Fragility (glass physics)

Fragility characterizes how rapidly the viscosity of a glass forming liquid approaches a very large value approximately 1012 Pa s during cooling.

Fragility is one of the most important concepts to understand viscous liquids and glasses.

Fragility may be related to the presence of dynamical heterogeneity in glass forming liquids, as well as to the breakdown of the usual Stokes–Einstein relationship between viscosity and diffusion.

Formally, fragility reflects the degree to which the temperature dependence of the viscosity (or relaxation time) deviates from Arrhenius behavior.

[1][2] 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:

[7] The Bruning–Sutton fragility parameter m relies on the curvature or slope of the viscosity curves.

Doremus indicated that practically all melts deviate from the Arrhenius behaviour, e.g. the activation energy of viscosity changes from a high QH at low temperature to a low QL at high temperature.

Changes that occur in the activation energy are unambiguously characterised by the ratio between the two values of activation energy at low and high temperatures, which Doremus suggested could be used as a fragility criterion: RD=QH/QL.

The Doremus’ criterion of fragility can be expressed in terms of thermodynamic parameters of the defects mediating viscous flow in the oxide melts: RD=1+Hd/Hm, where Hd is the enthalpy of formation and Hm is the enthalpy of motion of such defects.

[8] The fragility can also be expressed analytically in terms of physical parameters that are related to the interatomic or intermolecular interaction potential.

[9] It is given as function of a parameter which measures the steepness of the interatomic or intermolecular repulsion, and as a function of the thermal expansion coefficient of the liquid, which, instead, is related to the attractive part of the interatomic or intermolecular potential.

[10] Recent synchrotron radiation X-ray diffraction experiments showed a clear link between structure evolution of the supercooled liquid on cooling, for example, intensification of Ni-P and Cu-P peaks in the radial distribution function close to the glass-transition, and liquid fragility.

Advances over the last decade have linked this phenomenon with the presence of locally heterogeneous dynamics in fragile glass formers; i.e. the presence of distinct (if transient) slow and fast regions within the material.

[1][14] This effect has also been connected to the breakdown of the Stokes–Einstein relation between diffusion and viscosity in fragile liquids.