If the electronics of your apparatus is working fine, below are some possible explanations, yet such data are not fitting a Randless typical behaviour and I would not model them with circuits at all.

Negative real impedances

are sometimes associated with persistent current reductions

as potential increases; this might be characteristic of unstable

electrochemical systems e.g. when some of the following processes

might take place: a) potential-dependent adsorption/desorption of a

catalyst, b) electrostatic effects at low ionic strengths, as in the

reduction of anions at a negatively charged surface, or c) 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.

Reference: Xochitl D. Benetton, Navarro-Avila S., Carrera-Figueiras C. (2010) Electrochemical evaluation of Ti/TiO2-polyaniline anodes for microbial fuel cells using hypersaline microbial consortia for synthetic-wastewater treatment, Journal of New Materials for Electrochemical Systems, Vol.13., No. 1, p. 1-6. 

First, I would check/calibrate the system with a dummy cell of known parameters (Rs at least). Did it help?

Dear Tran

What is the upper frequency in your experiment?

Dave

If the electronics of your apparatus is working fine, below are some possible explanations, yet such data are not fitting a Randless typical behaviour and I would not model them with circuits at all.

Negative real impedances

are sometimes associated with persistent current reductions

as potential increases; this might be characteristic of unstable

electrochemical systems e.g. when some of the following processes

might take place: a) potential-dependent adsorption/desorption of a

catalyst, b) electrostatic effects at low ionic strengths, as in the

reduction of anions at a negatively charged surface, or c) 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.

Reference: Xochitl D. Benetton, Navarro-Avila S., Carrera-Figueiras C. (2010) Electrochemical evaluation of Ti/TiO2-polyaniline anodes for microbial fuel cells using hypersaline microbial consortia for synthetic-wastewater treatment, Journal of New Materials for Electrochemical Systems, Vol.13., No. 1, p. 1-6. 

Dear Benetton, can you please send full text file of the reference article, as you given for the above explanation. I would be very thankful to you, if you provide this article because i am also facing the same problem in my experiments. 

The full reference is cited above, for what I posted. Here you can download the article, yet I do not think it is any relevant for this discussion as a whole.

http://www.xoch.info/uploads/7/7/9/2/7792995/art01.pdf

I also recommend the text book of Orazem and Tribollet.

Kind regards

Xochitl

Dear all, 

Thank you so much about all replies.

@Mila Pravda: I didn't calibrate or check with a dummy cell because I don't know this method. After they connected this machine (SP-240) to computer, I used it to measure glassy carbon with reference electrode is Ag/AgCl, the counter is Platin. So, could you give me more information or papers about how to cablibrate/ run a dumbmy cell, please?Thank you so much.

@ Dave Loveday: the frequency range I used from 5 MHz to 100 mHz. 

@Christian Punckt and Xochitl Dominguez-Benetton : Thank you so much, I will read this book carefully. Really really thankful.

By the way, when I measured with the other machine (SP-150) with the limitation of upper frequencies is 1MHz, there was not the negative value, however, the semi-circles in the high frequency (higher than 500 KHz) was not stable. I wonder how the high frequencies leads the not good values in Nyquist?.

Therefore, the high frequencies in 5MHz of the machine (SP-240) in the above image leads the unstable negative values and I can not trust it, right? 

Or do you know how to adjust them to normal? please teach me.

I would suspect that your negative impedances are due to instrumental artefact.  It is difficult to make impedance measurements at such high frequencies without being very careful with your cell design.  In a large number of electrochemical applications there is not a lot of information above 100kHz

The placement of your reference electrode could be the problem. Besides the reference electrode probably does not work properly at high frequencies. Years ago (ninety eighties?) there was a paper on negative effects due to this. One solution was to add a just a Pt electrode to the reference electrode for the high frequencies. I'll try to find that old paper (Electrochimica Acta I think).

B.A. Boukamp

Negative impedance at high frequency is tipcally assigned to  instrumental artefact. Please verify your electrical contacts. This response is probably due to inductance of electrodes (wires/ contacts).

Here's a reference regarding impedance measurements at high frequency

F. Mansfeld, S. Lin, Y.C. Chen and H. Shih, "Minimization of High-Frequency Phase Shifts in Impedance Measurements", JES 135, 906 (1988)

You can also look at the this webpage http://www.gamry.com/application-notes/reference-electrodes/ Figure 3

Excellent reference, Dave. The frequent calibration and the frequency range of 1 Hz - 100 kHz should cover the electrochemical applications as outlined by Christian. It may be in your best interest if you could find a local post-doc supervising the EIS lab and get some training?

Excelent reference indeed; however, please note that it is from 1988 and frequency response analyzers have much evolved since them (more than 25 years ago!)

@Mila Pravda: thank you for your reply. My Professor is young and I'm the first student of hers so I hasn't got any senior for helping me. I need to consider the diameter of semi-circle of Nyquist plot for capacitor element but it only appear in high frequencies (from 5MHz to 22 KHz) with the machine SP-240 so I think the frequencies range (100 KHz-1Hz) is not enough for my measurement. How can I control the frequencies for trust impedance values?

Dear all, Thank all your references. Now I'm looking for them and firstly, I will read carefully. Please teach me more if you know how to explain it. Really thank you, all.

@Xochitl

Frequency response analyzers have evolved, but not reference electrodes.  Many people use reference electrodes designed for potentiometric measurements which have slow responses for potentiostats!  Especially as manufacturers try to go to higher and higher frequencies.

thanks for above responses.

please view this paper.

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