Taft equation, applications

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

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. 

Abstract—A review of the literature is presented for the hydrolysis of alkoxysilane esters and for the condensation of silanols in solution or with surfaces. Studies using mono-, di-, and trifunctional silane esters and silanols with different alkyl substituents are used to discuss the steric and electronic effects of alkyl substitution on the reaction rates and kinetics. The influences of acids, bases, pH, solvent, and temperature on the reaction kinetics are examined. Using these rate data. Taft equations and Brensied plots are constructed and then used to discuss the mechanisms for acid and base-catalyzed hydrolysis of silane esters and condensation of silanols. Practical implications for using organofunctional silane esters and silanols in industrial applications are presented. 

Nucleophilic substitutions of cycloalkylmethyl arenesulfonates C H2n-iCH20S02C6H4Z with anilines XCgH4NH2 in methanol at 65 °C have been studied.140 The reactivity order (given Z and X) n = 4>6>7>5 largely reflects the influence on steric effects of ling size, but the behaviour for n = 5 is anomalous. Application of the Taft equation in a form involving both polar and steric terms suggests that the retardation for n = 5 may be due to an enhanced polar (p cr ) term. 

B. Application of the Hammett-Brown- Taft Equation to Hydrogen... 

The correlations outlined above are empirical, that is, their applicability is proved by their success. The finding that the carrier alone or the concentration of platinum on the carrier did not change the parameters of the Taft equation to any essential degree makes possible some generalization of the results. All alkyl-substituted ethylenes are hydrogenated under the same mechanism, most likely through a simultaneous addition of both hydrogen particles to the Ti-adsorbed olefin (48, 78). 

Application of the simple two-parameter Hammett and Taft equations to heterogeneous catalytic data is possible if the solid catalyst introduces no other independent type of interaction between the substituent and... 

For testing the applicability of the Hammett and Taft equations the literature was searched for sets of reactivity data expressed in kinetic quantities and consisting of at least three structurally related compounds on the same solid catalyst. Some unsuccessful or only... 

The second application of a values for QS ARs in environmental sciences is for the estimation of values. In contrast to the substituent constants, the latter represent properties of the entire molecules and are used to quantify the degree of dissociation at a given (e.g. ambient) pH. In this way, like log values may appear in two ways as an endpoint by itself in hazard-assessment schemes and as a chemical descriptor to account for environmental conditions affecting chemical properties. For a large number of chemicals, values are available in the literature and may also be retrieved from databases. If such are not available and experimental determinations are not feasible, estimates may be obtained from a compound class-specific Hammett equation for aromatic substances or a Taft equation for aliphatic acids ... 

Figure 7.6 Application of Hammett and Taft equations to the rate of the hydrolysis of ketals that proceed according to mechanism (7.VII).

The relative importance of the hafide anion - HO - Cell interactions can be inferred from application of the Taft-Kamlet-Abboud equation to the UV-Vis absorbance data of solvatochromic probes, dissolved in cellulose solutions in different solvent systems, including LiCl/DMAc and LiCl/N-methyl-2-pyrrolidinone [96]. According to this equation, the microscopic polarity measured by the indicator, Ej (indicator), in kcalmol is correlated with the properties of the solvents by Eq. 1 ... 

The Hemmett equation is not applicable well to the reactions of aliphatic compounds partly due to some steric interference between the substituents and reaction site. For aliphatic compounds, Taft has proposed the following equation... 

The study of solute-solvent and solvent-solvent interactions in mixed solvents has been gaining significance in recent years61-64, because of the increasing application of these solvents. Casassas and collaborators67 have used the Kamlet-Taft multiparametric equation for the correlation of dissociation constants of acids in 1, 4-dioxane-water mixtures. They found that when the main solvent is retained the property does not involve significant changes in the cavity volumes and, in those cases, the pK in binary solvents can be described by equation 8 ... 

