Scattering, critical point

A further critical point are the intensities correlated to spectra of the pure elements. Calculated and experimentally determined values can diverge considerably, and the best data sets for 7 measured on pure reference samples still show a scatter of up to 10%. The use of an internal standard or a simultaneously measured external standard seems to be the most successful way to reducing the inaccuracy below 10%. (Eor a more detailed discussion of background subtraction and quantification see, e.g., Seah [2.9].)... 

Marsault-Herail F., Marsault J. P., Michond G., Levi G. Raman scattering Orientational motion and collision frequency in liquid CF4 from the triple to critical point, Chem. Phys. Lett. 31, 335-9 (1975). 

It is important to realize that even in the presence of traps, the measured Hall mobility refers to that in the higher conducting state (Munoz, 1991). Thus, a value of r significantly >1.0, and increasing with temperature in a certain interval, has been taken as an evidence in favor of traps in NP near the critical point (Munoz, 1988 Munoz and Ascarelli, 1983). Similarly, a nearly constant value of r near 1.0 in TMS over the temperature interval 22-164°C has been taken to indicate absence of trapping in that liquid. The scattering mechanism in TMS is consistent with that by optical phonons (Doldissen and Schmidt, 1979 Munoz and Holroyd, 1987). 

Application of this technique to measurements of the spectral distribution of tight scattered from a pure SF fluid at its critical point was present by Ford and Benedek The scattering is produced by entropy fluctuations which decay very slowly in the critical region. Therefore the spectrum of the scattered light is extremely narrow (10 - lO cps) and can only be observed by this light beating technique 240a)... 

Let us consider now behaviour of the gas-liquid system near the critical point. It reveals rather interesting effect called the critical opalescence, that is strong increase of the light scattering. Its analogs are known also in other physical systems in the vicinity of phase transitions. In the beginning of our century Einstein and Smoluchowski expressed an idea, that the opalescence phenomenon is related to the density (order parameter) fluctuations in the system. More consistent theory was presented later by Omstein and Zemike [23], who for the first time introduced a concept of the intermediate order as the spatial correlation in the density fluctuations. Later Zemike [24] has applied this idea to the lattice systems. 

Tn the critical region of mixtures of two or more components some physical properties such as light scattering, ultrasonic absorption, heat capacity, and viscosity show anomalous behavior. At the critical concentration of a binary system the sound absorption (13, 26), dissymmetry ratio of scattered light (2, 4-7, II, 12, 23), temperature coefficient of the viscosity (8,14,15,18), and the heat capacity (15) show a maximum at the critical temperature, whereas the diffusion coefficient (27, 28) tends to a minimum. Starting from the fluctuation theory and the basic considerations of Omstein and Zemike (25), Debye (3) made the assumption that near the critical point, the work which is necessary to establish a composition fluctuation depends not only on the average square of the amplitude but also on the average square of the local... 

Figure 6. Cloud-point curve for polystyrene in cyclohexane (%) determined from light scattering and (M) determined visually. The arrows indicate (from left to right) maximum of the cloud-point curve, maximum of the dissymmetry ratiof critical point.

FIGURE 8. A scatter diagram of the minimum energy Si—O bond length, R(Si—O), calculated for a number of hydroxyacid molecules vs the value of the electron density, p(rc), evaluated at (3,-1) critical points. The geometries of the hydroxyacid molecules used to prepare the plot were those of minimum energy at the Hartree-Fock 6-31++G level... 

This behavior matches quite well to the scenario that has recently been developed for 2D spin systems in the proximity to a quantum critical point [16] and is a direct fingerprint of the tendency to form local correlations. It has to be mentioned, however, that the lowest energy excitation still has triplet character. For compounds with closer proximity to quantum criticality, such as the 1/6 depleted triangular lattice (Kagome) [6] and the 1/5 depleted square lattice, also exists a dense singlet spectrum within the singlet triplet gap [17-20], Unfortunately no Raman scattering data for the related compounds are available up to now. 

The properties of a liquid mixture at or near a critical point (Stein and Allen, 1974) are complicated (Rowlinson, 1974) and will not be commented on further. Nevertheless, it seems likely that the kinetics of reactions in solvent mixtures near an LCST or a UCST may prove interesting in view of the report, admittedly not concerned with aqueous mixtures, that the rate of a Diels-Alder reaction increases by 30% within 0 01 K of the UCST for reaction in hexane + nitrobenzene mixtures (Wheeler, 1972). Measurement of the kinetics of reaction in such systems may prove difficult by spectrophoto-metric techniques because systems close to a critical point scatter light, but should be possible by electrical conductance measurements (Stein and Allen, 1973 Gammell and Angell, 1974). 

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