Length Scale of Dynamic Heterogeneities at the Glass Transition Determined by Multidimensional Nuclear Magnetic Resonance

Abstract

We directly measure the equilibrium length scale of dynamic heterogeneities close to the glass transition by means of a new multidimensional NMR experiment. The spatial information is gained from a proton spin diffusion experiment combined with two 2D 13 C exchange sequences via appropriate back and forth transfer of magnetization between 13 C and 1 H spins. For poly(vinyl acetate) at 10 K above the glass transition we detected a length scale of 3 6 1 nm. [S0031-9007(98)07244-5] PACS numbers: 64.70.Pf, 76.60. -k Supercooled amorphous systems exhibit a complex dynamic behavior (for a recent review, see Ref. [1], and references therein). For most glass-forming systems this results in highly nonexponential a relaxation. Recent experiments have demonstrated that the nonexponential time behavior is related to a superposition of relaxation processes, each characterized by an individual rate hence giving rise to the notion of dynamic heterogeneities [2-9], composed of slow and fast relaxators. Similar results have also been observed in polymer simulations [10].Hence dynamic heterogeneities are an essential ingredient of the glass transition. Two characteristic properties of dynamic heterogeneities-time scale of fluctuations of rates and length scale j het of temporary clusters of slow segments-are sketched in Fig. 1.Information about the time scale of fluctuations within the distribution of reorientation rates has already been obtained from reduced four-dimensional solid state exchange NMR (4D experiment) [3,6,7,11] and from photobleaching [5]. Application of the 4D experiment to a variety of polymers [3,6,11] and low-molar glass formers [7] has clearly shown that the fluctuations within the heterogeneous rate distribution occur on the same time scale as the relaxation process itself.The length scale j het of the dynamic heterogeneities may be related to that of cooperatively rearranging regions (CRRs), first postulated by Adam and Gibbs [12,13]. It is reasonable to assume that j het is an upper limit for the length scale of CRRs. As j het is a fundamental parameter of the glass transition, several attempts to determine its value have been reported. Most approaches, however, involve perturbations of the system itself. Either the liquids are confined to pores [14][15][16] or probe molecules are added to the sample [17][18][19]. Information about the characteristic length scale is derived from the dependence of the a-relaxation properties on the size of the confining structure or the probe molecule. Interpretation of these experiments has to take into account that, e.g., the relaxation in pores strongly depends on the surface properties of the host [15,16] and that large probe molecules may change the local dynamics. Within the model of cooperatively rearranging regions Donth has estimated the length scale of these regions to be close to 2 nm [13,20].Obviously it is desirable to have a method which allows one to directly measure the length scale of dynamic heterogeneities of the glass transition in a nonperturbative way. ...

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