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The Bisquert elements at the interface between the anode and electrolyte, and the cathode and electrolyte, are infinite series of resistors combined with parallel constant-phase elements plus resistors. Revised physical model of a Li-ion cell, with circuit elements superimposed. Thus we should include porous elements in our model circuit:ДЇigure 6. Modern batteries typically are designed with a high surface-area-to-volume ratio, that is, with many voids within the electrolyte. Overall, however, we can see that this model is defective. The goodness-of-fit, the П‡ 2 value, is 0.00274, which-surprisingly-is decent. The residual errors are obviously not random:ДЇigure 5. 3 on Li-ion cell data.Д®ven a glance shows that this fit, though more or less reproduces the shape of the data, has some problems. Fit using the equivalent circuit shown in Fig. Here we perform a fit with Gamry InstrumentsвЂ™ Echem Analystв„ў software:ДЇigure 4. First iteration of an equivalent circuit to a Li-ion cell. We add a вЂњstray inductanceвЂќ that may be cable- or instrument-related, to give a six-component equivalent circuit like this, created with Gamry InstrumentsвЂ™ Model Editor:ДЇigure 3. Sketch of physical model of Li-ion cell, with suggested electronic components corresponding to various parts of the cell. We start with some kind of physical model like that shown below:ДЇigure 2. Below is a Bode plot of the data.ДЇigure 1. LetвЂ™s examine an example, EIS data taken on a lithium-ion 18650 cell.

It is unacceptable to just keep adding electronic components to the model to create a good fit: the components must mean something in the real world. The basic rule is: Use the simplest model that fits the data. The least important of all is the goodness of fit, or П‡ 2 value! Second most important is being sure that the error bar for each ideal component in the model is smaller than the value calculated for that component, and that any residual errors are not systematic, but random. The most important of these layers of fitting is the representation of a real physical system. One can fit nearly any impedance spectrum using enough parameters, but the question then becomes, вЂњis the fit realistic?вЂќД«esides fitting the model to the data, we also want the fit to correspond to a real, physically intuitive system, with pores, insulating capacitative layers, and so on. In short, the answer is вЂњenough,вЂќ but not too many. If the data match the network (a вЂњfitвЂќ of the data to the model), then the network of components is deemed to be a valid model of those data.ДЇor a background on the technique of EIS, we recommend you read first our Application Note вЂњ Basics of Electrochemical Impedance Spectroscopy.вЂќ For a general discussion of modeling EIS data, see our Application Note вЂњ Equivalent Circuit Modeling Using the Gamry Electrochemical Impedance Spectroscopy Software.вЂќД«ut what constitutes a valid network of electronic components to use as a model? This Application Note discusses the ramifications for your EIS experiment when too many or not enough components are used in your model. The technique compares the observed data from an EIS scan to a hypothetical model network of resistors, capacitors, inductors, and other theoretical components. Electrochemical Impedance Spectroscopy (EIS) is now ubiquitous in the electrochemical research, development, and quality-control world.

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