Collapse temperature

Figure C2.5.6. Thennodynamic functions computed for the sequence whose native state is shown in figure C2.5.7. (a) Specific heat (dotted curve) and derivative of the radius of gyration with respect to temperature dR /dT (broken curve) as a function of temperature. The collapse temperature Tg is detennined from the peak of and found to be 0.83. Tf, is very close to the temperature at which d (R )/d T becomes maximum (0.86). This illustrates...

Bhattacharya and Gedanken [11] have reported a template-free sonochemical route to synthesize hexagonal-shaped ZnO nanocrystals (6.3 1.2 nm) with a combined micro and mesoporous structure (Fig. 8.1) under Ar gas atmosphere. The higher porosity with Ar gas has been attributed to the higher average specific heat ratio of the Ar which leads to higher bubble collapse temperatures. With an intense bubble collapse temperature, more disorder is created in the product due to the incompleteness of the surface structure that led to greater porosity. Importance of gas atmosphere has been noted when the same process was carried out in the presence of air which results in the formation of ZnO without any porosity. 

Using the spectroscopic technique previously described, Didenko et al., investigated the collapse temperature for rare gases in organic solvents (octanol and dodecane) with Cr(CO)6 as the spectroscopic probe [58]. They observed a trend in temperature consistent with that predicted based on differences in thermal... 

Fig. 14.10 (a)MBSL intensity as a function of the theoretical collapse temperature for the rare gases (reprinted with permission from reference [55], copyright 1976, Acoustical Society of America). 

The uses of inorganic metal compounds and rare gases to probe the conditions of cavitation collapse have become some of the most important methods available in fundamental ultrasonics. Quantitative determination of collapse temperatures and pressures, and qualitative determination of fundamental aspects of the nature of the cavitation field have been achieved, largely through SL spectroscopic methods. The presence of salts has a marked influence on properties on the acoustic systems, such as the extent of coalescence and bubble size, and the sonochemical activity and SL intensity. 

Tm is the on-set temperature of the softening process in the product and close to the collapse temperature, Tc. 

Fig. 1.53. Freezing and thawing plot of coffee extract with 25 % solids. UFW (g H20/g solids) as a function of temperature (Fig. 2 from [ 1.37])-I, Subcooling 2, collapse temperature.

Fig. 1.55.6. Collapse plot in log (TOF) versus UK. The extrapolated intersection of the two linear portions identifies the collapse temperature of the system. (Fig. 10 from [1.126]).

Morris et al. [1.126] proposed to use dielectric analysis (DEA) to predict the collapse temperature of two component systems. The background of DEA is explained and the take off frequency (TOF) is chosen as the best analytical method to identify the collapse temperature. Figure 1.55.5 shows the dielectric loss factor as a function of the frequency. 

The frequency at the minimum of this curve is called TOF by the authors. TOF varies with the temperature as shown in Fig. 1.55.6. The extrapolated intersection of the two linear portions identifies the collapse temperature. The predicted Tc by TOF for 10 % sucrose, 10 % trehalose, 10 % sorbitol and 11 % Azactam solution deviates from observations by a freeze-drying microscope (Table 1, from [1.126]) to slightly lower temperatures, the differences are -3 °C, -1.4 °C, 2.2 °C and 0.7 °C. 

Fig. 3.2. Collapse temperature of a sucrose solution as a function of the added citrate solution (%) (Fig. 3 from [3.6]).

Thermal measurements such as DSC and DTA can be used to determine the crystal collapse temperature. The presence of the exothermic peak is associated with the lattice collapse. As shown in Figure 4.44 for a steamed and unsteamed faujasite, the thermal stability improves with increasing silica/alumina framework. 

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