Cooperative strings and glassy interfaces

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 112; no. 27; pp. 8227 - 8231
• Main Authors: Salez, Thomas, Justin Salez, Kari Dalnoki-Veress, Elie Raphaël, James A. Forrest
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 07.07.2015; National Acad Sciences
• Subjects: cooperative rearrangement; Glass; glass transition; glass transition temperature; Mathematics; Molecular physics; Phase transitions; Physical Sciences; Polymer films; polymers; Probability; Temperature effects; Thickness measurement; thin films; glass transition; cooperative rearrangement; thin films
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.1503133112

We introduce a minimal theory of glass formation based on the ideas of molecular crowding and resultant string-like cooperative rearrangement, and address the effects of free interfaces. In the bulk case, we obtain a scaling expression for the number of particles taking part in cooperative strings, and we recover the Adam–Gibbs description of glassy dynamics. Then, by including thermal dilatation, the Vogel–Fulcher–Tammann relation is derived. Moreover, the random and string-like characters of the cooperative rearrangement allow us to predict a temperature-dependent expression for the cooperative length ξ of bulk relaxation. Finally, we explore the influence of sample boundaries when the system size becomes comparable to ξ . The theory is in agreement with measurements of the glass-transition temperature of thin polymer films, and allows quantification of the temperature-dependent thickness h ₘ of the interfacial mobile layer.