Scattering correlation

A log-log plot using K Km, /ccat and Acuncat data from the 18 separate cases of antibody catalysis exhibited a linear, albeit scattered, correlation over four orders of magnitude and with a gradient of 0.86 (Fig. 16).4 Considering the assumptions made, this value is sufficiently close to unity to suggest that the antibodies do stabilize the transition state for their respective reactions. However, even the highest A cat/A uncat value of 106 in this series (Tramontano et al., 1988) barely compares with enhancement ratios seen for weaker enzyme catalysts (Lienhard, 1973). 

The available data show a somewhat scattered correlation between the energy of activation and the diameter of the gas molecule, varying between the first and the second power of the molecular diameter of the penetrant molecule. In our experience the best correlation is obtained if En is assumed to be proportional to second power of the collision diameter (see Fig. 18.2, where the data of Table 18.3 for the collision diameters are used). If nitrogen is taken as the standard gas for comparison, we can use the product... 

Coefficients tpIf 12 Involved in the Rayleigh Isotropic and Depolarized light Scattering Correlation Functions Fzx(t) = 2N j2 j2 cp Sn(t) Rj1(t) Rj2(t) for the Successive Multipolar Induction Operators... 

Coefficients (pj 1 - 2 Involved in Raman Isotropic and Depolarized Light Scattering Correlation Functions Fu.(t) = Y.N,h,h wli 1 12 SN(t)Rj1(t)Rh(t)F+ for Successive Multipolar Induction Operators... 

Figure 2.24. The concept of orthogonality as shown by retention plots of two sets of columns for a variety of different analytes. (A) Since the log k data of the two columns (C8 and C18) are well correlated for most analytes, these two columns are expected to yield similar elution profiles. (B) The selectivity differences of a C18 and a polar-embedded phase (amide) column lead to very scattered correlation of their respective retention data. Methods using a C18 and a polar-embedded column are therefore termed orthogonal and expected to yield very dissimilar profiles. Diagram courtesy of Supelco, Inc.

The rates of Via and VIb in different solvents gave somewhat different correlations by the equation log (k/k0) = raY0Ts for aqueous ethanols and for other solvents, with m values of 0.82 and 0.78 for the latter, whereas Vic gave a very scattered correlation by this equation (17). Therefore, the rates were correlated by the equation log (k/k0 = mY0Ts + IN (38), where N is a measure of solvent nucleophilicity and l expresses the dependence on N. For Via, VIb, and Vic, values obtained in this way for m and l were 0.90, 0.91, and 0.93 and 0.26, 0.37, and 0.72, respectively, with correlation coefficients of 0.994, 0.994, and 0.977, repsectively. Whatever the merits of the dual correlation with Y0Ts and N, all three substrates showed enhanced rates in the ethanol solvents compared with the trends for the other solvents this result suggests that nucleophilic interactions are important. 

We now apply these results to the calculation of the light-scattering correlation functions for symmetric diffusors. From Eqs. (7.4.3a), (7.4.4), and (7.2.1) we find that... 

Thus we conclude that the tendency of chloroform molecules to orient with their symmetry axes parallel causes the total (light-scattering) correlation function to relax more slowly than the single-particle correlation function at large chloroform concentrations. 

Figure 1. Normalized experimental light-scattering correlation functions, obtained at i = 1030 cm for a solution of polystyrene (Mw= 96,400, w = 2.50%) in toluene subjected to various temperature gradients vr[18].

Details are given of the preparation of model ethyl acrylate-methacrylic acid copolymer latices by non-seeded semicontinuous emulsion copolymerisation. Polydispersity was examined using dynamic and static light scattering. Correlations between hydrodynamic volume and viscosity properties of the dispersions are discussed. The different character of the particle structure was confirmed by differences in particle disintegration after alkali addition or in the presence of methanol. 19 refs. 

When q Rg > 1, concentration fluctuations within single macromolecules dominate the correlation tunction. The calculation ot the light-scattering correlation tunction S q,x) tor a single macromolecule in solution is described in detail in Berne and Pecora. The chain is modeled as shown in Equation 5.10. Intramolecular concentration fluctuations resolve into a set ot modes with characteristic relaxation times that depend on the subchain friction coefficient, the overall radius ot gyration, and the temperature. The correlation txmction can be expressed as ... 

The rod length and diameter can also be inferred from d5mamic depolarized Rayleigh scattering. The translahonal and rotational diffusion coefficients can be determined. The depolarized light-scattering correlation function can be expressed as ... 

Here, Xj g, the light scattering correlation time is related to the single particle correlation time Tg = 1/(6Dj ), where Dj is the rotational txwnbling diffusion constant of the molecule, 92 the orientational pair correlation factor introduced above and j2... 

The failure to treat target and scattering correlation consistently can lead to results which are completely unphysical qualitatively, such as false resonances or false thresholds. On the other hand, it is this sensitivity to correlation that leads to the rich set of physical phenomena associated with... 

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