Original Research ARTICLE
Topological constraint theory for network glasses and glass-forming liquids: A rigid polytope approach
- 1University of California, Davis, United States
A variation of the topological constraint theory is proposed where an atomic network is modeled as a collection of rigid polytopes, and which explicitly distinguishes the bond angle constraints as well as rigid bond angles from flexible ones. The proposed theory allows for direct quantitative estimation of the fraction f of zero-frequency or floppy modes of the network. A preliminary model is proposed to connect the theory to the two key experimental observables that characterize glass-forming liquids, i.e., the glass transition temperature Tg and fragility m. The predicted values are tested against the literature data available for binary and ternary chalcogenides in the Ge-As-Se system. The Tg is related to f in this model by the activation entropy associated with the bond scission-renewal dynamics that is at the heart of transport and relaxation in glass-forming liquids. On the other hand, the large and temperature-dependent conformational entropy contribution of the 1-polytopes, i.e., the selenium chain elements in these chalcogenide glass-forming liquids, plays a key role in controlling the variation of m with f.
Keywords: supercooled and glassy state, rigid polytope, activation entropy, Glass tranisition, Fragility, topological constraint theory
Received: 15 May 2019;
Accepted: 14 Aug 2019.
Edited by:Matthieu Micoulaut, Sorbonne Universités, France
Reviewed by:Yann Gueguen, University of Rennes 1, France
Gerardo Naumis, National Autonomous University of Mexico, Mexico
Copyright: © 2019 Sen and Mason. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Prof. Sabyasachi Sen, University of California, Davis, Davis, 95616, California, United States, email@example.com