# The impact of the stretching exponent on fragility of glass-forming liquids

Authors
Type
Published Article
Journal
Journal of Thermal Analysis and Calorimetry
Publisher
Springer Netherlands
Publication Date
Sep 17, 2016
Volume
127
Issue
3
Pages
1975–1981
Identifiers
DOI: 10.1007/s10973-016-5828-5
Source
Springer Nature
Keywords
The paper compared two factors governing fragility. The first one is thermodynamic, depending on the change in configurational entropy. The second one is kinetic and is determined by the stretching exponent β. Using a simple mathematical development, we show that the kinetic term mK=f(βTg)∂lnβT/∂lnT|T=Tg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_{\text{K}} = f( {\beta_{{T_{\text{g}} }} } )\partial \ln \beta \left( T \right)/\partial \ln T|_{{T = T_{\text{g}} }}$$\end{document} is always smaller than 1, where Tg is the glass transition temperature and f(βTg)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f( {\beta_{{T_{\text{g}} }} } )$$\end{document} is the given functions of the stretching exponent at T = Tg. As a result, the contribution of the kinetic term on the fragility of strong glasses is <6 %. Fragile glasses have a larger value of fragility index m, and for them, the influence of the kinetic term is significantly smaller. In any case, the thermodynamic term plays the main role in fragility and the kinetic one can be neglected.