Relaxation hypersonic

From the experimental point of view, the method of Brillouin spectroscopy (BS) has played the central rote for the identification of the T transition. - In Section II we present an extension of this method which provides further indication for the existence of the transition and is a sensitive probe for identifying obscure hypersonic relaxation processes. 

The frequencies (70 and / °A (jj have to be determined for equivalent symmetry sound propagation directions as well as for the same polarization. So far the application of eq. (4) has not been restricted to isotropic materials. If hypersonic relaxation processes are active, two different cases have to be taken into account ... 

In the asymptotic limits of 2tc fi , where T denotes the main hypersonic relaxation time, the following relation holds. 

Fig. 21. Example of a hypersonic relaxation process obscuring a possible T transition. A T kink could be suspected near 360 K. (a) The D-fiinction compared with the refractive index clearly indicates a hypersonic relaxation (compare Figs. 2 and 3). (b) Sound frequency measured in (he 90A> geometry versus temperature. The formula of the oligomer is depicted in die inset of (a).

In order to obtain r s(A(0(d ) from 7s(o), it is necessary to assess what fraction of r s(o) is caused by conformational relaxation and reorienta-tional relaxation. This quantity has been obtained recently (21) and is near one-third. If we take into account the reduction in 7s(w) at the Brillouin frequency A(0(i), the calculated hypersonic volume viscosity r v( A(0(i)) now depends on temperature and is comparable with s(Ato>(i)). The above result illustrates that the analysis of Td) can be very complicated for chain-molecule fluids. 

Figure 8, Transition map for PIB. The hypersonic result corir siderahly extends the available frequency range. The primary (P) glass-rubber relaxation line and secondary (S) relaxation line are from Ref. 22.

Usually the primary (P) glass-rubber relaxation cannot be resolved from the secondary relaxation at hypersonic frequencies. However, this is not always the case. The Brillouin frequencies Awd) and tan 8 for polypropylene glycol (PPG) (13) are plotted versus temperature in Figure 9. Two tempratures of maximum loss are observed. The higher temperature loss at 100 °G and a frequency of 4.40 GHz correlates very well with the primary glass-rubber relaxation line determined by dielectric relaxation at gigahertz frequencies (13), The lower temperature loss at 50°G and a frequency of 5.43 GHz correlates with an extension of the secondary transition line. The transition map is shown in Figure 10. 

While a broader distribution of relaxation times would provide a better fit to the experimental data, a reasonable description of the hypersonic loss process is of a major relaxation with t approximately equal to 2.5 X 10 sec and a secondary process with t = 5 X 10 sec at 320 K. 

Insufficient ultrasonic data are available for an analysis of the relaxation in PIB, nonetheless the raw data (Figures 2a and 2b) indicate a similar process. The behavior of PDMS is more complicated. However, at least two relaxations appear to be associated with the major hypersonic loss process. 

Another approach to determining the viscoelastic properties of dense microemulsions at high frequencies is to conduct ultrasonic absorption experiments. In such experiments it has been found that the percolation process is correlated to a shift of the ultrasonic dynamics from a single relaxation time to a distribution of relaxation times [121]. Other experiments showed an increase in the hypersonic velocity for samples at and beyond the percolation threshold. The complex longitudinal modulus deduced from such experiments is also correlated with the occurrence of the percolation phenomenon, which suggests that the velocity dispersion is clearly correlated with structural transformations [122]. 

In viscous fluids, however, a coupling occurs between internal and external modes of freedom and translational motions. This structural relaxation process, characterized by a frequency >e, influences both the central line as well as the Brillouin doublet, depending on the frequency of this relaxation relative to the frequency of the hypersonic waves. In principal three different cases must be considered ... 

Figure 3 displays the hypersonic speed dispersion curves of CCl, at four different temperatures. The complete dispersion curve contains additionally an experimental point corresponding to the ultrasonic velocity, i.e. lying at a comparatively low frequency which is located on the ordinate axis. The fit has been made with the classical dispersion relation with the relaxation time, and the amplitude of the dispersion curve as free fit parameters according to the equation ... 

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