including the IDA electrode diffusion impedance derived in the theory. The program succeeded to accurately fit the EIS data (average MSE = 0.611), which using the Warburg element failed (average MSE = 54.86). Parameters such as the ratio of electrode bandwidth to gap width and diffusion coefficient can also be determined by fitting the data from a single EIS experiment. Another impedance calculation program is also given, which can aid researchers in relevant fields to model their systems more accurately.