The WLF Parameters

Although no extensive theoretical conclusions can at present be drawn from the calculated WLF parameters for the copol3mier systems, they are presented in Table 3 for the sake of cranpleteness for two counterion copolymer systems, i. e., Na+-Ca+ and Na -La .  

---

Eisenbach also discussed the significance of the WLF-parameters with respect to the fractional free volume at Tg and to the difference of thermal dilation coefficients of rubbery and glassy states. 

The magnitudes of the parameters of the Arrhenius and the Fulcher equations for the studied concentrated apple and grape juices are given in Tables 2-6 and 2-7, respectively. The physical interpretation of the three constants in the Fulcher equation is ambiguous, but by translating them in terms of the WLF parameters their significance can be clarified and it is functionally equivalent to the WLF equation (Ferry, 1980 Soesanto and Williams, 1981) ... 

The behavior of the WLF parameters can be explained using the free-volume concept. The two WLF parameters are described in the following form according to the free-volume theory developed by Cohen and Turnbull [105,106] ... 

As was already stated (see Figure 6), the temperature dependence of the shift factor aT is a function of the elastomer phase content. The strong effect of the rubber content on the temperature dependence of the shift factor aT could be explained by an increase in free volume of the SAN resin induced by the elastomer phase, as was suggested by Prest and Porter (13) for polystyrene-poly (phenylene oxide) blends. In order to verify this hypothesis, log aT experimental data for SAN and relative blends were used to calculate the WLF parameters and, in turn, the free volumes (f0) at the reference temperature (T0) and the thermal expansion coefficients (a) by the equation ... 

For materials that obey the time-temperature superposition principle, the dynamic moduli can be rescaled using appropriate shift factors to obtain a master curve. The temperature dependence of the horizontal shift factor is usually described by the WLF equation. Explain how the WLF parameters (Zi, Oj. and can be determined from a set of log % vs. temperature data. 

This is identical to the WLF expression provided the Vogel parameters and the WLF parameters are related as... 

PMMA (conventionai) 390.5 14.27 63.1 [81] 37,s of the softening dispersion. However, the T-dependence as reported is weaker than that given in the entry above. The reason for this discrepancy is not clear. We recommended the WLF parameters given in the entry above because they are corroborated by two different experimental measurements. 

Note that for many polymers the values of the WLF parameters are close to the so-called imiversal values, which are Ci = 17.44 and C2 = 51.6 K when Tr = Tg. (When no other information is available, the universal values for Ci and C2 can make useful approximations to actual behavior.)... 

The relationship between t and c as given in Eq. (1) was also experimentally derived for the epoxide oligomers [7]. Furthermore, each oligomer has the following relations [7] between the WLF parameters and the exponent m in Eq. (1) ... 

To is the reference temperature. The WLF equation follows from free volume considerations and is usually used within about 100 °C of the glass transition temperature. The data for the PVME are seen to follow the WLF equation quite well, with Cj = 7.3 and C2 = 220 K. (There are universal values of the WLF parameters... 

When considering the temperature dependence of the shift factor we found that, whereas for high molecular masses (above that between entanglements) the WLF parameters are the same... 

It should be mentioned that values of oj determined for a neat homopolymer, via the WLF equation, from viscosity measurements should not be used for a block copolymer unless the monomeric friction coefficients of the constituent blocks are identical. For instance, Wang et al. (2002) determined values of for neat poly(ethylenepropylene) (PEP), via the WLF equation, from viscosity measurements, and then used them to obtain logG versus log and logG" versus log T plots for EV-block-poly(dimethylsiloxane) (PDMS) copolymers in both the ordered and disordered states. Such an approach is not justified for the following reasons. (1) They tacitly assumed that the values of determined for a neat PEP at different temperatures were identical to those for the PEP-ft/oc -PDMS copolymer. Such an assumption would not be valid because the WLF parameters Cj and C2 for a neat PEP cannot be the same as those for microphase-separated PEP-fetoc -PDMS copolymer. Note that the difference in glass transition temperature between PEP and PDMS is very large (AEg 80 °C)" ... 

---