Critical enhancements

As discussed in [79], there is no critical enhancement of the thermal diffusion coefficient Dj, which retains its background value Db throughout the asymptotic critical regime. It appears reasonable to assume the same activation temperature Ta both for ab andZ) f ... 

The efficient homogeneous catalysis of chiral ammonium bifluorides of type 15 has been further utilized for achieving an asymmetric Michael addition of silyl nitronates to a,/ -unsaturated aldehydes. Here, chiral ammonium bifluoride 15b bearing a 3,5-di-tert-butylphenyl group was found to be the catalyst of choice, and the reaction of 16a with trans-cinnamaldehyde under the influence of (R,R)- 15b (2 mol%) in THF at —78 °C produced the 1,4-addition product 18 predominantly (18/19 = 24 1) as a diastereomeric mixture (syn/anti = 78 22) with 85% ee of the major syn isomer (Scheme 4.9). Further, use of toluene as solvent led to almost exclusive formation of the 1,4-adduct (18/19 = 32 1) with similar diastereoselec-tivity (syn/anti = 81 19), and critical enhancement of the enantioselectivity was attained (97% ee) [15]. 

Although the contribution is written with an emphasis on polyatomic gases, it also includes results for pure monatomic gases and mixtures containing monatomic species. Chapters 5 and 6 consider fluids at moderate and high densities as well as the critical enhancements to the transport properties and, therefore, complete this brief summary of the statistical theory of fluids. 

Similar results are obtained for thermal conductivity away from the critical region (where there is a significant enhancement, as discussed in Chapter 6). For viscosity, the critical enhancement is small and restricted to temperatures very close to the critical temperature. 

The equation (6.42) for the critical enhancement AXc is based on the mode-coupling theory of the critical fluctuations and contains only one adjustable parameter qj). Empirical equations for AXc containing more adjustable parameters have also been proposed (Sengersera/. 1984 Sengers 1985 Roder 1985 Roder era/. 1989 Perkins era/. 1991b). An example of such an empirical equation for AA.c of argon is presented in Chapter 14 of this volume. Empirical equations with an adequate number of adjustable parameters can be used to represent sets of experimental thermal-conductivity data. However, they cannot be used to predict the thermal conductivity of fluids in the critical region from a limited data set. 

In analogy with equation (6.19) each of the coefficients introduced in equations (6.43) and (6.44) is written as a sum of a regular background contribution and a critical enhancement, that is, a = a -f- Aofc. etc. Since the mode-coupling theory provides information... 

Mistura (1972) went on to estimate the enhancement of the thermal conductivity by inserting the critical enhancements of the transport coefficients into equation (6.47) and concluded that the enhancement vanishes at the critical point When Mostert Sengers (1992) and Anisimov Kiselev (1992) included the background effects, a qualitatively different result was obtained, namely, that the enhancement of the thermal conductivity is finite at the critical point... 

It should be pointed out here that the asymptotic description of the thermal conductivity is valid only extremely close to the critical point. Measurements on He + He (Cohen et al. 1982), methane + ethane (Friend Roder 1985 Roder Friend 1985) and CO2 + ethane (Mostert et al. 1992) seem to indicate that the thermal conductivity exhibits a critical enhancement similar to that observed for pure fluids. In Figure 6.7, as an example the experimental thermal-conductivity results for CO2 + ethane for a mole fraction of 25% CO2 in the one-phase region close to the critical isochore are presented, which were obtained by Mostert (1991). To reconcile the experimental data with the asymptotic result of equation (6.54), again a crossover theory is needed. Thermophysical quantities in fluid mixtures near a plait point undergo two types of crossover as the... 

Fig. 7.1. The thermal conductivity data surface for pentafluoroethane (R125) in terms of temperature and density. The critical enhancement of the thermal conductivity is aj arent in the isotherms closest to the critical point.

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