EIS (Impedance) Guide

Electrochemistry/EIS (Impedance) GuideMethod guide

Electrochemical Impedance Spectroscopy (EIS): Nyquist Plots, Equivalent Circuits and Measurement Tips

Electrochemical impedance spectroscopy (EIS) separates the processes in an electrochemical cell by how fast they are. This guide explains how to read Nyquist and Bode plots, choose an equivalent circuit and make sure the data are valid.

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What is EIS?

In EIS the potentiostat applies a small AC signal (typically 5–10 mV) on top of a DC potential and measures the current response over a wide frequency range, for example from 100 kHz to 10 mHz. The ratio of voltage to current is the impedance Z, with a real part (Z′) and an imaginary part (Z″).

Fast processes such as solution resistance appear at high frequency, charge transfer at intermediate frequency and diffusion at low frequency. That is why EIS is used almost everywhere: coating degradation, battery SEI, catalyst kinetics and label-free sensors.

Reading a Nyquist plot

Feature Element Physical meaning
High-frequency real-axis intercept Rs Solution and contact resistance
Semicircle diameter Rct Charge-transfer resistance; smaller means faster kinetics
Depressed semicircle CPE Non-ideal capacitance from rough or heterogeneous surfaces
45° line at low frequency Warburg (W) Semi-infinite diffusion
Near-vertical line Capacitor Ideal capacitive behaviour (supercapacitors, blocking electrodes)
Two semicircles Two R‖CPE Two processes, e.g. SEI and charge transfer, or coating and metal

Basic circuits and formulas

Randles circuitRs + [CPE ‖ (Rct + W)]The most common model for an electrode with charge transfer and diffusion.
CPE impedanceZ_CPE = 1 / [Q · (jω)^n]n = 1 is an ideal capacitor; n = 0.5 resembles Warburg. Effective capacitance can be derived from Q, n and R.
Semicircle apex frequencyω_maks = 1 / (R · C)Helps estimate capacitance from the frequency at the semicircle apex.

Steps for a good EIS measurement

  1. Make sure the system is stableEIS assumes the system does not change during the measurement. Wait for a stable OCP or current.
  2. Choose a small amplitudeUsually 5–10 mV rms to keep the response linear; noisy systems may use slightly more.
  3. Set the frequency rangeFor example 100 kHz–10 mHz; lower frequencies add measurement time dramatically.
  4. Reduce noiseUse a Faraday cage for high impedances and keep cables as short as possible.
  5. Validate the dataRun a Kramers-Kronig test before fitting; discard inconsistent points.
  6. Fit with a physically meaningful modelChoose the simplest circuit with physical meaning; DRT analysis helps determine how many processes there are.

EIS with Corrtest potentiostats

Corrtest EIS models (CS310M, CS350M, CS350Pro, CS1350Pro, CS2350M, CS310X) have a digital FRA up to 1 MHz (CS350Pro up to 5 MHz), with EIS-OCP, potentiostatic and galvanostatic EIS. CS Analysis software provides equivalent-circuit fitting, Kramers-Kronig validation and DRT. 10¹³ Ω input impedance suits high-resistance systems such as coatings and concrete.

Frequently asked questions

What is the difference between Nyquist and Bode plots?

Nyquist plots −Z″ against Z′ and makes processes easy to recognise; Bode plots |Z| and phase angle against frequency so frequency information is explicit.

Why is my low-frequency data scattered?

Usually the system changes during the measurement (non-stationary) or there is electrical noise. Stabilise longer, use a Faraday cage and check with a Kramers-Kronig test.

How long does one EIS measurement take?

From a few minutes to over an hour, depending on the lowest frequency and points per decade.

What is DRT?

Distribution of relaxation times converts impedance data into a distribution of time constants, so the number of processes can be identified without guessing a circuit first.

Need EIS measurements?

Use our electrochemical analysis service, or ask us which EIS potentiostat suits your system.

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