The a Scale

Some of the problems faced in deriving a viable a scale were hinted at previously. Two are outstanding (i) can we trust the /Sj or even tt values derived on the 

The key equation is (Eq. (11-6)), derived from Eq. (11.1) it may be shortened further if d = 0, that is, if a family of solvents with similar poIari2abihty characteristics is considered. The authors [5] set out the conditions required for a suitable indicator chiefly, that this should possess sufficiently strong proton acceptor abilities so that competitive solvent self-association should not materially influence the enhanced solvatochromic effects due to hydrogen bonding and that the a/s ratio should be sufficient ( 1) to ensure that the frequent imprecision of tr values do not introduce unacceptable uncertainties into the a-scale. 

Compounds 5-7 are indicators that have successfully been used in this way (Eigure 11.2). For phenyl methyl sulfoxide 5, four equations have been derived, of which the most impressive is Eq. (11.7), in which the shift of its 4-carbon atom is referenced (AS) to that of the 3-carbon atom in trifluoromethylbenzene [5]. For 6, the comparison involves its F resonance versus that of fluorobenzene itself [9] to give Eq. (11.8), whereas similarly for 7, its F resonance relative to internal fluorobenzene [10] gives Eq. (11.9). In the same way, the Dimroth-Reichardt betaine (8, R = Ph) [11] may be characterized [5] as Eq. (11.10)  

Other examples are given [6]. The authors note certain solvents that quite often have to be excluded from correlation equations for special reasons in particular t-butyl alcohol (Bu OH), as it is prone to steric comphcations acetic acid, because it is almost totally self-associated so incapable of interacting through its OH donor group and water, for reasons to be discussed below. 

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Draw a straight line through the points on the H scale and on the turning axis X. The point where the line intersects on the A scale will determine the conductor area required. In our case it is 1 squre inch or 645 mm. ... 

Figure 7-2 indicates that this intramolecular assistance takes place with those compounds having substituents to the right of X = OMe = —0.78), for in this portion of the a scale compounds 8 solvolyze more rapidly than do 7. At the X = OMe member, however, the two series have essentially identical reactivities, and this behavior continues at more negative cr. It. therefore, appears that intramolecular participation by the double bond occurs when it is needed when the X substituent is sufficiently electron-donating to stabilize the cation, intramolecular assistance is not needed, so it does not occur, and the saturated and unsaturated series show the same reactivity. 

This procedure was applied to numerous solvatoehromie seales [Z, xr. Et (30)], using 4-nitroanisole as the solute ineapable of H bonding. As in the development of the TT seale, the a scale is averaged over several processes. A (3 seale of HBA ability (basicity) was established in a similar manner. Table 8-17 lists some tt, a, and (3 values. ... 

Attempts have also been made to separate non-specific effects of the local electrical field from hydrogen-bonding effects for a small group of ionic liquids through the use of the k scale of dipolarity/polarizability, the a scale of hydrogen bond donor acidity, and the (i scale of hydrogen bond basicity (see Table 3.5-1) [13, 16]. 

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 a scale of solvent acidity (hydrogen-bond donor) and the (3 scale of solvent basicity (hydrogen-bond acceptor) are parameters derived from solvatochromic mea-siuements used in adsorption chromatography [51,54,55]. 

The a scale of hydrogen bond donor acidities measures the ability of a solvent to donate a proton in a solvent-solute hydrogen bond,... 

Hardness measured on a Shore durometer. In addition to the commonly used Shore A scale there are several others O, OO, B, C and D, designed to open out either the soft or the hard end of the A scale. 

At constant pH, the parameter p is dependent on the electronic effects of the nitrosoarene substituent(s). Using only definite acceptor substituted nitrosoarenes, a Hammett correlation on the a scale was obtained25. Separate investigation of fc2RSH and fc2(rearr) for a wider selection of nitrosoarenes reacting with GSH revealed reasonable correlation with Hammett a constants only for fc2RSH (p = +1.4). However, Utrearr) was found to fit better on the Hammett a+ scale (p+ = —3.5)30 [for further discussion of Utrearr) see Section II.D.l.b]. 

Taft RW, Kamlet MJ (1976) The solvatochromic comparison method. 2. The a-scale of solvent hydrogen-bond donor (HBD) acidities. J Am Chem Soc 98 2886-2894. 

