Structure quantitative treatment

Dispersion Characteristics The chief characteristics of gas-in-liquid dispersions, like those of hquid-in-gas suspensions, are heterogeneity and instabihty. The composition and structure of an unstable dispersion must be obsei ved in the dynamic situation by looking at the mixture, with or without the aid of optical devices, or by photographing it, preferably in nominal steady state photographs usually are required for quantitative treatment. Stable foams may be examined after the fact of their creation if they are sufficiently robust or if an immobilizing technique such as freezing is employed [Chang et al., Ind. Eng Chem., 48, 2035 (1956)]. 

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

When one compares the brutto polymerization rate constants, a measure of the reactivity of monomers during cationic homopolymerizations is obtained. It was found for p-substituted styrenes that lg kBr increased parallel to the reactivity, which the monomers show versus a constant acceptor 93). The reactivity graduation of the cationic chain ends is apparently overcomed by the structural influence on the monomers during the entire process of the cationic polymerization. The quantitative treatment of the substituent influences with the assistance of the LFE principle leads to the following Hammett-type equations for the brutto polymerization rate constants ... 

A general theory based on the quantitative treatment of the reaction layer profile exists for pure redox catalysis where the crucial function of the redox mediator is solely electron transfer and where the catalytic activity largely depends only on the redox potential and not on the structure of the catalyst This theory is consistent... 

The quantitative treatment of the electron-transfer paradigm in Scheme l by FERET (equation (104)) is restricted to the comparative study of a series of structurally related donors (or acceptors). Under these conditions, the reactivity differences due to electronic properties inherent to the donor (or acceptor) are the dominant factors in the charge-transfer assessment, and any differences due to steric effects are considered minor. Such a situation is sufficient to demonstrate the viability of the electron-transfer paradigm to a specific type of donor acceptor behavior (e.g. aromatic substitution, olefin addition, etc.). However, a more general consideration requires that any steric effect be directly addressed. 

Therefore, in a crosslinking process which is governed by the intramolecular crosslinking, the structure of the microgels is important. Currently, gel formation is qualitatively quite well understood by using the knowledge about the properties of microgels. However, a satisfactory quantitative treatment is still desirable. 

M. H. Abraham, New solute descriptors for linear free energy relationships and quantitative structure-activity relationships, in Quantitative Treatments of Solute/Solvent Interactions, P. Politzer and J. S. Murray, eds., Elsevier, Amsterdam (1994) pp. 83-134. 

One of the most noteworthy consequences of the refinement of these quantitative treatments of colour-structure relationships has been the stimulus it has given to the search... 

QEUC, see Quasi-molecular enlarged unit cell Quadricyclene, 20 323 valence isomerization of, 20 304 Quadricyclene, isomerization of, 24 146, 148 Quadrupolar interactions, 33 205-209 Quadrupole splitting, 26 126, 134, 140-142 Qualitative studies of simple reactions, 32 116 Quantitative treatment, structure effects, 29 155-162... 

The old and lasting problem of heterogeneous catalysis, the mechanism of alkene hydrogenation, has also been approached from the viewpoint of structure effects on rate. In 1925, Lebedev and co-workers (80) had already noted that the velocity of the hydrogenation of the C=C bond decreases with the number of substituents on both carbon atoms. The same conclusion can be drawn from the narrower series of alkenes studied by Schuster (8J) (series 52 in Table IV). Recently authors have tried to analyze this influence of substituents in a more detailed way, in order to find out whether the change in rate is caused by polar or steric effects and whether the substituents affect mostly the adsorptivity of the unsaturated compounds or the reaetivity of the adsorbed species. Linear relationships have been used for quantitative treatment. 

Computational modeling can be a very powerful tool to understand the structure and dynamics of complex supramolecular assemblies in biological systems. We need to sharpen the definition of the term model somewhat, designating a procedure that allows us to quantitatively predict the physical properties of the system. In that sense, the simple geometrical illustrations in Fig. 1 only qualify if by some means experimentally accessible parameters can be calculated. As an example, a quantitative treatment of DNA bending in the solenoid model would only be possible if beyond the mechanical and charge properties of... 

A quantitative treatment of the Jahn-Teller effect is more challenging (46). A major issue is that many theoretical models explicitly or implicitly assume the Bom—Oppenheimer approximation which, for octahedral Cu(II) systems in the vibronic coupling regime, cannot be correct (46,51). Hitchman and co-workers solved the vibronic Hamiltonian in order to model the temperature dependence of the molecular structure and the attendant spectroscopic properties, notably EPR spectra (52). Others, including us, take a more simphstic approach (53,54) but, in either case, a similar Mexican hat potential energy description of the principal features of the Jahn-Teller effect in homoleptic Cu(II) complexes emerges (Fig. 13). 

They said that a comb polymer with very short branches would not fulfil condition 1, and a star polymer would not fulfil condition 2 unless the branches were very much longer than the critical chain length but polymers having relatively few but long branches, especially ramified or tree-like structures, should fulfil these conditions. Subsequent work, summarised in Section 5, has largely borne out their predictions, though no quantitative treatment is yet available. 

Our objective in this work is to present surveys of the methods now available for the quantitative treatment of steric effects in the design of bioactive molecules. Commonly, this consists in the modification of a lead compound by structural changes which result in a set of bioactive substances. The bioactivity is determined and then related to structure. This is generally carried out by means of multiple linear regression analysis using a correlation equation of the type... 

The basic parameters which determine the kinetics of internal oxidation processes are 1) alloy composition (in terms of the mole fraction = (1 NA)), 2) the number and type of compounds or solid solutions (structure, phase field width) which exist in the ternary A-B-0 system, 3) the Gibbs energies of formation and the component chemical potentials of the phases involved, and last but not least, 4) the individual mobilities of the components in both the metal alloy and the product determine the (quasi-steady state) reaction path and thus the kinetics. A complete set of the parameters necessary for the quantitative treatment of internal oxidation kinetics is normally not at hand. Nevertheless, a predictive phenomenological theory will be outlined. 

This section is concerned with the quantitative correlation of reaction rates and equilibria of organic reactions with the structure of the reactants. We will restrict the discussion to benzene derivatives. The focus is on a remarkably simple treatment developed by L. P. Hammett in 1935, which has been tremendously influential. Hammett s correlation covers chemical reactivity, spectroscopy and other physical properties, and even the biological activity of drugs. Virtually all quantitative treatments of reactivity of organic compounds in solution start with the kinds of correlations that are discussed in this section. 

The quantitative treatment of surface phenomena involves an important uncertainty. It is convenient to regard the interface between two phases as a mathematical plane, such as SS in Figure 4.12. This approach, however, is unrealistic, especially if an adsorbed film is present. Not only will such a film itself have a certain thickness, but also its presence may influence nearby structure (for example, by dipole-dipole orientation, especially in an aqueous phase) and result in an interfacial region of varying composition with an appreciable thickness in terms of molecular dimensions. 

Structure-property relationships for metal-free organic magnetic materials, 45, 93 Substitution, aromatic, a quantitative treatment of directive effects in, 1, 35 Substitution, nueleophilic vinylic, 7, 1... 

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