Frequency dependence acoustic transitions

Transitions temperatures vary with the method and the rate of measurements. This is a potentially confusing situation. The transitions associated with the relaxation processes are highly frequency-dependent. Glass transition temperature obtained in measurement by dynamic methods [acoustic, dynamic mechanical analysis (DMA), ultrasonic, or dielectric methods] should reasonably be denoted as T to differ it from Tg measured, for instance, by DSC. At low fi equen-cies, that is, at 1 Hz or least, Ta is close to Tg. As the measurement fi equency is increased, increases while Tg remains the same, giving rise to two separate transition temperatures. In the literature, the distinction between the static and dynamic glass transitions is not always made clear. 

Fig. 14. Schematic views of (a) manifestation of transitions in a DMA spectrum, and (b) frequency dependencies of transition temperatures in polymers, measured by various techniques I, DSC, mechanical relaxation, radiothermoluminescence, thermostimulated depolarization II, mechanical and dielectric relaxation III, dielectric relaxation, NMR IV, ESR (probe method), Mandelstam-Brillouin scattering, acoustic measurements (From Ref 140),...

Time resolution of the enthalpy changes is often possible and depends on a number of experimental parameters, such as the characteristics of the transducer (oscillation frequency and relaxation time) and the acoustic transit time of the system, za, which can be defined by ra = r0/ua where r0 is the radius of the irradiated sample, and va is the speed of sound in the liquid. The observed voltage response of the transducer, V (t) is given by the convolution of the time-dependent heat source, H (t) and the instrument response function,... 

When a polymer exhibits a maximum in the imaginary part of the dielectric permittivity (the loss permittivity, e") at frequencies less than 200 Hz, it becomes possible to make comparisons with the frequency dependence of shear moduli and most specifically with the loss shear modulus, G". This has been done for polypropylene diol, also called poly(oxypropy-lene), where there is reported a near perfect superposition of the frequency dependence of the normalized loss shear modulus with that of the normalized loss permittivity as reproduced in Figure 3. The acoustic absorption frequency range of interest here is 100 Hz to 10 kHz, yet present macroscopic loss shear modulus data can be determined at most up to a few hundred Hz. Nonetheless, for X -(GVGIP)32o there is a maximum in loss permittivity, e", near 3 kHz that develops on raising the temperature through the temperature range of the inverse temperature transition. With the width of the loss permittivity curve a distinct set of curves as a function of temperature become... 

As in magnetic resonance with electromagnetic waves, the intensity of absorption is proportional to the energy quantum hv and the population difference hv/kT), giving in all cases a factor v /kT. Thus the intensity of the +2 transitions, involving the square of the hyperfine interaction, increases with the second power of the frequency. The position is dilferent for +1 transitions because of an additional frequency dependence their acoustic matrix elements involve the magnetic field, and their intensity thus rises with the square of the magnetic field. This introduces a further factor proportional to v, so that their intensity increases with the fourth power of the frequency. These frequency dependences have been confirmed in an experiment at liquid-helium temperatures where the frequency is varied from 800 to 1600 MHz, as shown in fig. 15. The measurements also verify that the absorption increases as T . 

Fig. 15. Frequency dependences of the enhanced acoustic NMR in H0VO4. The intensities of the strong dm = I transitions vary with the fourth power of the frequency, those of the Sm = 2 transitions with the square of the frequency. (Briggs et al. 1984.)...

The excitation spectrum is determined from the poles of D (q, energy states excitations). The latter enter via the frequency dependent susceptibility q V, interaction between both types of modes leads to a hybridization (Elliott et al., 1972). Due to the elastic scattering processes within a CEF-energy level there are 5 =o-contributions to the quadrupole susceptibility (see eq. 17.108). It was shown that these processes have to be included in the expressions for the elastic constants and therefore contribute to a Jahn-Teller phase transition. However they do not show up in the acoustic phonon dispersion which one would measure... 

Kinetic information on the molecular conformational change can be extracted from dynamic mechanical studies, as described in Chapter 10, from the closely related acoustic relaxation experiments described in Chapter 11, and from dielectric relaxation covered in Chapter 12. In all of these, the observation of a transition in the frequency dependence of the property under study yields a relaxation time for the molecular process. This in turn transforms into the kinetics of the movement. Again, the activation energy associated with the conformational change is obtained from the effect of temperature on the relaxation time, using either the Arrhenius equation or a related analysis. 

The acoustic properties of polymers are just as for many properties strongly dependent on temperature around the glass-rubber transition the sound speed decreases rapidly from a relatively high value at T < Tg to a relatively low value at T > Tg. During this transition the absorption shows a maximum value. An example is given in Fig. 14.4, where data for a poly(metacarborane siloxane) are displayed. The measurements were made in the longitudinal mode as a function of temperature at a frequency... 

In principle, the ultrasonic techniques described for solid-liquid flow measurement can be applied to measure air flow rate and particle velocity. Direct measurement of air flow rate by measuring upstream and downstream transit times has been demonstrated. But, the Doppler and cross-correlation techniques have never been applied to solid/gas flow because the attenuation of ultrasound in the air is high. Recent developments have shown that high-frequency (0.5-MHz) air-coupled transducers can be built and 0.5-MI Iz ultrasound can be transmitted through air for a distance of at least 1 in. Thus, the cross-correlation technique should be applicable to monitoring of solid/gas flow. Here, we present a new cross-correlation technique that does not require transmission of ultrasonic waves through the solid/gas flow. The new technique detects chiefly the noise that interacts with the acoustic field established within the pipe wall. Because noise may be related to particle concentration, as we discussed earlier, the noise-modulated sound field in the pipe wall may contain flow information that is related to the variation in particle concentration. Therefore, crosscorrelation of the noise modulation may yield a velocity-dependent correlation function. 

Acoustic streaming flow fields depend on acoustic wave properties, fluid properties, the geometry of solid boundaries, and presence of solid particles within the fluid. Depending on these factors, laminar, transitional, or turbulent flow with jets and vortices can be generated. The acoustic streaming effect is proportional to the sound pressure level and the square of the frequency of the pressure wave [1]. However, excessive heating... 

---