The Kohlrausch-Williams-Watts (KWW) and the Havriliak-Negami (HN) relaxation functions have been widely used to describe the relaxation behavior of glass-forming liquids and complex systems. While the HN relaxation function is a frequency function, the natural domain of the KWW relaxation function is time (although it has also been used with frequency-domain spectroscopies). A relationship among the parameters of the two models is suggested by the fact that both models yield an accurate description of real data. Nevertheless, this relationship cannot be an analytical one, since it is known that the HN and the KWW relaxation functions are not exactly Fourier transforms of each other. In order to Gnd out the nature of this relationship, a method which makes use of a distribution of relaxation times is proposed here. Numerical simulations following the KWW model have been assumed to describe the relaxation behavior in time; likewise, the HN description was assumed to be vahd for the frequency domain. From this work, a connection among the parameters of both models is obtained, which is expected to be valid for those experimental data that can be described by either the KWW or the HN model. This is the case for most, if not all, measurements on the dynamics in complex systems and glass-forming liquids that frequently appear in the literature. The proposed procedure has been tested by using dielectric-spectroscopy measurements, both in frequency and time domains to study the a relaxation in a glass-forming polymeric system, poly(hydroxy ether of bisphenol-A ).
The dynamics of the a relaxation in a glass-forming polymeric system, poly(vinyl methyl ether) (PVME) has been studied by means of dielectric and mechanical spectroscopies and nuclear magnetic resonance, as well as by means of quasielastic neutron scattering. By using these techniques we have covered a wide time scale ranging from mesoscopic to macroscopic times (10 ' -10' sec). The dielectric and mechanical data have been interpreted in terms of a Havriliak-Negami relaxation function, NHN.Nuclear-magnetic-resonance data were interpreted by means of a spectral density function J(e) based on C&HN. Neutron-scattering data were described in terms of a scattering law S(Q, co) which was also built starting from @HN. The results obtained from different experimental techniques indicate that the dynamics of the a relaxation in PVME can be well described by means of (i) a common temperatureindependent spectral shape and (ii) a common temperature behavior of the relaxation times. We deduce for the spectral shape very similar parameters by fitting the Havriliak-Negami relaxation function to the different experimental data. These shape parameters are found to be not very sensitive to changes of temperature. The resulting characteristic relaxation times follow a Vogel-Fulcher-like temperature behavior in the temperature range T~-5 K& T& T +150 K. Therefore, this implies a self-consistent description of the dynamics of the a relaxation obtained by very different probes in PVME.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.