Dynamical heterogeneities in glass-forming materials
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both contributions. An intuitive sketch for the example of one-dimensional translational dynamics is shown in Fig.1. Homogeneous contributions occur, e.g., by correlated backand-forth jumps (see theory section).
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Figure 1: (a) Sketch of the limits of heterogeneous and homogeneous relaxation (heterogeneous: different exponential processes, homogeneous: identical non-exponential processes). The slow processes in the heterogeneous limit correspond to the thicker line. In both limits the simple two-time relaxation functions f(t) of the whole ensemble are identical. (b) Visualisation of both limits for the example of one-dimensional dynamics. Left: superposition of a slow (thick line) and a fast particle both performing a one-dimensional random walk. Exchange processes between a fast and a slow rate, also indicated, do not change the type of relaxation! Right: identical one-dimensional dynamics with a strong preferencefor correlated back-and-forthjumps giving rise to homogeneous relaxation. In case the relaxation contains heterogeneous contributions it is possible to distinguish fast and slow segments (from now on we use the "polymer language"). Then one can ask the question on which timescales a fast segment becomes slow and vice versa, see Fig.2. In recent theoretical work this property has been quantified in terms of a rate memory parameter [7], see also [81,[9]. In general, information about the type of relaxation and the rate memory can be obtained from analysis of multi-time correlation functions. Experimentally they are accessible by multidimensional NMR-experiments (10]. This technique has been applied to both, amorphous polymers [4, 5, 9] and low molar mass systems [11]. Very recently, the information about the rate memory has also been obtained by fluorescence spectroscopy [12] and spectral hole burning in dielectric relaxation [13].
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Figure 2: (a) Sketch of fluctuations within the heterogeneous rate distribution. (b) Sketch of a bimodal distribution of rates with an exchange rate F. The purpose of this paper is three-fold. First, it summarizes the theoretical basis of the concepts of the type of relaxation and the rate memory. Second, application of these new concepts is exemplified for multidimensional NMR experiments as well as for computer simulations of a model polymer. Third, a rather detailed picture about the dynamics of polymers is extracted from the experimental and numerical results. Among others it is clarified how freezing influences the dynamics of polymers. THEORY General The translational dynamics of polymers is often analysed in terms of the incoherent scattering function p(0; At 01 )= (cosq l(t 1 )--(t 0 ))). (1) rl(ti) is the position of a segment at time ti, the brackets denote the ensemble average, Atij = tj - ti, and q-denotes a wave vector, see, e.g. [14]. Furthermore we introduce the abbreviation Afixj =_ (ti) - fl(tj). Here the properties of the system are correlated at two different time
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