The Cole-Cole, Cole-Dadvison, Havriliak-Negami and Williams-Watts analyses have been usually devised for analyzing complex permittivities (which corresponds to complex comliances, not moduli). The same analysis can be performed for complex electrical and mechanical moduli. Usually you are supposed to use the time-temperature superposition principle, i.e. to measure the complex properties at several temperature and shift them to form a master curve and plot it a real vs. imaginary parts. This approach assumes that the relaxed and unrelaxed moduli  do not exhibit temperature dependence, or maximum a linear one. The time-temperature superposition principle works only if the preexponential factor of the relaxation time exhibits a distribution but the activatin energy is the same for all. This is not always true.

Hello Sir,

I did the TTS and WLF fitting and to move forward  i need to do the wicket correlation followed by the Cole-Cole, Cole-Davisson, and Havriliac-Negami fitting. I had been searching for the last couple of months to do it but the exact way to calculate the complex modulus from DMA data followed by the fitting to the above said equations is missing. It will be very helpful if you can help me.

Some furher literature can be found in:

http://www.ncbi.nlm.nih.gov/pubmed/24491337

http://www.feec.vutbr.cz/EEICT/2012/sbornik/03doktorskeprojekty/05teoretickaelektrotechnikafyzikaamatematika/02-xabuet00.pdf

http://en.pudn.com/downloads160/sourcecode/windows/detail723527_en.html

http://arxiv.org/pdf/1205.6764.pdf

http://maelenn.aufray.free.fr/pdf/sades.pdf

I presume you have the master curve data E' and E" vs. log frequency. Fairly good initial estimates can be obtained by plotting the Cole-Cole diagram (E' as x axis, E" as Y axis). (The method is descived in several basic handbooks of dielectric spectroscopy, such as the bbokk of Peter Hedvig, or Jonscher). If I were you, I would simply write a a very basic Newton-Raphson algorithm using numerical derivatives to refine the initial guesses obtained by graphical methods. It usually converges within a few cycles. I remember to have written similar algorithms for complex dielectic formulae in heterogeneous media.

Please load up the E" vs. E" curves you obtained after master curve formation.

Dear Sir thank you very much for your mail. Attached please find the cole-cole plots( i aasume that you have written E" against E' .) I am attaching master curves for neat polymer along with the Cole-Cole plots for the neat polymer and blends. 

This part is really confusing some have calculated theoretical modulus (storage and loss) followed by fitting it with the experimental values. Looking frward to hearing from you

Sorry my message contained error. E' should be the x-axis, E" is the y axis. I presume that on your Fig. 5. this is the case and you labelled the axes in a reverse order. Looking at the data it seems that the neat polymer can be fitted, but the blends are less easy to fit, esepcially the limiting moduli, as they can be obtained only by extrapolation. Especially the high frequency moduli of the blends would be very uncertain. Regarding the master curves: it is possible that, in addition to horizontal shift factors linear vertical shift factor (in E') will also be needed to obtain good quality master curve. It seems that in the blend the minority component causes an enormous shift in the properties. It is also strange that you obtain different shift factors for E' and E", which is a warning of potential problems. Usually the shift factors are obtained by simultaneous fitting of both E' and E".

Dear Sir thank you very much for your kind mail. It will be very helpful if you can provide your help and support in moving forward and solving this problem. 

Dear Sir,

The minor component might be acting as a plasticizer which can be the reason for the enormous shift in properties. I can send you the excel/origin files to you.This will be an opportunity for me to learn it.

Please send me the excel fles. My private email address is [email protected]

Dear Sir, Thank you very much i have send the excel files to you. 

Cole-Cole or Wicket plot is described in "Dynamic Mechanical Analysis: A Practical Introduction", 2nd Ed, by Kevin P. Menard, page 167, followed by TTS master curve construction and evaluation. See attached document for theory and equations. Sarath, your question is from a long time ago, however I take the opportunity to answer now just as I am revising these theories for modelling DMA.

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