Frequency of maximum loss

In order to compare frequencies of maximum loss to l/( r), the frequency dependent susceptibility corresponding to the WW function was calculated as a function of / . The values of ra>max and r/( z ) are listed as a function of P in Table 1. The frequency of maximum loss correlates much better with the parameter r and depends only weakly on p. The exact relationship presented in the Table should allow data obtained from PCS to be compared properly to dielectric or mechanical relaxation data. 

In all the above three polymers only a single process is apparently observed in the time window for PCS (10-6 to 100 s). The shape of the relaxation function is independent of temperature. The temperature dependence of (r) follows the characteristic parameters observed for mechanical or dielectric studies of the primary (a) glass-rubber relaxation. Relaxation data obtained by many techniques is collected together in the classic monograph of McCrum, Read and Williams41. The data is presented in the form of transition maps where the frequencies of maximum loss are plotted logarithmically... 

In addition to knowing the temperature shift factors, it is also necessary to know the actual value of ( t ) at some temperature. Dielectric relaxation studies often have the advantage that a frequency of maximum loss can be determined for both the primary and secondary process at the same temperature because e" can be measured over at least 10 decades. For PEMA there is not enough dielectric relaxation strength associated with the a process and the fi process has a maximum too near in frequency to accurately resolve both processes. Only a very broad peak is observed near Tg. Studies of the frequency dependence of the shear modulus in the rubbery state could be carried out, but there... 

Ae with degradation is a useful measure of the accumulation of polar groups in the polymer. However, there appears to be considerable overlapping of multiple peaks, and in the early stages of the reaction, Ac, which Is determined from areas under curves in the e" vs 1/T plots is not readily accessible. The relaxation peaks are fairly S3immetrlcal and e" values at the frequency of maximum loss have been used as alternative data to follow reactions. 

Fig. 21.12. Summary of parameters from the SWD experiment for PET/PEN blends (1 1 by Weight) with fTEN = 11% at Tc = 96 C as a function of the crystallization time (a) At values for the o-relaxation, (b) Frequency of maximum loss, (c) Crystallinity index, Xc...

Many polymeric liquids display a maximum in G" at higher frequencies than those associated with the primary glass relaxation. The secondary maximum can have a relaxation strength (as measured by the value of the distribution of relaxation times) that exceeds the primary glass relaxation strength. The frequencies of maximum loss often obey tiie relation ... 

The dielectric relaxation time t can be calculated from the frequency of maximum loss t = A Cole-Cole plot of e" against e enables... 

When the frequency of an applied electric field is the same as the collision frequency, the field and the fluctuating dipoles interact and we get relaxation or resonance phenomena. In other words, the frequency of maximum loss, of energy absorption, is the molecular collision frequency. 

The dielectric losses at high frequencies are found to increase in intensity with increasing polarity of librating atomic groups in substituted polystyrenes (Fig. 18). In Ref. [78], the observations have been made on PPFS in which the aromatic nucleus contains the five fluorine atoms. As expected for heavier groups, the frequency of maximum loss drops to 3 cm"10 Hz) and the maximum loss amplitude rises compared to PS. 

In poly(trifluorostyrene) (PTFS) in which the backbone hydrogen atoms are substituted and we have again the phenyl nucleus, the frequency of maximum losses occurs at about 30cm (compared with 60cm in PS) and the loss amplitude is almost twice that in PS. This shows that the 5-process in polymers, at least of the given series, is primarily due to libration of the side group dipole, but also some properties of the backbone are important. 

Contour maps of dielectric constant and dissipation factor (or loss index) versus frequency and temperature are equivalent to three-dimensional plots— (see Figs. 38 and 39). (Ref 47 includes similar contour plots for several other plastics.) With the help of such contour plots, maximum or minimum dielectric losses can be determined within the range of frequency and temperature expected in a specific application. In addition, a frequency of maximum loss can be selected for optimum dielectric heating. 

The frequency of maximum loss v for a single relaxation time process is obtained from equation (15b) as... 

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