Hammett scale

Acidity measurements were again limited for the lack of suitable indicator base and even 1,3,5-trinitrobenzene, the weakest base used, was fully protonated (Ho —18.5) in the 22mol% solution of boron triflate. Extrapolation of this system to 40% B(CF3S03)3 in CF3SO3H would lead to an H0 value of —20 in the Hammett scale. Consequently, the acidity is comparable to that of the ternary system HSO3F-SbF5-S03. 

In spite of this interest of physical and biochemists, prior to the work of Hansch and Fujita there appears to have been no eifort to devise a scale of hydrophobicity analogous to the Hammett scale for electronic effects, or the Taft scale for steric effects. Part of this reluctance was due to the selection of the relevant solvent system for such a scale. In addition, biochemists who were interested in hydrophobic stabilization of protein structures needed only to consider the few hydrophobic amino acid side chains. 

Strength (Hammett Indicators) is not strictly applicable to microporous solids, although the Hammett scale is a convenient comparative index. As a result, a number of alternative approaches have been taken to determine the concentration, type and strength of acid sites within these solids. Most of these methods give relative scales of acidity, but it is broadly possible to calibrate these acidities to those observed for other acids. The methods fall into three broad categories direct measurements, measurement of interaction with un-reactive probe molecules and the use of catalytic test reactions. 

A Hammett plot of the pK values of p-substituted phenols against the Op values shows serious deviations for the members of the series at the extremes of the o scale, that is, for substituents that are strongly electron donating or electron withdrawing. It was recognized very early that such deviations could be rectified by choosing an appropriate o value for such substituents in effect, this means a different model reaction was adopted. The chemical basis of the procedure can be illustrated with the p-nitro substituent. The p-nitrophenolate ion is stabilized by through resonance as shown in 2. 

Using these indicators, Hammett was able to define a scale of acidity over the whole range from dilute aqueous solution to 100 per centl SC. 1... 

Over the years, the Hammett equation has been modified many times, usually by defining an alternative scale of a constants, the better to allow for special features found in some mechanisms, such as resonance stabilization and mesomeric effects. Thus, there are substituent scales known at cr+, er , crj, etc. The reader is referred to specialized treatises for further details.5-811... 

The Hammett equation is not successful for reactions of aliphatic compounds if the normal cr constants are used. A new scale of substituent constants, labeled cr, was invented to allow the extension of the method to such systems. The difference in the rates of hydrolysis of esters in basic versus acidic solutions is used to define the scale. The transition states are... 

The value of a for the methyl esters was chosen as 2.48, (not 1.00) so that the or values would be similar to the Hammett cr constants. Once established, the or scale can be used for many such reactions. Table 10-3 presents an abbreviated list of or constants.12... 

There are two main types of treatment, both involving multiparameter extensions of the Hammett equation, which essentially express the sliding scale idea. 

In the form of treatment developed by Taft and his colleagues since 195660-62, the Hammett constants are analyzed into inductive and resonance parameters, and the sliding scale is then provided by multiple regression on these. Equations 5 and 6 show the basic relationships. 

Much effort has been devoted to the attempt to set up scales of a0 values of general applicability. Only very limited success has been achieved in this direction150 and it seems naive to suppose that any simple LFER analogous to the Hammett equation could be successful in connection with the orthos fleet, except in rather limited and special situations. On the whole the various essays at scales of o0 values have not involved sulfinyl or sulfonyl... 

A good correlation with ordinary Hammett a values was based on 16 well-behaved substituents, and p-SOMe conformed well to this. Various other substituents showed deviations which were attributed to enhanced + R effects. These included p-SPh and this was explained in terms of 7t(pd) bonding, which was thus taken to play no part in the effect of p-SOMe on the methyl hyperfine splitting. More recently several 4-substituted benzyl radicals of the type RSO C6H4CH2 (n — 0,1 or 2 R = Me, Ph, Tol, COMe or OMe) have been examined by ESR spectroscopy249. The ability to delocalize spin density onto the substituent decreases in general as n increases and the effect of R depends on the oxidation state of sulfur. These authors have devised a new scale of substituent effects (sigma dot... 

Table IV lists comparative SD and / values for fittings of all of the reactions of Table II and III with each of the gr scales derived in this paper. The comparison includes figures for fittings with F and R values of Swain and Lupton (S L) and fitting with the Hammett equation. We believe the results given in Table IV provide a clear confirmation of the uniqueness and limited generality of the o/2(ba) scale. Very consistently, the fit achieved by the or (BA) scale is shown in Table IV to be superior by significant factors to that achieved by any of the other scales or by the simple op treatment. This fact is clearly reflected in the overall / values and the similarly weighted root-mean-square / values, F = y/lfnif lN, sum taken over all reactions. The value of F is. 067 for the basis sets of Table II (compare with overall / of. 058). The comparable F values are. 140 for Or, . 088 for S L, and. 155 for 0(p) with the data differences as explained in Table IV. For all sets of Table IV, the corresponding figures are. 073 for o (ba). -143 for a%, . 097 for S L, and. 209 for 0(py...

Finally, in this account of multiparameter extensions of the Hammett equation, we comment briefly on the origins of the a, scale. This had its beginning around 1956 in the a scale of Roberts and Moreland for substituents X in the reactions of 4-X-bicyclo[2.2.2]octane-l derivatives. However, at that time few values of o were available. A more practical basis for a scale of inductive substituent constants lay in the o values for XCHj groups derived from Taft s analysis of the reactivities of aliphatic esters into polar, steric and resonance effects . For the few o values available it was shown that o for X was related to o for XCHj by the equation o = 0.45 <7. Thereafter the factor 0.45 was used to calculate c, values of X from o values of XCH2 . ... 

The acidity function is determined by successive use of a range of indicators. Hammett and Deyrup started with p-nitroaniline, the pKAl of which in a dilute aqueous solution is 1.11 (the solvolysis constant has been identified with the acidity constant). Since in a dilute aqueous solution, Yb = Ybh+ 1, the acidity function for the aqueous media goes over to the PH scale. By means of p-nitroaniline, the acidity constant of another somewhat more acidic indicator is obtained under conditions such that both forms of each indicator are present at measurable concentrations. Then H0 as well as the p A2 of the other indicator is determined by using Eq. (1.4.40). By means of this indicator, values of H0 not accessible with p-nitroaniline may be reached. The H0 scale is further extended by using a third indicator and its p A, is determined in the same way (see Fig. 1.11). The concentration ratios are determined photometrically in the visual or ultraviolet region. Figure 1.12 shows the dependence of H0 on the composition of the H2S04-H20 mixture and was obtained as indicated above. 

Katritzky and his colleagues have used equilibrium proto nation to estimate the aromaticity of furan and similar heterocycles using 2,5-di-tert-butylfuran as substrate in sulfuric acid. In agreement with the foregoing discussion, the furan does not behave as a Hammett (i.e., oxygen) base but as a carbon base similar to azulene. On Reagan s Hc scale, the furan gave n = 1.22, correspond-... 

The exact p R+ value for 20+ could also not be determined by the earlier method. Therefore, dimethyl sulfoxide (DMSO)-water-tetramethylammonium hydroxide (0.011 M) system was used for the measurement. The H scale (Hammett acidity scale) for the system ranges from 12 in water up to 26.2 in... 

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