Evaluation of heterogeneity measures and their relation to the glass transition.

For most phase transitions, dynamic slowdown is accompanied by a static structure change. However, in the case of the supercooled liquid, which is a special liquid state below the melting temperature, one observes pronounced dynamic slowdown, i.e., diffusion coefficient, relaxation time, and viscosity change 10-14 orders of magnitude within a relatively small temperature range. This occurs without the pronounced static structure change observed in other phase transitions. Over the past several decades, there has been extensive research aimed to understand why the glass transition occurs, to establish what the glass transition exactly is, and to improve our understanding of how molecules move near to the glass transition. In the present work, we have examined the idea that the dramatic reduction in molecular mobility or dynamic slowdown in a supercooled liquid during cooling from above T(g) occurs because of the increasing length scale of heterogeneous subregions, or the cooperatively rearranging regions (CRR) proposed by Adam and Gibbs. Although there is little doubt about the existence of microscopic heterogeneous regions, the absence of the "universal" parameters to characterize the temperature dependent heterogeneity data and type of temperature divergence among different parameters over the same temperature range suggests the possibility that the heterogeneity itself may not relate to the CRR directly and thus may not be the key cause of the glass transition phenomenon. It remains an important research challenge to identify which, if any, of the heterogeneity parameters relates in a causal manner to the glass transition.