Determination of Charge Transfer Resistance from Randles Circuit Spectra Using Elliptical Fitting

Abstract

Physical and chemical phenomena of an electrochemical system can be described by electrochemical impedance spectroscopy (EIS). The spectral response of impedimetric biosensors is often modeled by the Randles circuit, whose parameters can be determined by regression techniques. As one of these parameters, the charge transfer resistance $\mathrm {R_{ct}}$ is often used as the sensor response. Regression in the laboratory environment is usually performed using commercial software, which is typically computationally intensive. Therefore, applications of biosensors outside the laboratory require more efficient concepts, especially when miniaturized or portable instrumentations are used. In this work, an approach for geometric elliptical fitting of the graph in the Nyquist diagram is presented and compared with the complex nonlinear least squares (CNLS) regression. The evaluation is based, on the one hand, on artificial spectra and, on the other hand, on real data from a immunologically sensitive field-effect transistor (IMFET) for cortisol measurement in saliva. For simulated noisy data, the average error in computing $\mathrm {R_{ct}}$ using the elliptical fit with $\mathrm {-2.7\% }$ is worse than using the CNLS with $0.024 \%$, but the former required only about of computation time compared to the latter. Applying the elliptic fitting to real data from an IMFET, the determination of $R_{ct}$ showed deviations of only $\mathrm 0.7\pm 2.7\%$ compared to CNLS. The impact of these variations on a standard addition method (SAM) was demonstrated for quantitative analysis of cortisol concentration. After application-oriented evaluations considering the possible accuracies, the elliptical fitting could prove to be a resource-saving option for the analysis of impedance spectra in mobile applications.