Modeling Electrochemical Impedance Spectroscopy Using Time-Dependent Finite Element Method

Abstract

A time-dependent electrochemical impedance spectroscopy (EIS) model is presented using the finite element method (FEM) to simulate a 2D interdigitated electrode in an aqueous NaCl electrolyte. Developed in COMSOL Multiphysics, the model incorporates ion transport, electric field distribution, Stern layer effects, and electrode sheet resistance, governed by the Poisson and Nernst-Planck equations. This model can predict the transient current response to an applied excitation voltage, which gives information about the dynamics of the electrochemical system. The simulation results are compared with the experimental data, reproducing key features of the measurements. The transient current response indicates the need for multiple excitation cycles to stabilize the impedance measurement. At low frequencies (<1 kHz), the voltage drop at the Stern layer is significant, while at higher frequencies (>100 kHz), the voltage drop due to sheet resistance dominates. Moreover, the amplitude of the excitation voltage influences the EIS measurement, higher amplitudes (above 0.1 V) lead to non-linear impedance behavior, particularly at low ion concentrations. Discrepancies at low frequencies suggest that Faradaic processes may need to be incorporated for improved accuracy. Overall, this model provides quantitative insights for optimizing EIS sensor design and highlights critical factors for high-frequency and low-concentration conditions, laying the foundation for future biosensing applications with functionalized electrodes.

Keywords: COMSOL model; electrochemical impedance spectroscopy; finite element method; simulations; time-dependent analysis.

Figure A1

EIS plot for comparison between the experimental data and the simulation results with various k_el and k_s parameter combinations for a 100 mM ion concentration. (a) |Z| plot and (b) phase shift plot.

Figure A2

EIS plot for comparison between the experimental data and the simulation results with various k_el and k_s parameter combinations for a 100 mM ion concentration. (a) |Z| plot and (b) phase shift plot.

Figure 1

(a) The voltage excitation signal and current response to evaluate the impedance at a particular frequency. (b) Schematic of the equivalent electrical components and elements for the impedance electrode in an electrolyte for a planar two-electrode system.

Figure 2

(a) Schematic representation of the IDE design for sensor validation in the laboratory. (b) Approximation of the IDE configuration adapted for a 2D geometry in COMSOL simulations.

Figure 3

(a) IDE sensor fabricated on a silicon substrate utilized for laboratory validation. (b) IDE sensor immersed in an aqueous electrolyte during laboratory measurements.

Figure 4

(a) Plots showing the applied voltage and the current response of (a) 1 mM NaCl electrolyte at 100 Hz and (b) 1 mM NaCl electrolyte at 464 Hz.

Figure 5

(a) Spatial profile of the voltage near the working electrode at various excitation frequencies (a) for 1 mM salt concentration and (b) for 100 mM salt concentration.

Figure 6

Bode plot of impedance as a function of excitation frequency for 1, 10, and 100 mM NaCl solutions obtained from laboratory experiments and simulations. (a) Impedance magnitude (|Z|) as a function of excitation frequency. (b) Phase angle as a function of excitation frequency.

Figure 7

Applied voltage and current response for 1 mM concentration and 0.1 Hz at (a) 70 mV and (b) 0.5 V excitation voltage amplitude.

Figure 8

(a) Values of |Z| for 1 and 100 mM salt concentrations at various amplitudes of excitation voltage. (b) Relative deviation of the |Z| values for various amplitudes of excitation voltage as compared to |Z_10mV| at 10 mV amplitudes of excitation voltage.

Figure 9

Voltage drop at the electrode surface due to the Stern layer and the sheet resistance for various excitation frequencies and ion concentrations.