Fragility of Polymeric Liquids: Correlations between Thermodynamic and Dynamic Properties
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Mat. Res. Soc. Symp. Proc. Vol. 455 0 1997 Materials Research Society
show near Arrhenius-like behavior (log aT - l/T), while the fragile liquids show complex nonArrhenius behavior and larger viscosity changes over the same temperature range. Figure 1, was constructed for 14 polymers using the following relationship which relates the viscosity q(T) and the viscosity q1(To) at a reference temperature T., to the temperature shift factor aT
log--lo((T ) --log a T,- C1(T-T) C2+T-T, r (T)
(I)
where C, and C2 are material constants in the WLF 2 relationship. We note that the Angell plot is often constructed using log q/Pa-s = 12 at TgIT= 1. Here we obtain a similar scaling by setting log aT =0 at T9. Consistent with the definition of Angell, a strong liquid is characterized as one with a fairly linear relationship and a much smaller change in viscosity with increasing temperature when compared to a fragile liquid which shows clearly nonArrhenius viscosity behavior and a strong initial dependence of viscosity on temperature. Here we chose to classify the polymers into 3 categories: strong, intermediate, and fragile. The classification results from the shift factor analysis for the 14 polymers analyzed in Figure 1 are given in Table 1. The classifications were defined by considering the changes in shift factor in the range of 0.6 < TgIT < 1. Strong liquids show a decrease of up to 11.0 decades in log aT over this range; whereas, intermediate strength is defined in the range of 11 to -14 in log aT. Fragile liquids are defined by a decrease of more than 14 decades in log aT. The names of the polymers represented as well as the values of the material constants C1, C2 , T., and Tg used to generate Figure 1 are given in Table 2. Fragility and Heat Capacity The heat capacity can also be used as a measure of strong or fragile behavior. Angell' proposed that small changes in heat capacity in going from the liquid to glassy state indicated strong liquids while larger changes indicated more fragile behavior. In his work, Angell used C, I/C pgas a measure of fragility and the values of CP,/CP9 for various polymers are given in Table 3 with the corresponding behavior classified in Table 1. Clearly the results do not correlate well with the segmental relaxation data. In particular both PE and PBD exhibit a relaxation response characteristic of a strong liquid yet the CPI/C.9 ratio is consistent with more fragile behavior. Another conflicting result is seen in the case of PC where the relaxation response suggests fragile behavior while the CP1/C Pgratio is consistent with a strong liquid. The change in heat capacity at Tg, ACW, is often used in glassy physics and can be related to the change in configurational entropy due to freezing in of polymer conformations upon cooling from the liquid to the glassy state. We propose here to use ACP as an alternative measure of the fragility and normalize it by the monomer molecular weight, M.. This normalization takes into account, in a sense, the effect of repeat unit size (molecular weight).
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