EIS Nyquist Plot Simulator: Impedance Spectroscopy Explained

simulator advanced ~12 min
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τ = 4.0 ms — Rct = 200 Ω, Cdl = 20 µF

The Randles circuit with Rs = 10 Ω and Rct = 200 Ω produces a semicircle from 10 to 210 Ω on the real axis. The Warburg tail extends at 45° at low frequencies, indicating mixed kinetic-diffusion control.

Formula

Z(ω) = Rs + Rct / (1 + jω·Rct·Cdl) + σω^(−1/2)(1 − j)
τ = Rct × Cdl (characteristic time constant)
ω_peak = 1 / (Rct × Cdl) (frequency at semicircle apex)

Listening to Electrodes at Every Frequency

Electrochemical impedance spectroscopy works like an MRI for electrode processes. By probing the system with tiny AC signals across a spectrum of frequencies — from megahertz to millihertz — it separates fast processes (electron transfer, ionic conduction) from slow ones (diffusion, adsorption). Each process shows up as a distinct feature in the impedance spectrum.

The Nyquist Diagram

The Nyquist plot is the standard visualization. A perfect semicircle in the high-to-mid frequency range indicates a single charge-transfer process characterized by Rct and Cdl. The leftmost intercept gives the solution resistance Rs, and the rightmost intercept gives Rs + Rct. A 45° linear tail at low frequencies signals Warburg diffusion in the bulk electrolyte.

Equivalent Circuit Modeling

Electrochemists fit impedance data to equivalent circuits made of resistors, capacitors, and specialized elements (Warburg, constant phase elements). The Randles circuit is the simplest physically meaningful model, capturing ohmic drop, charge transfer kinetics, double-layer charging, and semi-infinite diffusion. More complex models add additional RC loops for multi-step reactions or porous electrodes.

From Corrosion to Fuel Cells

EIS is indispensable across electrochemistry. Corrosion engineers measure polarization resistance to estimate metal dissolution rates. Fuel cell researchers separate membrane resistance from catalyst layer losses. Battery manufacturers use EIS for non-destructive quality control, identifying cells with high internal resistance before they enter service.

FAQ

What is electrochemical impedance spectroscopy (EIS)?

EIS is a technique that applies a small AC voltage perturbation across a range of frequencies and measures the resulting current response. The ratio gives complex impedance Z(ω) = Z' + jZ'', plotted as a Nyquist diagram (-Z'' vs Z'). Different features — semicircles, lines, arcs — correspond to different physical processes.

What is a Nyquist plot?

A Nyquist plot displays the imaginary part of impedance (-Z'') versus the real part (Z') at each frequency. A simple Randles cell produces a semicircle (charge transfer) followed by a 45° line (Warburg diffusion). The semicircle diameter equals Rct, and the high-frequency intercept equals Rs.

What is the Randles equivalent circuit?

The Randles circuit models a simple electrochemical cell as a solution resistance Rs in series with a parallel combination of double-layer capacitance Cdl and charge transfer resistance Rct, followed by a Warburg element for diffusion. It captures the essential physics of most electrode processes.

How is EIS used in battery research?

EIS diagnoses battery health by separating ohmic resistance (Rs), charge transfer kinetics (Rct), and diffusion limitations (Warburg). Aging cells show increasing Rs and Rct. Non-destructive EIS testing is standard in battery manufacturing quality control.

Sources

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