For Taft equation

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. 

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... 

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],... 

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.

Also other Type B and C series from Table II are consistent with the above elimination mechanisms. The dehydration rate of the alcohols ROH on an acid clay (series 16) increased with the calculated inductive effect of the group R. For the dehydrochlorination of polychloroethanes on basic catalysts (series 20), the rate could be correlated with a quantum-chemical reactivity index, namely the delocalizability of the hydrogen atoms by a nucleophilic attack similar indices for a radical or electrophilic attack on the chlorine atoms did not fit the data. The rates of alkylbenzene cracking on silica-alumina catalysts have been correlated with the enthalpies of formation of the corresponding alkylcarbonium ions (series 24). Similar correlations have been obtained for the dehydrosulfidation of alkanethiols and dialkyl sulfides on silica-alumina (series 36 and 37) in these cases, correlation by the Taft equation is also possible. The rate of cracking of 1,1-diarylethanes increased with the increasing basicity of the reactants (series 33). 

Positive slopes in partial correlations of small series for which the Taft equation is suitable. For a resonance parameter r = 0.8. 

Correlation analysis of solvent effects on the heterolysis of p-methoxyneophyl tosyl-ate has been performed by using the Koppel-Palm and Kamlet-Taft equations. The reaction rate is satisfactorily described by the electrophilicity and polarity parameters of solvents, but a possible role for polarizability or nucleophilicity parameters was also examined. 

Taft equation, log k /k ) = p a + 5 g, is —1-0 Fife and Milstien, 1967], but hexanoylchymotrypsin displays an enhanced rate of deacylation. The point for the hexanoyl group lies well above the line in a plot of log ( 3/ 0) - s> probably because of binding of... 

Taft equation (eq 16 in reference (36)) and reverse osmosis data on solute transport parameter Dam/K6 (defined by eq 12 later in this discussion) for different solutes and membranes (44,45,46), and (iv) the functional similarity of the thermodynamic quantity AAF+ representing the transition state free energy change (36) and the quantity AAG defined as... 

The structure of the reactant also influences the orientation, i.e. the ratio of 1- to 2-alkenes in the dehydration of 2-alkanols and the ratio of cis to trans alkenes. Table 4 shows that these ratios can also be correlated by the Taft equation. For the cis/trans ratio, a better fit was obtained with steric Es constants of substituents than with polar constants [127]. 

The relation between the acid strength of the catalysts and the mechanism has also been demonstrated by correlations [55,123] of the reaction parameter, p, of the Taft equation for the dehydration of secondary alcohols on A1203 + NaOH, Zr02, Ti02 and Si02 (see Table 4) with the sensitivity to pyridine poisoning, the heat of adsorption of water and diethylether and the kinetic isotope deuterium effects (Table 3) on the same catalysts (Fig. 5). The parameter p reflects the mechanism being... 

A clearer picture emerges from studies of substituent effects on the rate with a single catalyst. A series of alkyl chlorides (C2 to C6) was decomposed on a barium sulphate catalyst [184] and the rate data were correlated by the Taft equation. Large negative values of p were obtained, viz. —34.3 at 220°C and —40.3 at 280°C. Similarly, for a series of three alkyl bromides (ethyl, propyl and isopropyl) on silica—alumina, alumina—... 

A quantitative correlation of structural effects of four esters and four alcohols in the vapour phase transesterification on a macroreticular ion exchanger at 120°C was made using the Taft equation [441]. The authors found that rate coefficients [from eqn. (27)] yielded better correlation with steric (Es) than with polar (a ) parameters, while there was no significant difference between the correlations of the adsorption coefficients of alcohols, Kb, with both parameters. The correlations with Es yielded the slopes 1.4 and 0.6 for the reactivity of the esters and the alcohols, respectively, and —0.4 for the adsorptivity of the alcohols. The observed... 

Roberts269 has studied the hydrolysis of series of ethyl esters271 272 and alkyl benzoates273 in a limited range of water-dimethyl sulphoxide mixtures in some detail, and finds that the data for the hydrolysis of aliphatic ethyl esters (at 35°C in 85% dimethyl sulphoxide-water) fit the modified Taft equation (eqn. 5, p. 132). The values of p = 1.88 and 8 = 0.88 can be compared with p = 2.39 and 8 = 1.04 for 85% EtOH-water at the same temperature. The polar reaction constant is reduced in the dipolar aprotic solvent, consistent with a reduced degree of bond formation in the transition state, expected if the activity of the hydroxide ion is increased. However, Roberts considers that the sensitivity to steric effects, as measured by 8, would be reduced more substantially if bond formation were less advanced. It is difficult to accept this argument, since we... 

When a second nitrogen atom is introduced into the pyridine ring the basicity is reduced (pjRTa 5.23 for pyridine and 2.33 for pyridazine). The effect of the additional substituents on pKK depends on the position of the substituents (Table 3). An extensive set of pK values of pyridazine derivatives has been submitted to correlation analysis using the Hammett and the two Taft equations, which shows that the pKa values are most sensitive to the effect of a 2-substituent followed by the effects of 3- and 4-substituents. The interactions between nitrogen atom and 2-substituents represent over 70% of the inductive character. The composition of the effects of +M 4-substituents is significantly enriched in the resonance interactions, whereas -M 4-substituents interact with the nitrogen atom mainly by induction (77MI21201). 

Relationships between the nature of porphyrin and the redox potentials have been found. For example, The reduction potentials of 3,8-disubstituted DPIX DME and their pJsT, values are correlated by equation (24).145 Kadish et a/.146 have summarized porphyrin substituent effects by applying the Hammett-Taft equation (equation 25). 

---