I extracted the values of capacitance by using the formula: M''=(epsilon_{0})/2C.
What does it mean in the lower frequency region in my graph?
Can modulus discriminate between the electrode polarization and grain boundary polarization?
Dear Ala'eddin A. Saif ,
this is my M'' vs M' plot.what should I extract from this plot....
Thank you.
The electric Modulus was first suggested by Mc Crum et al to understand the dielectric relaxation in polymers. It is defined classically as the reciprocal of complex relative permittivity in analogy with the mechanical shear and tensile moduli being the complex reciprocals of shear and tensile compliance's. Under the electric modulus formalism one studies the space charge relaxation phenomena, M* representation is widely used o investigate ionic conductivity. Physically, electric modulus corresponds to the relaxation of the electric field in the material when the electric displacement remains constant. Thus, electric modulus represents the real dielectric relaxation process/s. The complex modulus describes the dielectric response of non-conducting materials. One can also use the formalism to analyse materials with non-zero conductivity. The usefulness of the modulus representation in the analysis of relaxation properties has been demonstrated in many ionic conductors and ceramics. One of the advantage of complex electric modulus formalism is that it can discriminate against the electrode polarization and grain boundary conduction process. A comparative study of impedance formalism and modulus
is useful. Whereas impedance formalism lay emphasis on grain boundary conduction process, the electric modulus represents the bulk effect in frequency domain. It helps us to separate the contribution from material components having similar resistances but different capacitance. Generally the explicit M' Vs. frequency plot should saturate and cross zero in ideal non-nonconducting materials. M' Vs. frequency plot should give corresponding peak if the relaxation is within the frequency window. Finally a plot between M" Vs M' is useful in finding the equivalent circuit components.
Dear Parmendra Kumar Bajpai ,
Thank you for giving broad explanation about Modulus spectrum.
I have a doubt on Impedance and modulus cole-cole plots.
Suppose I plotted Z'' vs Z' and M'' vs M' and both plots having two semicircles?
What does it mean and How to understand the plots?
Thank you.
Dear Kotagiri Gangaprasad,
Each of the "circles" correspond to a different electroactive element in your material, the one a higher frequencies correspond to the less resistive one. I.e. in case you are measuring a bulk material, in general, the first semicircle in the cole-cole plot (Z) will correspond to the grain boundaries resisitivity and the second one to the sum of grain boundaries and grains. Same with the M plots.
In general, the best way to approach impedance is first having an idea about the possible components you may have, then have a visual study of all the plots and then extract the information you need, but it's good to know exactly how your material is formed to be sure that the capacitance, conductivity... values that you're extracting correspond exactly to what you're looking for.
Hope this helps
Dear L. Miranda,
The extra feature of modulus spectrum is that "It can discriminate the same resistance but different in capacitance".
In the first plot:
Can I conclude the polarization in the material at low frequencies is effect due to the electrode and grain boundaries?
Thank you.
Dear Kotagiri Gangaprasad.
Each maximum in M'' corresponds to a conductivity relaxation time that can be represented as a RC parallel element. The magnitude of the maximum is inversely proportional to the permittivity that is proportional to value of C corresponding to that relaxation. In a linear plot the M'' values corresponding to interfacial phenomena are orders of magnitude below the values of the "bulk" M'' reposne. This representation is used to check the homogeneity of the "bulk" response and it is not indicated to study the interfacial phenomena. .
Dear Kotagiri Gangaprasad.
The complex modulus is the inverse of the complex permittivity. Hence
M=(eps'-ieps'')/(eps'**2+eps''**2)
Be careful when taking the reciprocal of a complex number! M'' is related to both real and imaginary parts of the permittivity (or capacitance).
Hi dear
Your semicircle seems to be non-ideal (Depressed semicircle) or deviation from Debye behavior. The origin of different relaxations can be due to Grains, Grain boundary, Sub-grain boundary, Electrode effect and also be due to Interface functional groups. Usually multiple relaxations can be associated with polycrystalline structure too.
You can observe these multiple relaxation from Cole-Cole plot, but some times this plot can't give you sufficient information. Then you can try Modulus plane plot or comparison between imaginary parts of M'' and Z''.
Usually electrode/interface effect occurs at Lower frequency, grain boundary at Intermediate frequency and bulk or grain at higher frequency.
Values of resistance can be calculated directly from Impedance data or you can fit these curves with some software e.g. Z-view or do simulation .
Actually the value of capacitance and resistance both, obtained from fitting actually gives us clue about the different electroactive regions. e.g. value of capacitance for bulk or grain( ~10^-12F) , Grain boundary (~10^-12F,10^-11F,10^-10F) and electrode or interface effect should be (~10^-10F,10^-9F,10^-8F).
Further you can look at these research papers, hope these papers will be helpful for you.
1) http://scitation.aip.org/content/aip/journal/apl/101/2/10.1063/1.4735278
2) http://scitation.aip.org/content/aip/journal/apl/101/25/10.1063/1.4772068
Regards