# Testing Lithium Ion Batteries

### Purpose of This Note:

This application note discusses electrochemical measurements on lithium ion batteries. Theory and general setup of lithium ion batteries are explained. Important parameters for characterizing batteries are described.

In addition, various experiments on coin cells are performed. They show how to gain information about a battery’s performance, e.g. capacity and voltage limits as well as long time behavior.

# The Constant Phase Element (CPE)

### What is a Constant Phase Element?

The Constant Phase Element (CPE) is a non-intuitive circuit element that was discovered (or invented) while looking at the response of real-world systems. In some systems the Nyquist plot (also called the Cole-Cole plot or Complex Impedance Plane plot) was expected to be a semicircle with the center on the x-axis. However, the observed plot was indeed the arc of a circle, but with the center some distance below the x-axis.
These depressed semicircles have been explained by a number of phenomena, depending on the nature of the system being investigated. However, the common thread among these explanations is that some property of the system is not homogeneous or that there is some distribution (dispersion) of the value of some physical property of the system.

#### CPE equations

Mathematically, a CPE’s impedance is given by

1 / Z = Y = Q° ( j omega )n

where Q° has the numerical value of the admittance (1/ |Z|) at omega =1 rad/s. The units of Q° are S•sn (ref 1).
A consequence of this simple equation is that the phase angle of the CPE impedance is independent of the frequency and has a value of -(90*n) degrees. This gives the CPE its name.

When n=1, this is the same equation as that for the impedance of a capacitor, where Q° =C.

1 / Z = Y = j omega Q° = j omega C

When n is close to 1.0, the CPE resembles a capacitor, but the phase angle is not 90°. It is constant and somewhat less than 90° at all frequencies. In some cases, the ‘true’ capacitance can be calculated from Q° and n
The Nyquist (Complex Impedance Plane) Plot of a CPE is a simple one. For a solitary CPE (symbolized here by Q), it is just a straight line which makes an angle of (n*90°) with the x-axis as shown in pink in the Figure. The plot for a resistor (symbolized by R) in parallel with a CPE is shown in green. In this case the center of the semicircle is depressed by an angle of (1-n)*90°

# Potentiostat Architectures – Passive I/E Converters

### A Common Potentiostat Design

This style of I/E Converter is well suited to potentiostats with output currents of a few tenths of an ampere up to several amperes. This scheme has been used by Gamry, PAR, Solartron, and perhaps others.

#### The I/E Converter is a “passive” design

The current path through the I/E converter only traverses passive components such as wires and resistors. No active components (such as op amps or transistors) are in the current path. The current measurement resistor is connected between the Working electrode and the potentiostat’s power supply ground (or “current return”).

#### The Working electrode is not at Virtual Ground

This is a consequence of the passive design. The working electrode voltage (vs the potentiostat’s internal ground) depends on the current flowing. In the sketch shown to the right, the working electrode will be at (i*Rm) volts. The actual voltage may be higher due to the resistance of the cell cable connecting the potentiostat to the working electrode!

# Potentiostat Architectures – Active I/E Converters

The Classical Potentiostat The schematic at the right is the classical potentiostat design shown in nearly every modern electrochemistry textbook. It has three basic features. The Working electrode is at Virtual Ground. The working electrode is at the same potential as the potentiostat’s electronic ground. This ground is often connected to Earth Ground. The electrometer Read more about Potentiostat Architectures – Active I/E Converters[…]

# References on Corrosion Theory and Electrochemical Corrosion Tests

Many of the following ‘references’ are available at Amazon.com and can be viewed at our Bookstore. DC Electrochemical Test Methods, N.G. Thompson and J.H. Payer, National Association of Corrosion Engineers, 1440 South Creek Drive, Houston, TX 77084-4906. Phone: 281-228-6200. Fax: 281-228-6300. ISBN: 1-877914-63-0. Recommended! Principles and Prevention of Corrosion, Denny A. Jones, Prentice-Hall, Upper Saddle Read more about References on Corrosion Theory and Electrochemical Corrosion Tests[…]

# Quantitative Corrosion Theory

In the previous post (Electrochemical Corrosion Measurements Primer) we pointed out that Icorr cannot be measured directly. In many cases, you can estimate it from current versus voltage data. You can measure a log current versus potential curve over a range of about one half volt. The voltage scan is centered on Eoc. You then fit the measured data to a theoretical model of the corrosion process.

