Critical, frequency temperature

This is essentially the same expression already given for the BWG approximation (Eq. (7.3)) with an additional function that combines the various vibrational frequencies of different bonds. In an ordered alloy the A-B bonds are expected to be stiffer than those of the A-A and A-B bonds, so the vibrational entropy of the ordered state will be lower than that of the disordered state, thus lowering the critical ordering temperature. 

Figure 4- Logarithms of the critical frequencies for absorptions A and B vs. the inverse of the absolute temperature for the four Na+ zeolites...

Fig. 2.38 Variation of e and with frequency. Space charge and dipolar polarizations are relaxation processes and are strongly temperature dependent ionic and electronic polarizations are resonance processes and sensibly temperature independent. Over critical frequency ranges energy dissipation is a maximum as shown by peaks in ...

This is a step function, where the critical frequency uo is the temperature dependent parameter. The expression... 

Figure 5.13 (top) displays the frequency spectra of the measured capacitance for temperatures ranging from 20 K to 300 K for a standard cell (ITO/PEDOT/MDMO-PPV PCBM/Al). The arrow indicates increasing temperatures. One clearly observes a step which is shifted to higher frequencies as the temperature increases. In order to evaluate the position of the steps, it is better to plot wdC/dw versus w, rather than C(u>) versus w. Figure 5.13 (bottom) shows the normalised deviated frequency spectrum of the capacitance. The steps now appear as maxima within the individual curves, and the corresponding critical frequency wq can be derived more ac-... 

More detailed measurements of the dependences Uth f) in pure and doped MBBA at various temperatures (for sandwich cells) were performed [76, 109]. The results of these measurements are represented in Fig. 5.20. The threshold of the vortical motion was taken as the onset of the circular tion of the solid impurity particles in the electrode plane. The shape of the curves in Fig. 5.20 depends on the electrical conductivity. With a high electrical conductivity the curves have a plateau in the low-frequency region and a characteristic dependence I7th oc at frequencies above the critical frequency. At the transition point to the nematic phase the threshold voltage of the instability does not change. It is shown in [109] that the height of the low-frequency plateau is proportional to and at frequencies of u > 47r(j/e the threshold field does not depend on <7. Moreover, it does not depend on the thickness of the sample, i.e., on the separation between the electrodes. 

Experimental phase diagrams for amorphous block copolymers were explored by Khandpur and co-workers (29). First, low-frequency isochronal shear modulus-temperature curves were developed on a series of polyiso-prene-h/ocA -polystyrene polymers to guide the selection of temperatures for the transmission electron microscopy and SAXS experiments to follow see Figure 13.14 (29). Both order-order (OOT) and ODT transitions were iden-tihed. The OOT are marked by open arrows, while the ODT are shown by hlled arrows. Since the ODT occurs as the temperature is raised, an upper critical solution temperature is indicated, much more frequent with block copolymers than with polymer blends. The regions marked A, B, C, and D denote lamellar, bi-continuous, cylindrical, and perforated layered microstructures, respectively. The changes in morphology are driven by the temperature dependence of Xn,... 

Many relaxation processes influence the dielectric spectra of FLCs. Apart from the usual l.f. and h.f. modes characterizing the reorientations of molecules around their principal axes, the Sm C phase shows at least two collective processes. One collective mode, the Goldstone mode (GM), is associated with the fluctuations of the azimuthal angle (the cone motion) it is observed in Sm C phase at low frequencies and is not an activated process. The second mode, the soft mode (SM), is connected with the tilt fluctuations its critical frequency falls in the kilohertz range, from ca. 50 to ca. 500 kHz. The soft mode shows a decrease of frequency in Sm A phase on approaching the transition Sm A -Sm C, but it survives to the lower temperature phase. In special conditions (e.g., after applying an appropriate strength of the bias field ) yet another collective mode can be observed (domain mode). 

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