Non-linear Least Squares Fitting

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Non-linear Least Squares Fitting

Description

You can model impedance spectra various equivalent circuits. For example, a Nyquist plot displaying two time constants is shown below:

 

Nyquist Plot - two time constants

 

It can be modeled by a number of different equivalent circuits.

 

UniqueModel_A
       
UniqueModel_B
       
UniqueModel_C

 

You cannot assume that an equivalent circuit with a good fit to a data set represents an accurate physical model of the cell. Even physical models are suspect in this regard. Whenever possible, verify the physical model before you use it. One way to verify the model is to alter a single cell component (for example increase the thickness of the layer of paint) and see if you get the expected changes in the impedance spectrum.

 

Gamry tip bulb

Treat empirical models with even more caution. You can always get a good-looking fit by adding lots of circuit elements to a model. Unfortunately, these elements have little relevance to the cell processes that you are trying to study. Drawing conclusions based on changes in these elements is especially dangerous. Empirical models should therefore use the fewest elements possible.