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 find 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 valid 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 α relaxation in a glass-forming polymeric system, poly(hydroxy ether of bisphenol-A).

Physical aging is a ubiquitous phenomenon in glassy materials and originates from the fact that they are generally out-of-equilibrium. Due to the technological and fundamental implications, this phenomenon has been deeply investigated in the last decades especially in glassy polymers. Here we provide a critical review of the latest hot debated themes in the field of physical aging in polymers and polymer nanocomposites. We first summarize the fundamental aspects of physical aging, highlighting its relationship with the polymer segmental mobility. A review of the methods employed to monitor physical aging is also provided, in particular those probing the time dependent evolution of thermodynamic variables (or related to) and those probing the (quasi)instantaneous polymer segmental mobility. We subsequently focus our attention on the two following debated topics in the field of physical aging of polymers: (i) the fate of the dynamics and thermodynamics of glassy polymers below the glass transition temperature (T_g), i.e. the temperature below which physical aging occurs; (ii) the modification of physical aging induced by the presence of inorganic nanofillers in polymer nanocomposites. With respect to the former point particular attention is devoted to recent findings concerning possible deviations from the behavior normally observed above T_g of both dynamics and thermodynamics deep in the glassy state. Regarding the effect of the presence of nanofillers on the rate of physical aging, the role of the modification of the polymer segmental mobility and that of purely geometric factors are discussed with particular emphasis on the most recent advances in the topic. The modification of the rate of physical aging in other nanostructured systems, such as polymer thin films, is discussed with particular emphasis on the analogy in terms of a large amount of interface with polymer nanocomposites.

The local dynamics of 1,4 polybutadiene below and above the merging of the α and β relaxations have been investigated by combining neutron spin echo (NSE) and dielectric spectroscopy. The study of the dynamic structure factor measured by NSE over a wide momentum transfer range allows us to characterize the α relaxation as an interchain process while the β relaxation originates from mainly intrachain motions. At temperatures below the merging, the dynamic structure factor can be described by a superposition of elemental processes for the β relaxation as obtained from dielectric spectroscopy. The elemental motions behind this process can be related to rotational jumps of the chain building blocks around their center of mass. Furthermore, we have been able to consistently describe the dynamic structure factor above the merging of the α and β relaxations by assuming that both processes are statistically independent. In the framework of this scenario a procedure for analyzing the dielectric response in the α-β merging region has been developed. Its application to the dielectric data allows us to describe the dielectric response in this region on the basis of the low temperature behavior of the α and β processes and without considering any particular change in the relaxation mechanism of these processes. The temperature dependence found for the relaxation time of the α process follows now the viscosity, a masked feature in the experimental data due to the merging process. In this way, we have been able to consistently describe the relaxation of both, the polarization and the density fluctuations, by using the same scenario, i.e., independent α and β processes, and considering the same functional forms and temperature dependences of the characteristic times of the two processes. © 1996 The American Physical Society.

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 over the last several years. The HN relaxation function is a frequency-domain function while the KWW function applies for the time domain. In a previous paper we discussed the interconnections between these two functions by presenting a method where we found that the best HN description in the frequency domain corresponds to a given KWW function in the time domain. From that work we proposed several empirical relationships that allow us to determine the HN parameters corresponding to a given set of KWW ones. It was also outlined how to proceed in the opposite way, i.e., to obtain the best KWW time-domain description corresponding to a given HN relaxation function in the frequency domain. This is what we develop in this work by varying the HN parameters in search of the values of the best KWW fits. Likewise we can put a limit to the region where the HN and the KWW functions are compatible in the sense that they can be equally used by just choosing the right parameter change. A confident confirmation of this procedure is that when the HN parameters reported in the literature for the α relaxation of glass-forming liquids are considered, their values fall directly upon this region, where we find that the HN and KWW functions deviate less. However, for other dynamical processes like secondary relaxations of polymers or the α relaxation of polymer blends the HN parameters reported indicate that a single KWW relaxation function is not able to describe the time-decay behavior.

We investigated the kinetics of enthalpy recovery of several glass-forming polymers at temperatures significantly below the glass transition temperature ($T_g$) and for aging times up to one year. We find a double-step recovery at relatively low aging temperatures for the longest investigated aging times. The enthalpy recovered after the two-step decay approximately equals that expected by extrapolation from the melt. The two-step enthalpy recovery indicates the presence of two time scales for glass equilibration. The equilibration time of the first recovery step exhibits relatively weak temperature dependence, whereas that of the second step possesses pronounced temperature dependence, compatible with the Vogel-Fulcher-Tammann behavior. These results, while leaving open the question of the divergence of the relaxation time and that of a thermodynamic singularity at a finite temperature, reveal a complex scenario of glassy dynamics.