Thermodynamic susceptibility

Inspection of the diagram shows that N2O lies above the line connecting N2 and NOj . Therefore, NjO is thermodynamically susceptible to disproportionation to N2 and NO3" in basic solution ... 

The preceding relationships have the common feature that they relate the mean square fluctuations of thermodynamic variables to the corresponding thermodynamic susceptibilities, i.e., the second derivatives of appropriate thermodynamic potentials. A general thermodynamic expression for fluctuations of a generalized density (p in a. homogeneous fluid reads... 

Meso-scale heterogeneities can be probed by the intensity of electromagnetic or neutron scattering at a selected wave number q, the instrumental scale. A good example of the scale-dependent meso-thermodynamic property is the isothermal compressibility of fluids or osmotic susceptibility of binary liquids near the critical point of phase separation. " In the limit of zero wave number and/or when the correlation length is small (c g 1) the intensity becomes the thermodynamic susceptibility, which diverges at the critical point as... 

Recently, Lundgren et al. (1982, 1985) however questioned the validity of the assumption that the measured FC-susceptibility is the thermodynamic susceptibility of a spin glass. They studied the time variation of the relaxation rate in spin glasses by ac- measurements and showed that the time range can be... 

The results of a comparison between values of n estimated by the DRK and BET methods present a con. used picture. In a number of investigations linear DRK plots have been obtained over restricted ranges of the isotherm, and in some cases reasonable agreement has been reported between the DRK and BET values. Kiselev and his co-workers have pointed out, however, that since the DR and the DRK equations do not reduce to Henry s Law n = const x p) as n - 0, they are not readily susceptible of statistical-thermodynamic treatment. Moreover, it is not easy to see how exactly the same form of equation can apply to two quite diverse processes involving entirely diiferent mechanisms. We are obliged to conclude that the significance of the DRK plot is obscure, and its validity for surface area estimation very doubtful. 

The temperature at which this reaction is canied out is limited by considerations of the possibility of re-evaporation of As2 molecules and gallium atoms from the GaAs him. The semiconduchng compounds are less susceptible to this problem than the separate elements because of the thermodynamic stabilities of diese compounds, as discussed above. 

Sulfur compounds, whether organic or inorganic in nature, cause sulfidation in susceptible materials. The sulfide film, which forms on the surface of much con-stmction materials at low temperatures, becomes friable and melts at higher temperatures. The presence of molten sulfides (especially nickel sulfide) on a metal surface promotes the rapid conversion to metal sulfides at temperatures where these sulfides are thermodynamically stable. High-alloy materials such as 25% Cr, 20% Ni alloys are widely used, but these represent a compromise between sulfidation resistance and mechanical properties. Aluminum and similar diffusion coatings can be of use. 

Figure 4. Susceptibility of the energy moment at To — 2. The symbols are static Monte Carlo results [1] and the curve is obtained from a local thermodynamic approximation [1] using the bulk susceptibilities from a Lennard-Jones equation of state [90], (From Ref. 1.)...

One common feature of all M + hydrocarbon systems mentioned in Sec. 1.2.2 is that none of the products resulted from cleavage of a C-C bond. This is a result of several factors. First, C-H bonds are less directional than C-C bonds (Sec. 1.1), allowing for multicentered bonding at the transition state, which tends to lower the barrier for C-H insertion relative to C-C insertion.2,18,22 Second, since M-H bonds are usually stronger than M-C bonds, intermediates resulting from insertion into a C-H bond are usually thermodynamically favored.141 Third, there are typically more C-H bonds in hydrocarbons than C-C bonds, so C-H insertion is also statistically favored. Finally, C-H bonds are more accessible to an incoming metal atom and are therefore more susceptible to insertion. 

Wilson et al. [27] showed that the introduction of steric hindrance in the 6-position of one or two of the pyridine groups was sufficient to fine-tune the ligand field and obtain crossover compounds. These systems have been investigated using a number of different techniques, both in the solid and solution phases. Thermodynamic parameters have been derived from variable temperature magnetic susceptibility data for the single methyl-substituted (23 ) (AH°=19.7 kj mol"1, A5°=39.8 J mol"1 K"1), the double methylsubstitut-... 

In general, polymorphism can be enthalpically and entropically driven and, in general, is susceptible to both thermodynamic and kinetic factors. 

Electrophilic substitution at the anthraquinone ring system is difficult due to deactivation (electron withdrawal) by the carbonyl groups. Although the 1-position in anthraquinone is rather more susceptible to electrophilic attack than is the 2-position, as indicated by jt-electron localisation energies [4], direct sulphonation with oleum produces the 2-sulphonic acid (6.3). The severity of the reaction conditions ensures that the thermodynamically favoured 2-isomer, which is not subject to steric hindrance from an adjacent carbonyl group, is formed. However, the more synthetically useful 1-isomer (6.7) can be obtained by sulphonation of anthraquinone in the presence of a mercury(II) salt (Scheme 6.4). It appears that mercuration first takes place at the 1-position followed by displacement. Some disulphonation occurs, leading to the formation of the 2,6- and 2,7- or the 1,5- and 1,8-disulphonic acids, respectively. Separation of the various compounds can be achieved without too much difficulty. Sulphonation of anthraquinone derivatives is also of some importance. 

Other quantities associated with second derivatives of the thermodynamic potential are also enhanced near the critical point demonstrating typical 1 / / l behavior, cf. [21], However numerical coefficients depend strongly on what quantity is studied. E.g. fluctuation contributions above Tc to the color diamagnetic susceptibilities... 

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