Molecule-independent parameters

As described earlier, ab initio molecular orbital methods12-17 for prediction of thermochemical data can be divided into three categories (1) those using very high level calculations with extrapolation, (2) those implementing moderate level calculations with molecule-independent parameters, and (3) those of moderate level calculations with molecule-dependent parameters. In this section we discuss some aspects of these different approaches. 

Due to very limited experimental data, ion-ion interaction-parameters had to be assumed to be independent of temperature. Ion-molecule interaction parameters 0 iy were estimated from experimental results on salting-out effects, while 0were set equal zero. 

On solids, the amount and strength of acid or basic sites are quite independent parameters, so both of them must be analyzed independently for a complete characterization. Additionally, several different families of acid sites may occur in the same solid surface, so their distribution must be characterized. The key to the effective utilization of microcalorimetry in heterogeneous catalysis is the judicious choice of gas-phase molecules for study. 

In Section 2 it was established theoretically that, relative to some molecule-fixed reference axes, a molecular order (alignment) tensor with five independent parameters was sufficient to describe the molecular orientation upon which the observed dipolar couplings depend. Based on knowledge of the order tensor and the molecular structure, it is possible to predict the corresponding RDCs. From this relationship, one might anticipate that... 

The concept of a unique hydrodynamic volume for all rodlike polymers was derived from examination of the Mark-Houwink constants, K and a, of the equation [rj ] = KMa. Macromolecules with values of a greater than unity are commonly accepted to be stiff or rigid rods. However, it was also found that such molecules (even for values of a less than unity) obey a relation illustrated by close concordance with the curve in Fig. lb (13) flexible, branched or otherwise irregular polymers, on the other hand, show dispersion around the upper part of the curve. The straight line curve in Fig. lb implies that the constants K and a are not independent parameters for the regular macromolecules to which they apply. Poly (a- and polyQJ-phenylethyl isocyanide) fall on this line the former has a value of a > 1 while the latter has a value a < 1 (14) both polymers give linear concentration dependence of reduced specific viscosity for fractionated samples... 

In many applications it is possible to determine 7l and, with more difficulty, 7s, but not 7sl- Therefore, it would be helpful to express 7sl through 7l and 7s. Since 7sl, 7l, and 7s are independent parameters we can only hope to find an approximate expression and we have to use additional information. Girifalco, Good, and Fowkes considered solids and liquids, in which the molecules are held together by van der Waals forces [270,271], Then, in a thought experiment they separated two materials at the interface (Fig. 7.11). The required work of adhesion per cross-sectional area is w = 71 + 72 — 712. Two new surfaces are formed while the interfacial area disappears. Rearrangement leads to... 

Mixtures of small molecules (acetone-benzene, ethanol-water) were considered first. In Figures 1 and 2, a comparison is made between the predicted and experimental low-pressure VLE data (21,22) for these systems. An excellent fit to the data is obtained in both cases, with the use of one apparently temperature independent parameter (k j) per binary. 

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