Molecular dynamics (MD) simulations on glass forming systems of very different nature, such as Selenium, ortotherphenyl, water, or Lennard- Jones liquids have shown a series of “universal features” for the non-Gaussian parameter α₂(t) corresponding to the self-motion of the atoms in the α-relaxation regime. The observed behaviour appears to be intrinsically related to the universal character of the α-relaxation. A combination of MD-simulations and neutron scattering on polyisoprene, based on a feedback procedure between the two techniques, has allowed us to establish that the above mentioned “universal features“ of α₂(t) are also found in glass-forming polymers. We show that these features are nicely captured by a simple anomalous jump diffusion model with a distribution of jump lengths.

The freezing of the structural (a) relaxation in a glass-forming system leads to the glass transition phenomenon – still one of the most intriguing problems in condensed matter physics. Therefore, the understanding of the molecular motions during this relaxation is of utmost importance to shed some light on the glass formation process. Neutron scattering (NS) and Molecular Dynamics (MD) simulations are essential for this goal. For instance, during the last years, extensive NS investigations of the incoherent scattering function F_s(Q,t) have allowed a universal behaviour for the self-atomic motions in the α-relaxation regime of glass forming systems, including polymers, to be established. As figure 1 evidences, F_s(Q,t) shows a stretched exponential or Kohlrausch-Williams-Watt (KWW) functional form characterized by the exponent ß: F_s(Q,t) exp[-(t/τ_w)^ß] with a characteristic time t/τ_w(Q) that clearly depends on Q (see e.g. [1,2]). This observation implies the diffusive nature of the atomic motions in this regime.

Furthermore, results on polymers accumulated over more than ten years [1,3] show that in the low Q-regime (approx. 0.2 <= Q <= 1.5 Å^-1) the Q-dependence of τ_w can be described as: t/τ_w Q^-2/ß (see for example the inset of figure 1). Considering this expression in F_s(Q,t), one immediately realizes its Gaussian form. This implies that for this process the non-Gaussian parameter α₂(t), which measures deviations ~ Q⁴ in the exponent of F_s(Q,t), has to be very close to zero.

A Gaussian F_s(Q,t) is in apparent contradiction to results from MD-simulations on glass forming systems other than polymers (Lennard-Jones liquids, water, ortho-terphenyl and Selenium), from which clearly non negligible values for α₂(t) have been deduced. Even features of universal character have been found for α₂(t); the existence of a maximum that increases with decreasing temperature and shifts according to the thermal behaviour of the structural relaxation time. Since deviations from Gaussian behaviour are usually understood as a signature of dynamical heterogeneities, conclusions in this direction have been drawn from such MD-simulations results. Thus the question arises: do glass forming polymers behave in a different way? We note that a close look at the data in the inset of figure 1 suggests deviations from the proposed Gaussian law τ_w(Q) . Q^-2/ß in the high Q-range. At this point, in order to reach some deeper understanding we decided to take a twofold approach: we performed fully atomistic MD-simulations [4] and neutron scattering measurements on the same polymer, polyisoprene (PI). The experiments included NSE (ILL and Jülich, see some results on figure 1) and IN13 measurements, extending the investigated Q-range as much as possible, especially towards high Q. Using a sample with deuterated methyl groups (PId3) the experimental results mainly reflect the self motions of the main chain protons, that can also be followed from the atomic trajectories delivered by the MD-simulations. Figure 2 shows the Q-dependence of τ_w obtained from the two approaches. First of all, we note an impressive agreement between both kinds of results, validating the MD-simulations. Moreover, the data unequivocally confirm the Gaussian-like behaviour in the Qrange approx. Q <= 1 Å^-1, while clear signatures of deviations become evident at higher Q-values. Having validated our MD-simulations, we can take advantage of them and compute magnitudes that are not easily experimentally accessible, like α₂(t) and the mean squared displacement < r²(t)> of the main chain protons. They are shown in figure 3(a), while figure 3(b) displays the calculated F_s(Q,t) for several Q-values. As reported for the other glass-forming systems, a main maximum is indeed found for α₂(t) at t* 4 ps, just in the early stages of the decaging process identified with the a-relaxation. The shadowed area in figure 3 shows the region where α₂(t) takes significant values. We can immediately see that for low Q-values this area only covers the initial part of the slow decay (a-regime) of F_s(Q,t). However, as Q increases, the marked time range starts to cover almost completely the slow decay. This naturally explains the finding of the deviations from Gaussian behaviour of F_s(Q,t). at high Q-values. What could be the origin of such deviations? The way the characteristic time departs from the Gaussian expectation (figure 2) strongly reminds us of the very well known manifestations of the discrete nature of diffusion in simple jump diffusion models. Based on this similarity, we have proposed a model that considers a distribution of elementary jump lengths underlying the anomalous diffusion undergone by the atoms in the a-process [5,6]. As can be appreciated in figure 2, such an extremely simple approach allows a very accurate description of the Q-dependence of τ_w in the whole Q-range investigated. The associated distribution of jump lengths (inset of figure 2) has a maximum at about 0.4 Å. We emphasize that this model also semiquantitatively reproduces the behaviour of α₂(t) [see figure 3(a)], within its range of validity (above 1 ps approximately) [5,6]. It is finally noteworthy that the main “universal features” reported in the literature for α₂(t) are also naturally deduced in this approach [5,6]. This suggests that the essence of the universal deviations from Gaussian behaviour in the self-motions of atoms during the structural relaxation regime lies in the distribution of discrete steplengths underlying the anomalous diffusion. Initial analysis of the MD trajectories confirms this model of diffusion and detailed analysis is underway.