Recently I've been working on the calculation of ion diffusion coefficient using EIS measurement. I found that in many literatures the authors plotted the real impedance (Z') against ω^(-0.5) to get the linear relationship for calculation.
If i am not mistaken, ω = 2*π*f, and a lower border of 0.01 Hz gives a highest value of ω^(-0.5) to nearly 4, but a paper showed ω^(-0.5) value above 4 (Fig. 10b) while claiming that the EIS was tested in the frequency range of 0.01–100,000 Hz (10.1016/j.electacta.2015.01.015), is this possible?
If I did not get it, please tell me the right equation.
They use that frequency range because at higher frequencies the ionic conductivity is obtained. However, for ion diffusion coefficient they are using the low frequency values when Warburg impedance applies.
You're right, Sergio,
The w^(-0.5) function is decreasing when increasing the frequency. At 0.01 Hz w^(-0.5) is about 4 rad^(-0.5) and at a frequency of 100,000 Hz is 0.00126 rad^(-0.5). According to equation 1, it should be an equation of the type y-a+bx (being a=Re+Rct and b=sigma).
this is best explained in reference 48 (10.1016/j.electacta.2009.08.020). The Zre vs w^(-0.5) chart refers to low-frequency dispersion, the increasing values in the Nyquist diagram.
Best regards
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