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. ...

We study the relation of the potential energy landscape (PEL) topography to relaxation dynamics of a small model glass former of Lennard-Jones type. The mechanism under investigation is the hopping betweem superstructures of PEL mimima, called metabasins (MB). From the mean durations τ of visits to MBs, we derive effective depths of these objects by the relation Eapp = d ln τ /dβ, where β = 1/kBT . Since the apparent activation energies Eapp are of purely dynamical origin, we look for a quantitative relation to PEL structure. A consequence of the rugged nature of MBs is that escapes from MBs are not single hops between PEL minima, but complicated multi-minima sequences. We introduce the concept of return probabilities to the bottom of MBs in order to judge whether the attraction range of a MB was left. We then compute the energy barriers that were surmounted. These turn out to be in good agreement with the effective depths Eapp, calculated from dynamics. Barriers are identified with the help of a new method, which accurately performs a descent along the ridge between two minima. A comparison to another method is given. We analyze the population of transition regions between minima, called basin borders. No indication for the mechanism of diffusion to change around the mode-coupling transition can be found. We discuss the question whether the one-dimensional reaction paths connecting two minima are relevant for the calculation of reaction rates at the temperatures under study.

In this review a systematic analysis of the potential energy landscape (PEL) of glass-forming systems is presented. Starting from the thermodynamics, the route towards the dynamics is elucidated. A key step in this endeavor is the concept of metabasins. The relevant energy scales of the PEL can be characterized. Based on the simulation results for some glass-forming systems one can formulate a relevant model system (ideal Gaussian glass-former) which can be treated analytically. The macroscopic transport can be related to the microscopic hopping processes, using either the strong relation between energy (thermodynamics) and waiting times (dynamics) or, alternatively, the concepts of the continuous-time random walk. The relation to the geometric properties of the PEL is stressed. The emergence of length scales within the PEL approach as well as the nature of finite-size effects is discussed. Furthermore, the PEL view is compared to other approaches describing the glass transition.

It is possible to formulate the thermodynamics of a glass forming system in terms of the properties of inherent structures, which correspond to the minima of the potential energy and build up the potential energy landscape in the high-dimensional configuration space. In this work we quantitatively apply this general approach to a simulated model glass-forming system. We systematically vary the system size between N=20 and N=160. This analysis enables us to determine for which temperature range the properties of the glass former are governed by the regions of the configuration space, close to the inherent structures. Furthermore, we obtain detailed information about the nature of anharmonic contributions. Moreover, we can explain the presence of finite size effects in terms of specific properties of the energy landscape. Finally, determination of the total number of inherent structures for very small systems enables us to estimate the Kauzmann temperature.

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