Fragility plot

Ito et al. observed a remarkable similarity between kinetic fragility plot and normalized entropy data, namely, Kauzmann plot, exhibited in a scaled- / , form sheds considerable light into the role of excess entropy... 

Analysis of the so-called fragility plot, in which —log [D(T, p)] is depicted as a function of reduced temperature Tr/T, where the reference temperature Tr is taken to the temperature at which the diffusivity reaches some small but fixed value, indicates that with an increase in density, the fragility of the liquid increases [53]. 

The fragility plot of Angell is reproduced in Fig 3.20(a) (In rj vs TgIT). However, plots of similar kind using T as an iso-viscosity... 

Figure 2.10 Schematic representation of three h3rpothetical glass formers spanning the whole range of fragility. Plots are based on the modified VTF equation for glass formers with m values of 16, 55, and 200 [55].

This approach has been applied extensively in recent years to polymers [16,27-31]. From comparisons of segmental relaxation times for various polymers made on the basis of 7g-scaled Arrhenius plots, correlations between the shape of the relaxation function and chemical structure have been demonstrated [3,16,32,33]. Fragility plots are also useful in interpreting the relaxation behavior of polymer blends, since the relaxation function itself is complicated due to inhomogeneous broadening [34-37]. 

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.

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],...

Figure 32. The a-relaxation times for the glass formers studied in the present work (cf. Fig. 27). In addition data of diglycidyl ether of bisphenol A (DGEBA) and phenyl glycidyl ether (PGE) are included time constants as obtained from DS data sets of m-TCP and 2-picoline were combined with xrl from conductivity and light scattering measurements, respectively, (a) Relaxation times as a function of T Ts. The systems differ by the slope of Ta at Tg. (b) By plotting xr, as a function of the rescaled temperature z = m(T/Tg — 1) the effect of an individual fragility is removed and a master curve is obtained for systems with similar To. Solid line represents Eq. (41) with Kf) — 17. (c) Upper part master curve for xa according to Eq. (42). Deviations of the data from Eq. (42) (solid line) indicate break-down of the VFT equation. Lower part The ratio lg(ra/rvft) shows deviations from a VFT behavior most clearly. Dashed vertical lines indicate shortest and fastest tx, respectively, observed. All the figures taken from Ref. [275].

Figure 2.3 TgScaled Arrhenius plot showing data for molten salts ZnCl2 and calcium potassium nitrate (CKN), with data for the calcium nitrate hydrate (CaNOs-W ) and the tetrafluoroborates of quaternary ammonium (MOMNM2E, M= methyl, E = ethyl) and 1-n-butyl-3-methyl-imidazolium (BMI) cations, and the bis-oxalatoborate (BOB) of the latter cation, in relation to other liquids of varying fragility (from Xu, Cooper, and Angell [15]).

Equation (4-5) typically applies up to temperatures of Tg + 50 C or so. For higher temperatures, an Arrhenius temperature-dependence often applies for small-molecule liquids, even if they are fragile glass formers. For example. Fig. 4-6 shows a plot of 1/ logio(/oo/fp) versus temperature for propylene carbonate, where fp = Incop is the peak frequency (in... 

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