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 ).

In this paper, we have addressed the question of the dynamic miscibility in a blend characterized by very different glass-transition temperatures, Tg, for the components: poly(ethylene oxide) and poly(methyl methacrylate) (PEO/PMMA). The combination of quasielastic neutron scattering with isotopic labeling and fully atomistic molecular dynamics simulations has allowed us to selectively investigate the dynamics of the two components in the picosecond-10 nanoseconds scale at temperatures close and above the Tg of the blend. The main focus was on the PEO component, i.e., that of the lowest Tg, but first we have characterized the dynamics of the other component in the blend and of the pure PEO homopolymer as reference. In the region investigated, the dynamics of PMMA in the blend is strongly affected by the alpha-methyl rotation; an additional process detected in the experimental window 65 K above the blend-Tg can be identified as the merged alphabeta process of this component that shows strong deviations from Gaussian behavior. On the other hand, pure PEO displays entropy driven dynamics up to very large momentum transfers. Such kind of motion seems to freeze when the PEO chains are in the blend. There, we have directly observed a very heterogeneous and moreover confined dynamics for the PEO component. The presence of the hardly moving PMMA matrix leads to the creation of little pockets of mobility where PEO can move. The characteristic size of such confined islands of mobility might be estimated to be of approximately 1 nm. These findings are corroborated by the simulation study, which has been an essential support and guide in our data analysis procedure.

Using broad-band dielectric spectroscopy (10−2–109 Hz) the merging of the α- and β-relaxations has been investigated for a polymer, syndiotactic poly(methyl methacrylate) (PMMA), in which the dielectric losses are dominated by a strong β-relaxation. The asymmetrically shaped β-relaxation cannot be described by a Cole–Cole function, not even at low temperatures where the α- and β-relaxations are well separated in frequency. At higher temperatures close to Tg (=404 K), the weak α-relaxation enters our dynamic window and rapidly merges with the β-relaxation. To investigate this merging process we first used a simple addition of two Havriliak–Negami (HN) equations to fit the spectra. The obtained relaxation time for the β-relaxation then displays a kink in its temperature dependence close to Tg. To gain further understanding of the merging, the data were analyzed by means of a regularization method in order to calculate the corresponding distributions of relaxation times directly from the actual measurements without the need of invoking any parametrical fitting functions. From these distributions we obtained the relaxation functions in time domain which were analyzed by adopting an ansatz proposed by Williams which implies that the α- and β-relaxations are statistically independent processes. The dynamics in the merging region of PMMA can then be described using extrapolations of the β-relaxation from low temperatures and the kink in the temperature dependence of the relaxation time of the β-relaxation obtained in the simple addition approach, is explained in terms of overlapping effects between the α- and β-processes, i.e., without invoking any change of relaxation mechanism.

We present fully atomistic molecular dynamics simulations for a realistic model of a glass-forming polymer: polyisoprene. The simulations are carried out at 363 K and extend until 20 ns. We calculate the self-part of the Van Hove correlation function G(s)(r,t), the mean-squared displacement , the second-order non-Gaussian parameter alpha(2)(t), and the incoherent intermediate scattering function F(s)(Q,t) for the main chain protons. In addition, we also calculate the density-density correlation function F(Q,t)/F(Q,0) and the second-order autocorrelation function M2(t) for different C-H bonds of the main chain. alpha(2)(t) shows a broad maximum centered at a time t(*) approximately 4 ps, which corresponds to the intermediate region of between microscopic dynamics and sublinear diffusion. The analysis of F(s)(Q,t), F(Q,t)/F(Q,0), and M2(t) focuses on the second slow step which is associated to the alpha relaxation. Following the usual experimental procedure this decay is described in terms of a Kohlrausch-Williams-Watts (KWW) function: A exp[-(t/tau)(beta)]. In the Q range below Q(max), where Q(max) is the value at which the static structure factor shows its first maximum, the Q dependence of the KWW relaxation time of F(s)(Q,t) follows a law tau approximately Q(-2/beta). This kind of Q dependence corresponds to a Gaussian behavior of G(s)(r,t) and F(s)(Q,t). This law has been experimentally found in this Q range for different polymers. In the higher Q range-not easily accessible experimentally-strong deviations from the Gaussian behavior manifest. This crossover from Gaussian to non-Gaussian behavior can be understood in the framework of the mode coupling theory as well as in terms of a crossover from homogeneous to heterogeneous dynamics. This last interpretation opens a possible way of rationalizing the apparent contradiction between the neutron scattering and relaxation techniques results concerning dynamical heterogeneity of the alpha relaxation.

We performed quasielastic neutron scattering experiments and atomistic molecular dynamics simulations on a poly(ethylene oxide) (PEO) homopolymer system above the melting point. The excellent agreement found between both sets of data, together with a successful comparison with literature diffraction results, validates the condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field used to produce our dynamic runs and gives support to their further analysis. This provided direct information on magnitudes which are not accessible from experiments such as the radial probability distribution functions of specific atoms at different times and their moments. The results of our simulations on the H-motions and different experiments indicate that in the high-temperature range investigated the dynamics is Rouse-like for Q-values below approximately 0.6 A(-1). We then addressed the single chain dynamic structure factor with the simulations. A mode analysis, not possible directly experimentally, reveals the limits of applicability of the Rouse model to PEO. We discuss the possible origins for the observed deviations.