Towards a Molecular View of Glass Heterogeneity

摘要

In spite of the technological importance and ubiquity of glasses in our lives, we still lack a clear understanding of what actually happens when a non-crystallizing liquid is cooled down and turns into a disordered solid. As temperature is lowered, the liquid's viscosity increases by several orders of magnitude, and relaxation appears to come to a stop. For practical purposes, the glass-transition temperature T_g is defined as the point where relaxation becomes too slow to measure, when the viscosity reaches about 1 TPa-s. On a logarithmic scale of viscosity, there is no apparent accident or remarkable point on the viscosity curve, only a smooth Arrhenius law for strong glasses, such as silica, or a Vogel-Fulcher law for fragile glasses, such as most molecular glass formers. Combining the material's shear modulus (which characterizes its elasticity) with this viscosity, we can define a characteristic time, which, for a homogeneous medium, is scale-independent. This time, called the alpha relaxation time, can be seen as the reorganization time of the material, down to molecular scales. A characteristic shear modulus of 1 GPa and the glassy viscosity of 1 TPa-s therefore give a relaxation time of 1000 s, the reorientation time of a typical molecule at the glass transition (15 orders of magnitude longer than the relaxation time of a small molecule in the normal liquid phase, 1 ps). The above simple argument relies on the assumption of a spatially homogeneous medium and conveys a picture of the glass as a "liquid in slow motion". However, it has been known for a long time that this naive picture is deeply misleading. Adam and Gibbs have explained why the cooperation of many molecules is necessary to obtain large viscosities, within larger and larger cooperatively rearranging regions (CRRs) as the viscosity increases. Such a highly hierarchical arrangement of molecules is totally incompatible with the structure of the high-temperature liquid, in which all molecular correlations are short-ranged. The structure of a glassy liquid must therefore differ in profound ways from that of the high-temperature liquid. Although glass-forming materials have long been known to present heterogeneity,'3 no structural differences spring to the eye from regular ensemble measurements. Presumably, the inhomogeneities responsible for the cooperating rearranging regions are too subtle to show up and are averaged out in most ensemble measurements. Therefore, to understand glassy behavior, one must include heterogeneity as an essential part of the material description.