Dielectric and conductivity relaxation in poly(3,4‐ethylenedioxythiophene) nanotubes

Abstract

The charge carriers relaxation dynamics in synthesized poly(3,4‐ethylenedioxythiophene) nanotubes has been investigated as a function of frequency and temperature through the framework of dielectric permittivity, modulus formalism and impedance formalism. The fitting of experimental data of real part of dielectric permittivity and imaginary part of modulus with Havriliak‐Negami equation and Bergman modified Kohlrausch‐Williams‐Watts function indicates the presence of non‐Debye type relaxation process in the synthesized poly(3,4‐ethylenedioxythiophene) nanotubes. The scaling of imaginary part of modulus and impedance formalisms have been performed to understand the charge carrier relaxation dynamics in the synthesized samples, which suggests the presence of time temperature superposition principle in the nanotubes. The red shifting of the band from 1440 cm−1 to 1430 cm−1 in micro‐Raman spectra indicates the conformational transition from benzenoid to quinoid structure with increasing dopant concentration. The linear increase of imaginary part of dielectric permittivity with decreasing frequency is ascribed to the higher contribution from dc conductivity as compared to that from the electrode polarization effects. POLYM. ENG. SCI., 56:448–457, 2016. © 2016 Society of Plastics Engineers

Identification of relaxation processes in pure polyethylene oxide (PEO) films by the dielectric permittivity and electric modulus formalisms

“…This Bergman loss function has no counterpart M ′( f ) formulation. Bergman‐like loss function of Equation was employed by several researchers to curve‐fit M ′′( f , T ) − f data of undoped PEO and solid PEO‐based electrolytes and composites Another approach based on M ′( f ) and M ′′( f ) formulas derived from Debye, CC, CD, and HN empirical ‐formulas and used Chutia and Kumar, although their formulas are very much mathematically and analytically intricate, to analyze M ′( f ) − f and M ′′( f ) − f data of some materials.…”

“…Various ways are often used to display measured data of dynamic relaxation response of a sample in the frequency domain such as the Argand diagrams (complex‐plane plots) and Bode‐like plots, each of which has its own merits and limits in interpreting the ac‐data . The directly measured electrical quantities of a material sample, at temperature T , in common ac‐measurements are the macroscopic complex impedance and/or complex admittance , where ω (=2π f ) is the angular frequency of the ac‐signal applied to the sample and .…”

“…Argand diagrams depict the imaginary part against real part of a complex electric quantity over a range of frequencies, from which one may infer a plausible electrical circuit model that describes relaxation mechanisms operative in the sample; yet, such electric representation is not much inspiring and is difficult to appraise visually complex circuit network of nonideal electrical elements, as different circuit combinations yield same effective impedance of the sample, or real heterogeneous systems, where diverse conduction and relaxation processes dominate in different frequency ranges. A Bode‐like plot displays the real or imaginary part of a complex electric quantity against frequency, which often provides more prospectus for reliable interpretation of the frequency‐domain spectral shape arising from diverse conduction and polarization mechanisms …”

“…One had to achieve a global solution of the problem when utilizing traditional curve‐fitting of loss data measured over a wide frequency range to a combination of multi‐constant permittivity dispersion functions. In practice, however, it is rather difficult to isolate the real dielectric dispersion spectra of a sample from low‐frequency relaxation processes arising from interfacial/electrode polarization and dc conduction . The as‐measured loss spectrum is then less inspired and the numerical curve‐fitting analysis of loss data becomes remarkably complicated, and it is not easy or always reliable to detach the effect of dc conductivity, specially when its contribution is much larger than the amplitude of the real dielectric relaxation and/or when a low‐frequency relaxation of similar power‐law frequency dependence (eg, Jonscher's term) is present, a procedure that is crucial for interpretation and subsequent reliable analysis of experimental dielectric data …”

“…It is thus a necessity to search for other analytical approaches that might overcome difficulties encountered when the permittivity formalism is adopted to analyze the broadband ac‐impedance data or that would be capable to remove/separate or efficiently treat the low‐frequency contributions of dc conduction and interfacial/electrode polarizations to the measured permittivity spectra of a material . A methodology that is widely adopted, despite of some criticism and no consensus among the dielectrics community, for analyzing the as‐measured ac‐impedance of a semiconductive/dielectric sample is the electric modulus formalism, via which the low‐frequency permittivity contributions could be split apart or minimized from the coexisting low‐frequency relaxations of dielectric origin (dipolar reorientations or molecular motions) . Modeling of the as‐measured data of ac‐impedance of a dielectric sample in terms of frequency‐domain electric modulus may provide complementary insights into the problem of understanding its electric responses on equal footing with representations based on electric permittivity or impedance/admittance (resistivity/conductivity) formalisms …”