The Influence of Geometry-Induced Frequency Dispersion on the Impedance Response of Interdigitated Electrodes

Abstract

Interdigitated electrodes consist of interlaced electrode and counterelectrode fingers deposited on a non-conductive substrate. The electrode digits typically have a length on the order of millimeters, a width on the order of micrometers, and a separation distance on the order of micrometers. The diminutive dimensions of the electrochemical cell allow for low-noise impedance measurements and allow for the extraction of the electrical properties of the media in contact with the electrodes. Interdigitated electrodes are commonly utilized in measurements employing electrochemical impedance spectroscopy. Applications for interdigitated electrodes include the detection of contaminants, anti-corrosion coatings, and label-less detection of cells and viruses. Previous modeling of interdigitated electrodes was achieved by conformal mapping and finite-element methods and yielded estimates of the high-frequency ohmic resistance. The objective of our work was to determine the influence of geometry-induced frequency dispersion on the impedance response of interdigitated electrodes. Three aspects of the interdigitated electrode geometry were analyzed using finite-element simulations: the working-electrode width, the counterelectrode proximity to the working electrode, and the working electrode height. The meshing and domain size followed that developed for a disk-electrode geometry, for which ohmic resistances were obtained within 0.0009% of the analytic solution for an isolated disk electrode.1 The observations of the simulated impedance responses provided insight into the interpretation and analysis of data obtained using an interdigitated-electrode geometry. The ohmic response of the electrolyte may best be described as a complex frequency-dependent ohmic impedance with asymptotic real values of ohmic resistance in the high- and low-frequency limits.2 For an isolated flat embedded rectangular electrode, the geometry-induced frequency dispersion yielded a low-frequency ohmic resistance that was 1.29% larger than the high-frequency ohmic resistance. The high-frequency ohmic resistance was equal to that obtained for a primary current distribution. In the presence of a mirror-image counterelectrode, the ohmic resistances at high and low frequency were reduced up to an order of magnitude in comparison to an isolated electrode. The ratio of the low-frequency and high-frequency ohmic resistance ranged from 1.014 to 1.951 and was a function of the distance between the electrodes. Simulations were also performed that accounted for a finite electrode height for equal electrode width and spacing. Two characteristic frequencies were identified in the simulations; one that corresponded to the geometric capacitance of the interdigitated electrochemical cell, and one that corresponded to onset of low-frequency geometry-induced frequency dispersion. References Newman, “Resistance for Flow of Current to a Disk,” Journal of the Electrochemical Society, 113(5) (1966), 501-501.Huang, V. Vivier, M. E. Orazem, N. Pébère, and B. Tribollet, “The Apparent Constant-Phase-Element Behavior of an Ideally Polarized Blocking Electrode: A Global and Local Impedance Analysis,” Journal of The Electrochemical Society, 154 (2007), C81-C88.