Interpreting Electrochemical Impedance Spectroscopy Measurements

Key Takeaways

• Electrochemical cells are normally discussed as DC elements, but they can be driven with an AC source.

• When driven in AC, an electrochemical cell has some impedance that is measured using electrochemical impedance spectroscopy.

• By looking at an electrochemical impedance spectrum, different chemical processes that govern electrochemical reactions can be determined.

Smartphone batteries can be attributed to electrochemical impedance spectroscopy measurements, which are used in a battery’s design.

If you’re reading this article on a smartphone, then you can thank electrochemical impedance spectroscopy measurements for help with designing the battery. As part of battery design and testing, these measurements are used to monitor reaction kinetics, state of Charge (SoC), lifetime, temperature, and faults within cell packs. 

This frequency-sweeping technique is simple to perform. It also provides a single measurement of multiple physical processes, giving systems designers a simple way to greatly understand the kinetics of their electrochemical cells.

What Is Electrochemical Impedance Spectroscopy?

Electrochemical cells are complex electrical systems, and they have different factors that contribute to overall impedance. Electrochemical impedance spectroscopy is a frequency sweep technique used to measure the impedance of an electrochemical cell over a broad frequency range. In terms of circuit models to describe an electrochemical system, electrochemical impedance spectroscopy is used to measure resistance, capacitance, and inductance by monitoring the current response while the frequency of an AC source is swept.

Electrochemical systems involve multiple chemical processes, where different processes have different characteristic time constants governing their transient behavior. The objective of electrochemical spectroscopy is to determine the kinetic parameters that govern these various processes in an electrochemical system. By sweeping over a range of frequencies, different factors contributing to impedance can be identified in different frequency ranges. 

Electrochemical impedance spectroscopy measurements can be gathered by applying an AC source to the cathode and anode of an electrochemical cell. Once the data is gathered, it can be used to extract circuit parameters in the Randles cell, which is a standard circuit model for describing the electrical behavior of an electrochemical cell.

The Randles cell model can be used to describe electrochemical cell impedance in terms of circuit models.

The above model describing electrochemical impedance is purely linear, which matches the real behavior of electrochemical cells at a low input signal level. At a high input level, many electrochemical cells will exhibit a nonlinear response. 

Analyzing nonlinear electrochemical impedance spectroscopy measurements is its own field of electrochemistry; take a look at this review article for more information on the subject. Let’s look in more depth at linear electrochemical impedance spectroscopy analysis, which governs the majority of situations encountered in practice.

Visualizing Electrochemical Impedance Spectroscopy Data

There are two ways to visualize electrochemical impedance spectroscopy measurements. One is a classic log-log plot, which will show the impedance at different frequencies. The other is a Nyquist plot, which compares the real and imaginary parts of electrochemical impedance.

Log-log Impedance Spectrum

A log-log plot of the impedance spectrum for an electrochemical cell is one way to visualize the transition between different dominant physical processes in an electrochemical cell. This is among the simplest plots to construct using electrochemical impedance spectroscopy data. Both frequency and impedance (magnitude) are plotted on logarithmic scales; plateaus in the plot show when different physical processes dominate in determining the electrochemical impedance. The slope in each region of the plot is also shown.

Nyquist plot and corresponding Bode plot examples for electrochemical impedance spectroscopy measurements.

Nyquist Plot

A Nyquist plot is constructed by plotting the negative imaginary impedance versus the real part of the impedance for individual electrodes or the electrochemical cell itself. An example is shown below alongside the corresponding Bode plot, which shows impedance magnitude and phase. At the peak in the Nyquist plot, we have a corresponding dip in the phase of the Bode plot. These points are shown in the example graphs below.

Nyquist plot and corresponding Bode plot examples for electrochemical impedance spectroscopy measurements.

A typical Nyquist plot for an electrochemical impedance spectroscopy plot may not look anything like the above example, depending on the physical processes that dominate the cell’s electrochemical behavior. Once the Warburg impedance of the cell takes over, the impedance curve will diverge from the typical semicircular shape in the Nyquist plot and will become linear. This tends to occur near the peak in the Nyquist plot as frequency is swept. The corresponding peaks in the Nyquist plot denote a transition between different dominant physical processes governing the electrochemical reaction in the cell.

The image below shows how different portions of a circuit model for an electrochemical cell produce curve sections in a Nyquist plot. These different curve sections can be superimposed on each other to produce a very complex looking Nyquist plot. This allows the different portions in a circuit model for an electrochemical cell to be determined simply by looking at different sections in the Nyquist plot. In these plots, W is the Warburg impedance.

Nyquist plots for circuit blocks in the Randles cell model.

Simulations of Electrochemical Systems

Once the various Randles cell circuit blocks are extracted from measurements, a systems designer can integrate a circuit model with the larger system and run simulations for an entire circuit. If the designer has a circuit model for the cell, they can run SPICE simulations for a cell and any external circuitry, just as they would do with any other circuit diagram. As we’re generally working with linear systems in electrochemical impedance spectroscopy, any of the standard simulations can be run without further approximations in the system.

The front-end design features from Cadence can be used to build circuit models for a range of systems based on electrochemical impedance spectroscopy measurements. You can use the modeling and simulation applications in PSpice Simulator to simulate electrochemical system behavior and design supporting circuitry. The set of analysis tools in PSpice can also help you optimize your design’s interactions with an electrochemical system.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.