Viscous Liquids and the Glass Transition: A Potential Energy Barrier Picture

Abstract

Recent attempts have been made to assess the relative merits of the free volume and entropy theories of viscous flow in glass-forming liquids by accurate measurement of viscosity over wide temperature ranges, and subsequent comparison with the equations derived from these theories. In the author's view, this effort is misguided. The theories are crude and qualitative, and such tests are too stringent. It is better to make qualitative or semiquantitative comparison of a wide variety of physical phenomena; judged by this criterion, the entropy theory appears more successful. It is conjectured that further progress can be made by accepting the crude, naive character of any model we are likely to find tractable for the foreseeable future, and recognizing both the values and limitations of such models. A picture of the flow process in viscous liquids is proposed, in an attempt to answer certain questions about the molecular steps in flow either answered unsuccessfully or ignored by present theories, in the hope that it will lead a model closer to molecular reality but still sufficiently tractable to allow some range of predictive value. The model is based on the idea that in “viscous” liquids (shear relaxation time ≥10−9 sec) flow is dominated by potential barriers high compared to thermal energies, while at higher temperature, this will no longer be true. Certain concepts borrowed from the continuum theory of lattice defects are joined to a qualitative description of viscous flow due to Orowan, to provide a picture which leads to some qualitative predictions about flow and relaxation in the liquid and glassy states.

Relationship between the Nonexponentiality of Relaxation and Relaxation Time in the Problem of Glass Transition

“…After a concordant LRE, a local region supports less stress after the event than before; therefore, other local regions in the system should support more stress after that event than before. 35 Let ∆p be the increase of shear stress on a current LRE due to previous concordant LREs. If n is the current number of LREs, ∆p is a monotonically increasing function of n. The increase of stress on a currently relaxing region increases its activation barrier, V. It has been argued that V is given by the elastic shear energy of a surrounding liquid.…”

The jamming scenario—an introduction and outlook

“…Goldstein [130] has proposed that the slowing down of the dynamics is associated with the emergence of meta-stable states as a liquid is cooled. Such a roughening of the energy landscape is predicted by mean-field models of liquids and spins [131][132][133][134] at the so-called mode-coupling temperature T MCT .…”

Detailed microscopic analysis of self-interstitial aggregation in silicon. II. Thermodynamic analysis of single clusters

“…Each of these configurations, ␣, ͑so called inherent structures͒ can be identified by a local energy minimum, V ␣ , in the multidimensional potential-energy landscape ͑PEL͒ that defines the overall system. 43,44 For solids and certain fluid states, the system can be assumed to spend the majority of its time in one of the local minima, only occasionally making excursions over the saddles separating the minima. Based on these ideas, as applied in previous work on supercooled liquids and glasses, 45,46 a direct computational approach for measuring the total ͑classical͒ free energy of a defect cluster has been developed; a brief discussion of the method is provided here and further details are given in Ref.…”

“…1͑b͔͒ arises from the fact that higher formation energy configurations are increasingly spatially extended and therefore can generate more local minima in the potential energy landscape. 43,44 Several of the relaxed configurations for a given cluster were manually verified to correspond to welldefined local minima within the energy landscape. These configurations were perturbed by introducing small, random atomic displacements, and subsequently re-relaxed to the same local minimum.…”