Hammett s success in treating the electronic effect of substituents on the equilibria rates of organic reactions led Taft to apply the same principles to steric, inductive, and resonance effects. The Hammett o constants appear to be made up primarily of two electronic vectors field-inductive effect and resonance effect. For substituents on saturated systems, such as aliphatic compounds, the resonance effect is rarely a factor, so the o form the benzoic acid systems is not applicable. Taft extended Hammett s idea to aliphatics by introducing a steric parameter ( .). He assumed that for the hydrolysis of esters, steric and resonance effects will be the same whether the hydrolysis is catalyzed by acid or base. Rate differences would be caused only by the field-inductive effects of R and R in esters of the general formula (XCOOR), where X is the substituent being evaluated and R is held constant. Field effects of substituents X could be determined by measuring the rates of acid and base catalysis of a series XCOOR. From these rate constants, a value a could be determined by Equation (5.9) ... 

The alternative approach is the attempt to quantify substituent effects, and this has been most successfully done by the Hammett equation and its various extensions (Hammett, 1970). Here one set of free energy data is compared with another set. One set is taken as standard (originally the dissociation constants of benzoic acids) and other rate or equilibrium data are compared (by logarithmic plots). So much has been written about this treatment that discussion here is unnecessary. Absolute values of a (the substituent constant) are not to be expected, in fact one would expect a different a for every reaction (i.e. for every p). In the present context it is important to note that both the Hammett equation and the closely related Taft treatment are based on systems where solvation is known to be important and therefore the application of these treatments using parameters derived from solution phase studies to reactions in the gas phase may be of uncertain value. 

Another important treatment of multiple interacting solvent effects, in principle analogous to Eq. (7-50) but more precisely elaborated and more generally applicable, has been proposed by Kamlet, Abboud, and Taft (KAT) [84a, 224, 226], Theirs and Koppel and Palm s approaches have much in common, i.e. that it is necessary to consider non-specific and specific solute/solvent interactions separately, and that the latter should be subdivided into solvent Lewis-acidity interactions (HBA solute/HBD solvent) and solvent Lewis-basicity interactions (HBD solute/HBA solvent). Using the solvato-chromic solvent parameters a, and n, which have already been introduced in Section 7.4 cf. Table 7-4), the multiparameter equation (7-53) has been proposed for use in so-called linear solvation energy relationships (LSER). 

Dealing with this type of multiparameter correlation analysis, a series of twelve articles entitled Solubility Properties in Polymers and Biological Media was published by Kamlet, Taft, Abraham et al. (Part 1 [273]...Part 12 [274]), as well as another series entitled Solute Solvent Interactions in Chemical and Biological Systems (Part 4 [358]... Part 7 [359]). The application of the LSER equation (7-58) to the prediction of solubilities of organic nonelectrolytes in water, blood, and other body tissues has been reviewed [286],... 

Reliable pATa values are not often available, although reasonable estimates ( 1 unit) can be calculated. Kabachnik and Mastryukova showed that the Hammett equation is applicable to organophosphorus acids, deriving substituent constants for substituents on phosphorus. These are claimed " to be superior to Hammett/Taft parameters. ... 

Taft s polar substituent constant, a, applicable to aliphatic systems is based on the notion that free energy relationships can exist between rate processes as well as between rate and equilibrium processes (Equations 3-5, Chapter 1). A rate process can thus be employed as a reference reaction. A simple example of such a Class II rate-rate free energy relationship is shown in Figure 3 where the reaction of phenoxide ion with 4-nitrophenyl-substituted benzoate esters is compared with the corresponding reaction of hydroxide ion, which therefore becomes the reference free energy change. 

So far, there has been no suitable experimental material available for practical application of the suggested relations, which requires that the original equations of the Hammett and Taft type would be perfectly satisfied in a number of solvents. 

Application of the multipaxaineter extrathexmodynamic technique to this series, where and R were alkyl groups, reveeded a good relationship between the A inhibitory pot cy (isorelative activity to DSG) and the substitu t partition constant (rr) and Taft steric factor (Es) in the position (equation 1, where the figures in parentheses are we Student t vedues for the coefficients of the equation and n, r, s, F and p have their usual statistical meaning). 

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