Fragility parameter

In estimating the fragility parameters, it is convenient to work in terms of an intermediate random variable known as the factor of safety F. This is defined as the ratio of the grouiiti-aeederation capacity A to the safe shutdown earthquake (SSE) acceleration used in plant tlesign. 

Figure 8. The fragility parameter m is plotted as a function of the NMT nonlinearity parameter Xnmt- The curve is predicted by the RFOT theory when the temperature variation of >o is neglected. The data are taken from Ref. [49]. The disagreement may reflect a breakdown of phenomenology for the history dependence of sample preparation. The more fragile substances consistently lie above the prediction, which has no adjustable parameters. This discrepancy may be due to softening effects.

This relation enables evaluating the fragility parameter Ks as well as the structural relaxation times r over the whole temperamre range To < T < Ta-Because T] depends on polymer microstructure and molar mass, Ap likewise exhibits the same dependence. Computations of Ks within the entropy theory have not been possible before. 

Figures 11 and 12 analyze the variation of the fragility Kg with polymer class and with molar mass, respectively. The fragility parameter Kg is the slope of the curves depicted in Fig. 11. (Figure 11 departs from Fig. 10 only by the use of a...

Figure 11. Same as in Fig. 10, but the configurational entropy ScT is normalized by the product of the critical entropy si and the activation energy Ap (estimated from Eq. (42) and the computed crossover temperature 7i). According to Eq. (41), the slope of the resulting curves defines the fragility parameter K. (Used with permission from J. Dudowicz, K. F. Freed, and J. F. Douglas,... 

Figure 14. The fragility parameter v t = Ti/ Ti — Tg) calculated from the LCT as a function of the inverse number l/M of united atom groups in individual chains for constant pressure (P = 1 atm 0.101325 MPa) F-F and F-S polymer fluids. The single data point denoted by o refers to high molar mass F-S polymer fluid at a pressure of P = 240 atm (24.3 MPa).

Equation (3.9) clearly indicates that ionic conductivity could be improved by lowering the Tg of the system. The difference in the temperature dependences of ionic conductivity (and viscosity) for ion-conductive glass-forming materials has been discussed by Angell et al. using fragility parameters [115]. 

Fig. 3.53 Viscosity data from Fig. 3.51 plotted against the volume (normalized by the ambient-pressure volume). The curves are fits obtained by the free-volume theory (eqn 3.9.5), the resulting parameters being for methanol, B = 2.22 0.05 and V = 33.8 0.1 A for 1,2-propanediol, S = 6.7 0.3 and 14 = 71.9 0.5 A. Extrapolation of these fits to T = 10 Pa s gives the indicated glass-transition pressures, P. The strong curvature of the methanol data indicates the more fragile behavior of this fluid, which is reflected in the fragility parameters (calculated from equation 5 given by Cook et a .)F For methanol mp = 289 6 and for 1,2-propanediol mp = 123 5.

It describes the temperature dependence of viscosity in an undercooled liquid, where rjo and are constants, and D is the fragility parameter. Undercooled liquids with large D values (>50) are referred to as strong , and those with low D values (<10) as fragile . Molecular mobility behaves in a similar way and t, the mean relaxation time, may also be described in a similar fashion ... 

An estimate of the fragility of a given glassy preparation is required to enable a reliable calculation of its shelf life to be made. The estimation of the fragility parameter itself requires a number of thermoanalytical measurements to be performed. Three methods, in decreasing order of experimental rigour, are given below. 

Replacing AE with A j- at a single temperature, an alternative fragility parameter m can be defined by... 

Figure 9 Diagrammatic representations of typical DSC scans of the glass transition showing the quantities required for the determination of the fragility parameter and To. The first scan, usually taken after storage (annealing), reveals an endotherm of the relaxation enthalpy, which disappears after recooling and immediate reheating...

The fragility parameter is normally large for liquids that exhibit the non-Arrhenius-type temperature dependence of the relaxation time. One extreme example is glycerin. Its fragility parameter is as high as 200 (Boehmer et al. 1993 Richer and Angell 1998). 

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