This equation was originally introduced for systems where the interactions he between those of the two reactions that define the a and the a+ scales with the parameter r+ intended to lie between 0 and 1. However, log w (and pK ) require values significantly >1 (Table 1.4), which is consistent with the idea that a+ underestimates the effect of para n donors on reactions of fully formed cations. The rate constants for the cation-forming reaction of Eq. 1 (log fen) on the other hand correlate with slightly < 1. In other words, these show a reasonable correlation with CT+, which is not surprising since both and refer to rate constants of reactions forming carbocations. 

Durometer. The Durometer hardness test was developed for and is used for determining the hardness of elastomers. The Durometer is a hand-held, spring-loaded instrument which when pressed against the sample forces a conical steel indenter into the surface. Durometer hardness numbers range from 0 to 100 and are read directly from the attached dial indicator. Several load scales are available, but the A scale (8 N = 822 gf) and the D scale (44.5 N = 4.54 kgf) are most common. Specifics of the test procedure are discussed in ASTM D2240 (2). Lighter load scales and larger diameter indenters are available for very soft materials such as foam. 

In the form of treatment developed by Taft and his colleagues since 195626-28, the Hammett constants are analysed into inductive and resonance parameters, and the sliding scale is then provided by multiple regression on these. Equations 4 and 5 show the basic relationships, the suffix BA signifying benzoic acid. The a/ scale is based on alicyclic and aliphatic reactivities (see below),... 

The A scale instruments have a frustoconical indentor, whereas the D scale has a pointed conical indentor. The scales overlap but the stresses on the material are different. There are also micro units available for measurements on small pieces of material, including "0"-rings. Figure 9.1 illustrates the method of operation of the Durometer hardness testers. 

Conversions between the mpy, ipy, ond ipm systems ore read directly from the A scale... 

Figure 21. Light scattering (LS) spectra of 2-picoline for different temperatures T > Tg (indicated as numbers) plotted as a function of rescaled frequency vxa solid line interpolation by a Cole-Davidson (CD) susceptibility, dotted line power-law indicating locus of the minimum (T > Tg), cf. Eq. 35 (adapted from [183]) below, say 175 K, the evolution of the spectra changes, i.e. the a-scaling fails.

X = Y = Z)] give a completely linear Y-T correlation against the a scale with an r value of 0.76 for the substituent range from p-dimethylamino to p-nitro (Yukawa et al., 1966). On the contrary, less satisfactory Y-T correlations are obtained for the pXr+ values for monosubstituted triphenylmethanols [3(X,H,H)j or for the log(k/ko) values for the solvolysis of the corresponding chlorides, in which the s-tt-ED p-methoxy substituent exhibits a higher r value than that for the other w-ED groups. In the monosubstituted [3C (X,H,H)], apparently only the s-7r-ED-substituted aryl tends to enter into coplanarity with the cationic orbital, to exert its maximum resonance effect. 

We also know that the a-scaled ordinary Hausdorff distances for each set of a-cuts taken for each a value as a a fulfill the triangle inequality... 

The a scale proposed to measure solvent hydrogen bond acidity, i.e. the ability of a bulk solvent to act as hydrogen bond donor toward a solute, was derived from 16 diverse properties involving 13 solutes as averaged values [Taft and Kamlet, 1976 Kamlet et al., 1983]. 

The a scale was proposed for solute HBD acidity based on log f values for 1 1 complexation of series of acids against a given base in dilute solution of CCI4 [Abraham et al., 1989b]. Forty-five Unear equations have been solved for each considered base by a series of acids ... 

Taft, R.W. and Kamlet, MJ. (1976). TTie Solvatochromic Comparison Method. 2. The a-Scale of Solvent Hydrogen-Bond Donor (HBD) Acidities. J.Am.Chem.Soc., 98, 2886-2894. 

Human loudness perception depends in a complex manner on both frequency and the overall loudness of sound. (For example, bass is more difficult to hear in music played at low volume than in the same music played at high volume.) To capture this behavior, two weighting scales have been developed for use in sound hazard analysis. The most common of these is the A weighting scale, which is commonly used to assess occupational and environmental noise. The A scale weights sounds in the 1000-6000 Hz range much more heavily than low-frequency sounds. The A-weighted intensities (dBA) of some common sounds are listed in Table 5. By contrast, the C weighting scale is used for very loud sounds and is a much flatter function of frequency. 

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