Frequency shift factor

Fig. 9.10 (A) Frequency shift factors aj and (B) modulus shift factor bj as a function of temperature. Reprinted from [40],...

The frequency dependence of G" also progresses monotonically with silicate loading from co10 for PCLC1 to co0 65 for PCLC5. The frequency shift factors for the PCLC samples appear to be independent of the silicate loading consistent with the results for the frequency shift factors previously obtained for PCL [54]. 

Because t] data are obtained at low strains with minimal alteration of the STD structure, they provide unique opportunities for studying applicable models. Further, empirically obtained frequency shift factor (Ferry, 1980) has been used successfully in time-temperature superposition studies on food polymer dispersions (Lopes da Silva etal., 1994), and the applicability ofsimilar, if not identical, scaling of frequency was explored for STDs (Yang and Rao, 1998a). 

These frequency shift factors can be easily translated into temperature shift factors and show a linear relationship for both PE/EMA-Zn-40 and PE/EMA-Zn-20 as a function of PE content. Earnest and Macknight (16) have indicated that the At s reflect a difference in the enthalpies for the two types of interactions Involved (H-bonding versus thermoreverslble crosslinking). These authors state that, as the percent ionization is increased in an EMA-salt, the At for (EMA-salt-EMA-ester) should Increase accordingly. Following this argument, but chosing EMA as the reference, the At for (EMA-salt-EMA) is expected to increase as the... 

Figure 1. Linear dynamic oscillatory shear response of the 50K PBA based Si02 hybrid sample. The data collected at temperatures between 30 and 80 °C were reduced to a single master curve using the principle of time-temperature superpositioning. The horizontal frequency shift factors (af were similar to that for the pure PBA homopolymer.

Example calculation for quartz. We show, as an example, the calculation of a partition function ratio for quartz at 25°C (Table 2). The input data are taken from the compilation of frequencies and frequency shifts factors (ra /ra) given in Polyakov and Kharlashina (1994), with minor modifications (see below). The shift factors in this compilation are mostly from Sato and McMillan (1987), who directly measured the spectrum of quartz. The degeneracy column in the table gives the number of vibrational modes with a particular frequency, and therefore the number of times that mode must be counted in the calculations. Including degeneracies, there are 27 vibrational modes. 

The frequency shift factor, ar, has been related to the free-volume fraction,/ [Ferry, 1980]. There is a direct correlation between/and the Simha-Somcynsky (S-S) hole fraction, h [Utracki and Simha, 2001b]. Under ambient pressure, h depends on the reduced temperature [Utracki and Simha, 2001a] ... 

When oscillatory shear data are being shifted, the frequency shift factor is simply a, and the reduced frequency is ... 

---