The model we will use for the corrosion process assumes that the rates of both the anodic and cathodic processes are controlled by the kinetics of the electron transfer reaction at the metal surface. This is generally the case for corrosion reactions. An electrochemical reaction under kinetic control obeys Equation 1-1, the Tafel Equation.

Equation 1-1

# Electrochemical Corrosion Measurements Primer

Most metal corrosion occurs via electrochemical reactions at the interface between the metal and an electrolyte solution. A thin film of moisture on a metal surface forms the electrolyte for atmospheric corrosion. Wet concrete is the electrolyte for reinforcing rod corrosion in bridges. Although most corrosion takes place in water, corrosion in non-aqueous systems is not unknown.

Corrosion normally occurs at a rate determined by an equilibrium between opposing electrochemical reactions. The first is the anodic reaction, in which a metal is oxidized, releasing electrons into the metal. The other is the cathodic reaction, in which a solution species (often O2 or H+) is reduced, removing electrons from the metal. When these two reactions are in equilibrium, the flow of electrons from each reaction is balanced, and no net electron flow (electrical current) occurs. The two reactions can take place on one metal or on two dissimilar metals (or metal sites) that are electrically connected.

Figure 1-1. Corrosion Process Showing Anodic and Cathodic Current Components.

Figure 1-1 diagrams this process. The vertical axis is potential and the horizontal axis is the logarithm of absolute current. The theoretical current for the anodic and cathodic reactions are shown as straight lines. The curved line is the total current — the sum of the anodic and cathodic currents. This is the current that you measure when you sweep the potential of the metal with your potentiostat. The sharp point in the curve is actually the point where the current changes signs as the reaction changes from anodic to cathodic, or vice versa. The sharp point is due to the use of a logarithmic axis. The use of a log axis is necessary because of the wide range of current values that must be displayed during a corrosion experiment. Because of the phenomenon of passivity, it is not uncommon for the current to change by six orders of magnitude during a corrosion experiment.

# Quartz Crystal Microbalance

The Quartz Crystal Microbalance (QCM) is an exciting tool for the electrochemist. With it, the researcher can now follow not only the current that flows, but the weight changes of the electrode, too! This is a valuable tool when studying reactions which involve films, adsorbates, metal deposition, corrosion, or monolayer formation. It is sensitive enough Read more about Quartz Crystal Microbalance[…]

# Fitting EIS Data – Adding Components

One guideline that I have heard recommended (although I cannot give a reference for it) is that data over a decade range of frequency is required to support each circuit component.

All curve-fitting software should report some measure of the “goodness of fit.” Often this is the chi-squared parameter ( X2 ) or a value related to it. Boukamp makes the recommendation that the value of X2 should decrease by tenfold if a new circuit element is introduced into the circuit model. The tenfold decrease provides the justification for including the new circuit element. If the inclusion of an additional circuit element does not substantially improve the goodness-of-fit (as evidenced by the decrease in the X2 value), then based on Occam’s Razor, you should keep the simpler model, or continue your search for an improved one.

The old joke about the ability to “fit an elephant” if you use enough parameters is all too true with impedance data. Each component added to the model should have a physical explanation. Adding components only because they make the fit look better (smaller X2) without a physical interpretation is the equivalent to “fitting an elephant.”

# Reference Electrodes

### Introduction

This Application Note presumes that you have a basic understanding of potentiostat operation. If you are not that knowledgeable concerning electrochemical instrumentation, please read Potentiostat Fundamentals before continuing. Experienced potentiostat users may skip the primer and read on.

It’s only natural that electrochemists concentrate on the working electrode. After all, reactions at the working electrode are what they study. However, the reference electrode shouldn’t be ignored. Its characteristics can greatly influence electrochemical measurements. In some cases, an apparently “good” reference electrode can cause a complete failure of the system.

For reliable reference electrode performance, you should assign a “Lab Master” and treat it very, very carefully so it can serve as a standard for your other reference electrodes. Never use the Lab Master in an actual experiment. The only purpose of the Lab Master is to serve as a check for the other reference electrodes. If a reference electrode is suspected to be bad, you can check the potential versus the Lab Master. You can do that with a voltmeter, or with your Gamry Potentiostat by running and open circuit potential. If the potential difference is less than 2-3 mV, it’s OK. If it’s higher than 5 mV, it needs to be refreshed or discarded.