Fragility

In glass physics, fragility characterizes how rapidly the dynamics of a material slow down as it is cooled toward the glass transition: materials with a higher fragility have a relatively narrow glass transition temperature range, while those with low fragility have a relatively broad glass transition temperature range. Physically, fragility may be related to the presence of dynamical heterogeneity in glasses, as well as to the breakdown of the usual Stokes-Einstein relationship between viscosity and diffusion.

Formally, fragility reflects to what degree the temperature dependence of the viscosity (or relaxation time) deviates from Arrhenius behavior. This classification was originally proposed by Austen Angell. The most common definition of fragility is the "kinetic fragility index" m, which characterizes the slope of the viscosity (or relaxation time) of a material with temperature as it approaches the glass transition temperature from above:

${\displaystyle {m}:=\left({\partial {\log _{10}\eta } \over \partial \left(T_{g}/T\right)}\right)_{T=Tg}={\frac {1}{\ln 10}}\left({\partial {\ln \eta } \over \partial \left(T_{g}/T\right)}\right)_{T=Tg}={\frac {T_{g}}{\ln 10}}\left({-\partial {\ln \eta } \over \partial T}\right)_{T=Tg}}$

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