Electrochemical Impedance Spectroscopy of a Screen-Printed Electrode Biosensor (Inductive Loop!!) 

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It would be most likely accurate to consider the iR drop to be the first, or highest frequency, intersection in such cases where there are multiple intersections. A notable exception would be something like where an artifact is observed at high frequency showing weird curls that are not attributable to a real process, as with the example in this video. Otherwise, even with the circuit fitting the value for the leading resistor would correspond to where the highest frequency intersection roughly is.

Ferro/ferricyanide is soluble in water and I would assume that your enzymetic electrodes are also stable in water. Additionally I am assuming that the ferro/ferricyanide is sold with a potassium cation (potassium ferrocyanide). As such, I might recommend using an aqueous electrolyte of KCl for studying your system. Also, your buffer solution might also be a good candidate as an electrolyte. I hope this was helpful.

The initial semicircle-type feature (usually before the loop part) should be represented by the Randles RC part. You can usually see this in action by dragging the value for the resistor back and forth. It shows the semicircle width growing and shrinking in conjunction with the value change. The R-L combo in parallel does correspond to the loop, or essentially like an inverted semicircle. The idea of it forming a complete circle I think is somewhat of a coincidence of the two features, and only when the values are such that it physically appears that way. There is no real significance to the idea of a perfect circle being formed. The value of the R-L resistor is also apparently inversely proportional to the upside-down semicircle width, and that 3rd tier of the circuit model as best I can tell is related to the process therein - that is, if it is a corrosion process, it's somehow related to the impedance of the corroding film/surface in some way. But, as I think I note in this video and everywhere I discuss this model and these phenomena, there is really no consensus or firm explanation to this model and process. It is in many ways the model used to fit these kinds of features from experience because it simply works mathematically.

@@Pineresearch I would like to contribute an observation to your explanation based on my experience with circuit fitting and encountering a high-frequency inductive loop in my EIS data. I noticed that by introducing a resistor in series with CPE Q2 in your 3-tiered circuit model, the fitting software gains greater flexibility in capturing the high-frequency inductive loop, which may not be immediately apparent. This additional resistor essentially determines the width of the initial circle (typically small), without altering the width of the upside-down semicircle. Allow me to provide an overview of the effects of the three different resistors now present in the 3-tiered circuit model: 1. The resistor in series with the CPE (Q) determines the width of the initial semicircle. 2. The resistor in series with the inductor (L) determines the width of the upside-down semicircle. 3. The standalone resistor determines the width of both the initial and upside-down semicircles while maintaining their relative sizes constant. I hope that this suggestion and minor modification to the 3-tiered model can be helpful to others who are facing the challenge of fitting a high-frequency inductive loop. However, I want to clarify that I cannot provide a physical explanation for why the additional resistor proves effective. It is solely based on my personal experience, where the presence of a third resistor has facilitated the fitting software in capturing the inductive loop, particularly when there is a significant difference in the widths of both semicircles.

@@TarikZahzah-ns2bu Thanks for the suggestion. It could be a useful addition to this model, though as you acknowledged in your last paragraph the trouble is mainly the interpretation (or lack thereof) of its physical meaning. While it can be instructive (and I do this personally quite often, actually) to describe circuit elements in terms of "the size of this semicircle or feature on the Nyquist plot," in general that is not the goal and is, by itself, insufficient for comprehensive EIS analysis. The primary exception to this, as I have admitted many times and do so in this video, is that the inductor value is mostly meaningless (or, at the very least, unknown as to its correlation to a real phenomenon). The point, however, is that while it can be helpful as a user to consider "resistor 1 represents semicircle width 1" et al., mainly as a tool for obtaining better circuit fit, ultimately the explanation is better-suited as being "resistor 1 represents the charge transfer resistance of process 1, and it appears as the semicircle width 1." With the aforementioned inductor as a notable exception, in general it is wise to severely limit the number of times you are unable to justify such circuit elements in this fashion and choose to include them simply because the lines match the dots. So mainly, while your suggestion is appreciated, I am simply offering a word of caution in this regard as it relates to rigorous EIS data analysis.