Thermodynamics final comment

A final comment we ean use these thermodynamic values to calculate the equilibrium eonstants according to ... 

Final comment. Complete thermodynamic and kinetic studies have been made to identify new individual polysulfide phases. The static membrane gauge method appears to be the most promising for controlling the equilibrium state in the systems. This method is also the main source in constructing Ps T-x equilibrium diagrams, which provide valuable data for crystal-growth processes of the intermediate polysulfides. 

As a final comment on the BWR equation, we quote Hopke and Lin (12) on the problem of the determination of the BWR constants "In our regression work, we found that attempts to fit pure component and binary mixture data alone will not yield a unique set of optimal BWR s parameters for a given component. On the contrary, many widely different parameter sets can give about the same fit to the data. Moreover, the different parameter sets will yield different results when used to predict thermodynamic properties at conditions outside of the temperature and pressure range of the data base used to determine the parameter sets. Also, extrapolation of light hydrocarbon parameters to obtain estimates of parameters for heavier hydrocarbons is Impossible unless a unique set of optimal parameters is obtained."... 

Finally, we wish to make a brief preliminary comment on what seems to us an important application of our approach Many thermodynamic and kinetic quantities vary cyclically with internal rotations. A commonly presented quantity is the (repulsion) potential. It is then interesting to see, how this property varies with the symmetry rather than with the traditional torsion angle. The results for a model sinusoidal potential (Figure 9a) are shown in Figure 9b. Let us first detail how the potential follows this new process coordinate The DVl potential line varies smoothly with S, starting at the eclipsed 5 = 0 value and dropping to zero potential at the staggered 5 = 22.22 value then it reverses and climbs back up to the maximum... 

From the point of view of molecular theory, the coefficients dpu jdp2 are fundamentally related to structural properties of these fluids - OZ direct correlation functions (Eq. (6.71), p. 141) - as is discussed in detail subsequently in Section 6.3 on the Kirkwood-Buff theory. Alternatively, these coefficients could be explicitly evaluated if an explicit statistical thermodynamic model, as in the discussion here, were available for the unmixed fluids. Finally, these comments indicate that much of the iirformation supplied by these coefficients is susceptible to measurement... 

The principal guideline is that reversible reactions are governed by thermodynamic considerations, while irreversible reactions are controlled by kinetic factors. After we have looked at a few general principles, we will examine these two topics in a little more detail. Finally, in this chapter, we will make a few general comments on catalysts, with particular reference to acid/base catalysis. 

The factors in the left hand column depend only on the nature of the components, whereas those in the right hand colunm depend on the conditions of the self-assembly reaction. It is perhaps useful to comment on the importance of component activity for self-assembly reactions involving labile metal ions, the final self-assembled product will be the thermodynamically stable one [4]. The formation of this product will thus be governed by the law of mass action, and must therefore be a function of the free activities of the components, and not merely of their relative concentrations. This effect is certainly of importance in biological self-assembly, most biological systems having well developed mechanisms for the control of activities. 

Finally, a few comments about the uniqueness of polymer crystal structures and phase space localization are warranted. Almost all crystallizable polymers exhibit polymorphism, the ability to form different crystal structures as a result of changes in thermodynamic conditions (e.g., temperature or pressure) or process history (e.g., crystallization conditions) [12]. Two or more polymorphs of a given polymer result when their crystal structures are nearly iso-energetic, such that small changes in thermodynamic conditions or kinetic factors cause one or another, or both, to form. Polymorphism may arise as a result of competitive conformations of the chain, as in the case of syndiotactic polystyrene, or as a result of competitive packing modes of molecules with similar conformations, as in the case of isotactic polypropylene. In some instances, the conformational change may be quite subtle isotactic polybutene, for example, exhibits... 

Finally, it seems appropriate to comment on evidence for complex ions afforded by the electronic spectra of 3d ions in view of the earlier discussion (Section III, A, 4) of the difficulty of assessing these from particularly thermodynamic data for melts with a common anion. The spectroscopic studies in LiCl-KCl, the most studied solvent to date, certainly seem to be as presumptive a collection of evidence for the formation of complex ions in the melt as are the similar results in inert solvents which are so frequently used as proof of their identity. At the very least, a discrete environment rather than a wide range of configurations is evidently present (see Wilmshurst, 1963), since broadening of transitions energies is no more than that which usually accompanies an increase in temperature. Even more powerful evidence has been accumulated for the correctness of the assignment of the spectral data for the melts to a given complex ion in that the data are in many cases substantially identical with those for accepted complexes in aqueous solution or in crystals of known structure, either pure or in dilute solid solution. It does not seem particularly important that the complex ion symmetry and stabffity can be accounted for at least quali-... 

---