Taft equations

The application of the Taft equation, derived from the Hammett equation (262)... 

Table III-55 shows the verification of the Taft equation. The result is analogous to that obtained for 3-alkylpyridines.

TABLE m-55. VERIFICATION OF THE TAFT EQUATION FOR THE KINETICS OF OUATERNIZATION OF 5-ALKYLTHIAZOLES (254)... 

Equation (7-51), the Taft equation, provides good correlations for many aliphatic reactions. The scope of this relationship is illustrated by Table 7-10. The reaction constant p has been interpreted along the lines described for the Hammett p values. 

The second aspect is more fundamental. It is related to the very nature of chemistry (quantum chemistry is physics). Chemistry deals with fuzzy objects, like solvent or substituent effects, that are of paramount importance in tautomerism. These effects can be modeled using LFER (Linear Free Energy Relationships), like the famous Hammett and Taft equations, with considerable success. Quantum calculations apply to individual molecules and perturbations remain relatively difficult to consider (an exception is general solvation using an Onsager-type approach). However, preliminary attempts have been made to treat families of compounds in a variational way [81AQ(C)105]. 

Taft equation, 229-230 Temperature, effect on rate, 156-160 Temperature-jump method, 256 Termination reaction, 182 Thermodynamic products, 59 Three-halves-order kinetics, 29... 

In contrast to the steric effoits, the purely electronic influences of substituents are less clear. They are test documented by linear free-energy relationships, which, for the cases in question, are for the most part only plots of voltammetrically obtained peak oxidation potentials of corresponding monomers against their respective Hammett substituent constant As a rule, the linear correlations are very good for all systems, and prove, in aax>rdance with the Hammett-Taft equation, the dominance of electronic effects in the primary oxidation step. But the effects of identical substituents on the respective system s tendency to polymerize differ from parent monomer to parent monomer. Whereas thiophenes which receive electron-withdrawing substituents in the, as such, favourable P-position do not polymerize at all indoles with the same substituents polymerize particularly well... 

The Hammett equation is not the only LFER." ° Some, like the Hammett equation, correlate structural changes in reactants, but the Grunwald-Winstein relationship (see p. 452) correlates changes in solvent and the Brpnsted relation (see p. 337) relates acidity to catalysis. The Taft equation is a structure-reactivity equation that correlates only field effects. ... 

A large number of modifications and refinements have been made on this equation, the most relevant being those which attempt to separate inductive < j and mesomeric Taft equation. In addition to substituent constants based on reactivity, acidity and the like, a variety of spectroscopically derived constants such as those from... 

It is follows from Equations (6.23) and (6.24) that the coefficient a in the Polany-Semenov equation depends not only on parameters Are and a but also on the incidental factor such as the range of variation of enthalpies of the selected series of reactions. The same situation is observed for coefficient p in the Hammett and Taft equations (see Equation [6.2]) [11],... 

Monoparametric equation A relationship in which the effect of structure on a property is represented by a single generally composite parameter. Examples are the Hammett and Taft equations. 

In terms of equilibrium constant, the Taft equation is written as... 

Hammett equation use, 17 92-96 of published data, 17 83-99 soUd catalysts limitations, 17 78-83 Taft equation use, 17 85-92 linear free energy relationships, 29 158-159 multiplet theory of, 19 1-195 of nature of catalyst, 19 159-176 metals, 19 159-161... 

The broad applicability of LFERs for heterogeneous catalytic reactions has been demonstrated independently by Kraus (23) and Yoneda (24-27). The first author concentrated mostly on the established relationships such as the Hammett and Taft equations, whereas Yoneda has concentrated particularly on correlations with reactivity indices and other quantities. Since then, LFERs have been widely applied to heterogeneous catalytic reactions, and experience has been gained as to the suitability of each different type. An important step has been made toward an interpretation of the slopes of linear correlations (parameter a in Eq. 3) as the quantities that are closely connected with reaction mechanisms. 

Among Type A relationships, the Hammett and Taft equations are most frequently employed for noncatalytic reactions. When utilizing them for catalytic reactions we must consider the reliability of the substituent parameters and their suitability for the given structural type of reactants. The Hammett equation... 

In order to gain an insight into the mechanism on the basis of the slope of a Type A correlation requires a more complicated procedure. Consider the Hammett equation. The usual statement that electrophilic reactions exhibit negative slopes and nucleophilic ones positive slopes may not be true, especially when the values of the slopes are low. The correct interpretation has to take the reference process into account, for example, the dissociation equilibrium of substituted benzoic acids at 25°C in water for which the slope was taken, by definition, as unity (p = 1). The precise characterization of the process under study is therefore that it is more or less nucleophilic than the reference process. However, one also must consider the possible influence of temperature on the value of the slope when the catalytic reaction has been studied under elevated temperatures there is disagreement in the literature over the extent of this influence (cf. 20,39). The sign and value of the slope also depend on the solvent. The situation is similar or a little more complex with the Taft equation, in which the separation of the molecule into the substituent, link, and reaction center may be arbitrary and may strongly influence the values of the slopes obtained. This problem has been discussed by Criado (33) with respect to catalytic reactions. 

However, there are enough examples of slope values that can be interpreted safely as will be shown in the following sections. These are the catalytic reactions for which the slopes of the Hammett and Taft equations have been found to be significantly different from zero, being well in the positive or negative range. Otherwise, careful comparison with the values for related processes has to be made, as Dunn (55) has pointed out. 

Fig. 1. Correlation of the rates of primary alcohol dehydration (40) (series 1 from Table II) in the coordinates of the Taft equation (8) for different separations of the reactants molecules into the parts substituent-link-reaction center.

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