Numerical deconvolution approaches for dielectric characteristics of complex composite materials based on liquid crystals and oxide nanopowders

Abstract

Dielectric spectroscopy is a well-known method to characterize different liquid or solid (nano) materials such as liquid crystals, polymers, composites, ceramics etc. More the material structure is complex, more the molecular dynamics are put in evidence with difficulty. In many such cases, the analysis of the spectra with the classic Havriliak-Negami (H–N) functions is hard to apply or even fails. Therefore, we propose a simple numerical approach (with two different procedures) for the deconvolution of complex spectra in dielectric spectroscopy (DS). The final goal is to obtain the frequency of maximum loss (fmax) depending on the temperatures, Arrhenius diagram, and the activation energy/energies. The developed procedures have as their starting point the “logarithmic derivative of the permittivity”. To our knowledge, these procedures have not yet been presented in the literature. The proposed first numerical processing allows a better separation of the different relaxation processes, a decrease in the contribution of the electrical conductivity and a better localization of the frequencies where the dielectric loss has maximum values. The second of the procedures is applied in certain particular situations, and the other procedure is more general. Where the former can be applied, it is equivalent to using the classical H–N functions in terms of obtaining the fmax, but it is simpler to apply. The first procedure uses an “artificial” and simpler H–N function, in which the fewer fitting parameters have no physical meaning, but allow a good localization of the frequency of maximum dielectric loss. The proposed procedure was applied on experimental data of dielectric spectroscopy obtained on pristine materials (nematic mixture E7 and ZnO) and composites E7-ZnO, obtained by a “green technology”. The complicated spectra of the dielectric permittivity presented by these samples represent the suitable test to highlight the advantages but also the limitations of our approach. Comparing the values of the activation energy obtained for the two procedures is the criterion for verifying their correctness. The volume of processed experimental data is large, for this reason we present only the results obtained based on numerical approaches. The differences between the results obtained with the two procedures are small. The procedures can be considered as alternatives to the application of fitting with H–N functions. One procedure replaces H–N by eliminating the use of functions with complex variables and the method of least squares and has the advantage that it can apply non-specialized software like Origin. The other allows a better analysis of spectra being an improved-modified H–N approach. Proposed procedures are sufficiently effective to be used in the dielectric spectroscopy data analysis of a wide variety of liquid crystals, composites, ceramics, nanomaterials, etc.