The way you are asking the question suggests that you have chosen an equivalent circuit because it fits the data, but this is not a good way to do EIS interpretation. You need to select a circuit that fits what you believe is happening, i.e. where you know what each of the terms mean in terms of real physical processes.

On the question of Rp, there are two different answers, depending of how you define Rp. By comparing the value of Rp measured with linear polarization (which is where the term comes from) Florian Mansfeld argued that Rp is the low frequency intercept of the impedance with the real axis. However, this implicitly includes the solution resistance (as it does of course when using LPR), and if you want to apply the Stern-Geary relationship, to do need to exclude the solution resistance, hence taking the difference between the high fequency and low frequency intercepts with the real axis. To avoid confusion with Rp (as determined by LPR) many workers prefer to call this the charge-transfer resistance, Rct. This is not the end of the story, however, as with EIS you can often separate the kinetic resistance from the diffusional impedance, and you can choose to use either to calculate Icorr, though the B value will be different.

The resistance includes outing resistance and inner resistance,or we call high frequency resistance and low frequency resisitance.but the solution resistance is not in them.

The easiest way to find Rp is simply the difference between the high frequency and low frequency intercepts with the X-axis on a Nyquist plot of the data or your model circuit. Rp is a real value and therefore does not include any of the imaginary components of the impedance.

Rp is real part of the impedance. If you do have a semicircle at high frequency, it is the diameter of it. Solution resistance does not play any part in the formation of the semicircle.

The way you are asking the question suggests that you have chosen an equivalent circuit because it fits the data, but this is not a good way to do EIS interpretation. You need to select a circuit that fits what you believe is happening, i.e. where you know what each of the terms mean in terms of real physical processes.

On the question of Rp, there are two different answers, depending of how you define Rp. By comparing the value of Rp measured with linear polarization (which is where the term comes from) Florian Mansfeld argued that Rp is the low frequency intercept of the impedance with the real axis. However, this implicitly includes the solution resistance (as it does of course when using LPR), and if you want to apply the Stern-Geary relationship, to do need to exclude the solution resistance, hence taking the difference between the high fequency and low frequency intercepts with the real axis. To avoid confusion with Rp (as determined by LPR) many workers prefer to call this the charge-transfer resistance, Rct. This is not the end of the story, however, as with EIS you can often separate the kinetic resistance from the diffusional impedance, and you can choose to use either to calculate Icorr, though the B value will be different.

Thanks for the answer, I have attached my Neq plot. so the difference between the highest freq and the lowest but the Neq does not show the frequencies. However my range is from .01 to 10000. so how can I get the charge transfer resistance???

At high freq, you do not seem to have a semicircle. Try to fit the arc to a semicircle. The intercept would be the approximation of Rp. The Rp seems very large. There are programs to do so.

Based on your Nyquist plot the solution resistance is very small compared to the charge transfer resistance, so your original question is not relevant in this case, as Rp and Rct are virtually the same. Your real problem is extrapolating to very low frequency to estimate the low frequency limit. You can use your fitted circuit to do this, but a simpler circuit (e.g. a Randles circuit) would be just as good if it was appropriate for the system you are studying.

You may increase your confidence in the Equivalent circuit used and the Rct values measured by obtaining the corrosion rate value through Stern-Geary equation and Faraday’s law, and compare it with corrosion rate values obtained by independent techniques (Gravimetrric measurements or others)

Although your circuit may fit the data, it seems a little strange. In particular, a Q in series with a parallel (RQ) is not common, except if the exponent of this Q is close to 0 (and then it acts as a resistor). Of course I don't know your system, but I would advise you to take into account the physical meaning of the circuit.

Hi Roto Roto, Do u mean I tried to complete my semi-circuit so it will intercept with the X axis and that intersection is my Rct??

Hi Robert Alan Cottis,

thank you for uyour help. I am wondering do you mean that if I use R(QRct), then I can consider that Rct is my Rp and calculate the corrosion current density from there using the equation icorr= B/Rp and ignore the solution resistance?? Actually I choose the data because I though that I am having two layers and the inner layer is porous which is really difficult to judge because even with SEM is difficult to see about 3-7nm layer. therefore, I may use either the simple Randles circuit and assume that I have one protective layer which is mixed of oxide layer and protein or R(QR)(QR) and assuming that I am having two layers.

Hi Rana Hirzallah,

Yes, that is what I mean. You may have a look at my paper, although not quite close, as a reference. Roto Roto, Gilles Villemure, Journal of Electroanalytical Chemistry, Volume 527, Issues 1–2, 31 May 2002, Pages 123–130.

Hi Rana

Essentially you need to estimate the impedance at very low frequency, when the phase shift has fallen to near-zero. If the circuit is a simple semi-circle on the Nyquist plot, this corresponds to Rs(QRct) and the intercept will be Rct+Rs, so you can easily determine Rct (and in your case Rs

Rp means a low frequency limit of Re(Z), when frequency tends to zero.

Hi Roto,

Thanks a lot I'll have a look to the paper

Hi Robert,

I have attached the simulation for the same solution using three different circuit.

Perhaps, the arc of the impedance diagram is no principally linked with the charge transfer resistance of the substrate corrosion reaction, but rather with the ohmic resistance of the thin oxide layers present on the surface of the material.

Hi Rana,

I have seen your simulations .You dont put you into the confusion. Take the Rct value as the Rp both are equal only .

You dont want to consider the Q and Solution resistance for the calculation of Icorr

The Q is the capacitance it is not resistance

In the second simulated value .Use the Rct 2 as Rp value..

The Rct 1 will corresponds to your coating or passive layer etc...

hello everyone!

how could i calculate the charge transfer resistance and solution resistance based on the Nyquist plot? My Equivalent circuit and Nyquist plot are here attached.

Thanks