Fragility index

While the viscosity-temperature plots provide a clear visual estimate of fragility, it is more convenient to establish a single parameter that provides a quantitative measure of fragility. Several measures have been proposed, but the most commonly used fragility index is the m fragility or steepness index defined as [52, 55]  

Although Fig. 2.5 shows an excellent match between E j and E for As-Se glasses, it must be pointed out that significant mismatches in absolute values have been reported in some other systems [19]. 

However, the trend in and E is found to be systematically the same as a function of r . Hence, Fh remains a useful parameter to investigate the correlation between fragility and mean coordination. 

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Figure 5. The horizontal axis shows the value of fragility as computed from the thermodynamics by the RFOT theory, and the vertical axis contains the fragility directly measured in kinetics experiments. Here m is the so-called fragility index, defined according to m = [(ilogjoi(7 )/(i(l/7 )]j,. m is somewhat more useful than the fragility D, because deviations from...

III. Relationship between Fragility Index and Characteristics of Glass-Forming Liquids... 

This review chapter is focussed on surveying current developments on a topic of considerable current interest, namely, the concept and the corresponding phenomenonology of steepness or fragility index as a quantitative measure of... 

The steepness index or the fragility index m is defined as follows [105] ... 

III. RELATIONSHIP BETWEEN FRAGILITY INDEX AND CHARACTERISTICS OF GLASS-FORMING LIQUIDS... 

A comparison of Eqs. (2.20) and (2.18) leads to a remarkable expression that relates the fragility index, a kinetic property, with measurable thermodynamic quantities... 

Figure 2.2. A plot of the predicted fragility of several glass-forming polymeric liquids versus average experimental fragility index (adapted from Ref. 56). The solid line denotes the points for which the y-axis and the x-axis are equal, is a guide to the eye. The predicted correlation indicates an intricate connection between thermodynamic and kinetics of supercooled polymeric liquids [56],...

Consequently, we have a relationship between fragility index and the VTF constants [18,48] ... 

A comparison of this equation with Eq. (2.22), yields the desired relationship between fragility index and Narayanaswamy-Moynihan nonlinear parameter x [115]... 

Consequently, Eq. (2.42) expresses a metric between fragility index and the width of the glass transition region. 

Sokolov and coworkers have introduced a quantity R (T) that is a measure of the relaxational to the vibrational contribution in low-frequency Raman scattering [124], If R (T) is defined as the ratio of intensity minimum to intensity maximum at the Boson peak at a temperature T, then a correlation is observed between R (Tg) and the fragility index for glassy systems such as SiC>2, GeC>2, B2O3, PS, salol, PB, PVC, and o-terphenyl [124],... 

At temperatures below 1 K, the ratio of the constant pressure heat capacity Cp of the glass relative to the Debye heat capacity CDebye of a solid increases [124], Consequently, we introduce a quantity R2 defined as the ratio of Cp(glass) to that of the Debye heat capacity CDebye(solid) [124], Specifically, if R2 is normalized as R2 = (Cp/CDebye) lmn ] / [(Cp/coebye)rnax], then a correlation is observed between this quantity and the fragility index [124],... 

In this section we briefly address the issue of whether there is a connection between fragility index and the characteristics of glass-forming liquids below the glass transition, that is, in the glassy state. 

It has been recently realized that the activation enthalpy of the Johari-Goldstein beta ((3) relation is cross-correlated with the glass transition temperature of the alpha (a) relaxation of various glass formers [168,169]. This indicates a deep link between the fragility index of the a and the [3 relaxation [170],... 

Likewise, quantities derived from dependences of xa on P (V) and T (S), such as the steepness or the fragility index m = ii(log10x,j/d(Tg/T) T=T, are determined by both thermodynamics and many-body dynamics. These two factors may not affect m in the same proportion. For example, in some glass-formers the many-molecule dynamics may not be severe (i.e., smaller n), but the dependences of iJ( on the thermodynamic variables are strong, or vice versa. This scenario is observed for PC, KDE, and PDE, which have narrow dielectric dispersions (smaller n), but their m values are larger compared to other glass-formers [140]. Another example is the fact that m usually decreases with applied pressure. For any chosen xa, at elevated pressure the temperature can be raised to maintain xa constant. In particular, the P and T combinations can be chosen to... 

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