Drago parameters

Double Heck reaction, 42 494 Double layer interface, 30 223-225 Double nucleophilic displacement, capped cyclodextrin, 32 437 Double-pulse method, 38 31 Double recognition models, 32 451 52 Doublet mechanisms, 30 43, 45, 47 Drago parameters, 38 212 Drougard-Decrooq equation, 30 345, 356, 371 Dry evaporation, perovskite preparation, 36 246-247... 

The adsorption of ammonia, pyridine, trimethylamine, and triethylamine on silica and silica-alumina was studied microcalorimetrically by Cardona-Martinez and Dumesic (18, 105). The calorimetric results of this study were correlated successfully in terms of Drago parameters for each catalyst. These parameters describe well the acidic properties of silica and the strongest sites (Lewis acid sites) on silica-alumina and may allow the prediction of heats of adsorption for a wide range of basic molecules with known Drago parameters on these sites. Parameters to describe the strength of the Brpnsted sites could not be determined because the contribution from these sites could not be studied independently. 

Previous attempts to estimate Drago parameters for solid surfaces met with limited success. Fowkes and co-workers (198-201) calculated Q and Ex values for SiOj, TiOj, and Fe Oj using a combination of UV and IR spectroscopies and a flow calorimeter. They determined heats of adsorption of pyridine, triethylamine, ethyl acetate, acetone, and polymethylmethacrylate (PMMA) in neutral hydrocarbon solutions. However, their results did not provide consistent Q/Ea parameters for the surface acid sites. It should be noted that the heats determined were for high surface coverages, and these values provide a lower bound for the actual acid strength distribution. 

FIGURE 4.13 Six parameters for base softness. Three (ji, D, and AAi/(C-I)) are discussed by Chen et al. (2000). is the volume polarization, is derived from the Drago parameters Cg and and is the reciprocal of the LUMO-HOMO energy difference. Values from Mu et al. (1998). 

Drago and co-workers have correlated a large body of enthalpies of adduct formation in Lewis acid-base systems, including some solvents as reactants, with this four-parameter equation ... 

The parameters and Ca are associated with the Lewis acid, and Eg and Cb with the base. a and b are interpreted as measures of electrostatic interaction, and Ca and Cb as measures of covalent interaction. Drago has criticized the DN approach as being based upon a single model process, and this objection applies also to the — A/y fBFs) model. Drago s criticism is correct, yet we should be careful not to reject a simple concept provided its limits are appreciated. Indeed, many very useful chemical quantities are subject to this criticism for example, p o values are measures of acid strength with reference to the base water. 

Eaq and Caq are the tendency of acid A and base B to undergo ionic and covalent bonding, respectively. Equation (2) resembles that proposed by Drago et al. (18) to model heats of complex formation of acids and bases in solvents of low dielectric constant. Only Lewis acids of ionic radius greater than 1.0 A obey Eq. (2). For all smaller Lewis acids, a third pair of parameters has to be introduced ... 

Hydrogen bonding is a special type of acid-base interaction (see Chapter 9). Probably the most important equation relating hydrogen bond strengths is the equation known as the Drago four-parameter equation,... 

Table 9.7 Acid and Base Parameters for Use in the Drago Four-Parameter Equation.

The double-scale four-parameter enthalpic equation proposed in 1965 (54) and successfully developed by Drago et al seems to be the best tool so far available for correlating and predicting the formation enthalpies of Lewis adducts in the gas phase or, if really necessary, in solution. 

Drago and co-workers Introduced an empirical correlation to calculate the enthalpy of adduct formation of Lewis acids and bases ( 5). In 1971, he and his co-workers expanded the concept to a computer-fitted set of parameters that accurately correlated over 200 enthalpies of adduct formation ( ). These parameters were then used to predict over 1200 enthalpies of interaction. The parameters E and C are loosely Interpreted to relate to the degree of electrostatic and covalent nature of the Interaction between the acids and bases. This model was used to generalize the observations involved in the Pearson hard-soft acid-base model and render it more quantitatively accurate. 

Number of heats used to determine the parameters for the specified base. The solvent recommended for getting enthalpies for comparison is indicated in parenthesis H stands for cyclohexane, hexane or gas phase and C, carbon tetrachloride or gas phase. See M. S. Nozari and R. S. Drago J. Am. Chem. Soc. 94, 6877 (1972). i>) Tentative value calculated from data limited to acids with similar C/E ratios. 

Pearson (2) and Drago and Weyland 38) proposed a two-parameter equation for the equilibrium constant K for the reaction between A and B... 

In spite of the fact that theoretically the approach of Drago is more sound, the use of the AN and DN numbers of Guttman is more accepted. These numbers can also characterize amphoteric materials and the available data base is much larger for this theory. Schreiber [30], for example, lists these parameters for a large number of polymers and other components used in polymer systems. 

Drago and coworkers have proposed a number of ways of expressing enthalpies of reactions in toms of contributing parameters of acids and bases. The first was... 

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