Dear Dr. Davi Alves Marques ,

I suggest you to have a look at a similar, previous question present on RG “What is the meaning of negative value of resistance from EIS study?”, focusing on my answers and on that of Dr. Ioannis Samaras, available at: https://www.researchgate.net/post/What_is_the_meaning_of_negative_value_of_resistance_from_EIS_study

My best regards, Pierluigi Traverso.

Dear Davi Alves Marques

After the well addressed answer by Pierluigi Traverso, I would like to review some of what published about the possible interpretation for the presence of a negative resistance in a Nyquist equivalent circuit as follow:

D.D. Macdonald reported in [1] on pp237 the following:

"The appearance of negative resistance is not simply a theoretical artifact because it has been observed experimentally for a number of systems. A good example of this phenomenon is provided by the work of Keddam et al. on the active-to-passive transition on iron in 1 M H2SO4 (Figure 13). Thus, if the impedance is measured at point A, which lies within the active-to-passive transition, the impedance locus intersects the real axis at w --> o at a negative value, although at high frequencies much of the impedance locus lies within the first quadrant."

Keddam et al., state In [2] on pp261 the following:

"From these results, it can be corroborated that the current shoulder observed in the pH 4 solution is actually related to the prepassivation process because the low-frequency capacitive branch of diagram E4 is compared to the capacitive branch leading to the negative polarization resistance (limit of the zero frequency of the electrode impedance which is equal to the slope of the steady-state polarization curve)."

A. E. Bolza´n • L. M. Gassa [3] on pp 279 and pp 283 investigated the following:

"At potential values associated with the formation of the anodic oxide layer on gold, a negative resistance is recorded, indicating the passivation of the electrode surface."

"When the presence of a negative resistance sets in, i.e. the passivation of the electrode surface likely related to the formation of an oxide film at the monolayer level takes place. The appearance of the negative resistance in the Nyquist plots corresponds to the current decrease appearing in the voltammogram at those potentials:

Finally, Xochitl Dominguez-Benetton in [4] said:

"when the active surface available for electron-transfer decreases as polarization raises (for example, when the interface shows activity peaks followed by passivity stabilization); in these cases, a part of the polarization curve (or voltammogram if it is the case) has a negative slope—the value of the impedance at zero frequency is related to the slope of the steady-state polarization curve—then the impedance measured in the potential range where this occurs is found with a negative real part."

Now it becomes clear that the process of active-to-passive transition is responsible for the presence of a negative resistance in which an increase in voltage results in a decrease in electric current due to formation of passive protective barrier layer.

Hope the above explanations are useful.

Best regards

[1]https://ceramrtr.ceramika.agh.edu.pl/~szyszkin/tmp/tmp1/Some%20Advantages%20and%20Pitfails%20of%20Electrochemical%20Impedance%20Spectroscopy.pdf

[2]https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.916.1977&rep=rep1&type=pdf

[3]https://link.springer.com/content/pdf/10.1007/s10800-013-0621-7.pdf

[4]https://www.researchgate.net/post/What_is_the_negative_value_of_PEIS_in_my_Nyquist_plot

The Nyquist diagram does not show the Warburg impedance behavior. I suggest fitting a circuit equivalent to a constant phase element without Warburg.

Rs[Cdl II Rct]

Dear Davi Alves Marques,

What I understand trying to interpret here. This is my own opinion.

Nyquist Equivalent Circuit (NEC) semicircular plot does not mean to have a negative resistance. NEC plot is normally used to evaluate electrochemical impedance plotted data in graph used real impedance data along the x-axis and the negative imaginary data is along the y-axis which mostly characterize the frequency dependence of impedance responses. By getting two of intercept one at the high frequency intercept on the plot, the real axis value may give the solution resistance and another low frequency intercept of the real axis provides a summation of the polarization resistance and the solution resistance. Therefore, the semicircle diameter almost equivalent to the polarization resistance but not the negative resistance. Large polarization resistance of a metal means have a high corrosion resistance and a low corrosion resistance when small.It does mean a solution resistance and moreover a polarization resistance. When uniform corrosion rate is there it may be inversely proportional to the polarization resistance.

Ashish.

In a Nyquist plot, a negative resistance appears as a semicircle in the lower right quadrant that goes below the x-axis. A negative resistance means that the impedance decreases as the voltage increases, which is the opposite behavior of a regular resistor where the impedance increases with the voltage.

In an equivalent circuit, a negative resistance can be represented by a resistor and a voltage source in series, where the voltage source has the opposite polarity to the voltage drop across the resistor. This combination creates a net negative resistance. Negative resistance is not a passive component and cannot be realized with conventional passive components like resistors, capacitors, and inductors. It can only be realized with active components like transistors and diodes.

In electrochemistry, negative resistance is often observed in systems that undergo electrochemical reactions. It can be caused by the formation of a gas bubble or an electroactive species that creates a counter voltage. Negative resistance can also occur in semiconductor devices like tunnel diodes, where the current decreases as the voltage increases, resulting in a negative differential resistance region in their characteristic curve.