P-Value measurement

The Hammett p values measured by changing the para-substituent on the nucleophile in DMF and methanol (Table 23) support this conclusion. The smaller magnitude of the p value in methanol indicates that the change in charge on the nucleophilic sulfur atom is smaller on going from the initial state to the transition state in methanol than it is in DMF. Therefore, S Ca bond formation must be much less complete (the S Ca bond is longer) in the transition state in methanol. 

FIGURE 2.1.16 (a) Polar plot of the mobility at the rubrene a-b surface (the angle is measured between the b axis and the direction of current flow), (b) The four-probe measurements of the channel conductivity and the contact resistance (inset) as a function of along the b and a axes the p. values measured along the b and a axes are 15.4 cmWs and 4.4 cmWs, respectively. (From Sundar V. C. et ah, Science, 303, 1644, 2004.)... 

Ideally, measurements should be made at as many magnetic field strengths as possible, so that a unique fit of the experimental data to a particular model, may be obtained. As already mentioned, in addition to measuring the p values, measurement of relaxation times will help to substantiate the model chosen. 

Corresponding scales can be derived, e.g. from log P values measured in n-octanol/water, heptane/water, and other systems [192], from the water dragging... 

There is also evidence for the role of acylium ions in some acyl substitutions, such as the reactions of acyl halides with nucleophilic reagents in acetonitrile, nitromethane, and ethanol and the hydrolysis of some acyl fluorides. 203,206,207 ylium ions are more likely candidates for reaction intermediates under acidic conditions. Bender reported that the hydrolysis of a series of substituted methyl 2,6-dimethylbenzoates in 9.7 M sulfuric acid proceeds through an acylium ion intermediate. Hydrolysis of a series of substituted 2,6-dimethylbenzoyl chlorides in 99% CH3CN-H2O was determined to involve an acylium intermediate under acidic or neutral conditions, and p values (measured by cr" ) were found to be -3.85 and -3.73, respectively. The value of p under basic conditions was -I-1.20, suggesting that the base-promoted reaction does involve a tetrahedral addition intermediate. ... 

Substituents can be introduced not only into the betaine solute, but also into the surrounding solvent molecules. Let us consider a betaine dye solution in various alcohols R-OH with different alkyl groups R. An enhanced hypsochromic shift of the solvatochromic absorption band with increasing hydrogen-bond donor ability of the alcohols should be obtained. This is indeed the case(25). As Figure 9 shows, even exists a linear correlation between the modified E.p-values, measured in nine different alcohols, and Taft s polar substituents constants for the alkyl groups R of these alcohols(25). 

Here again the sensitivity of the betaine dye to changes of substituents - as given by its different chemical reactivity - is solvent-dependent. This sensitivity is lower in the more polar solvents, and vice versa. For example, the Hammett reaction constant p for this alkylation reaction, measured in polar acetonitrile as solvent, is with -0.15 considerably smaller thati the corresponding p-value measured in the less polar solvent chloroform, which amounts to -0.40(26). 

After V and the corresponding p values measured by a series of experiments, then... 

The existence of this situation (for nonporous solids) explains why the ratio test discussed above and exemplified by the data in Table XVII-3 works so well. Essentially, any isotherm fitting data in the multilayer region must contain a parameter that will be found to be proportional to surface area. In fact, this observation explains the success of Ae point B method (as in Fig. XVII-7) and other single-point methods, since for any P/P value in the characteristic isotherm region, the measured n is related to the surface area of the solid by a proportionality constant that is independent of the nature of the solid. 

The hydrophobic constant r is a measure of the contribution of a substituent X to the lipophilidty of compound R-X compared with R-H. The constant representing the solvent/solvent system, analogously to Hammett s p constant for the reaction type, was arbitrarily set to 1 for octanol/water and thus does not appear in Eq. (7). The lipophilidty constant ti allows the estimation of log P values for congeneric series of compounds with various substituents (see Eq. (8)). 

The applicability of the two-parameter equation and the constants devised by Brown to electrophilic aromatic substitutions was tested by plotting values of the partial rate factors for a reaction against the appropriate substituent constants. It was maintained that such comparisons yielded satisfactory linear correlations for the results of many electrophilic substitutions, the slopes of the correlations giving the values of the reaction constants. If the existence of linear free energy relationships in electrophilic aromatic substitutions were not in dispute, the above procedure would suffice, and the precision of the correlation would measure the usefulness of the p+cr+ equation. However, a point at issue was whether the effect of a substituent could be represented by a constant, or whether its nature depended on the specific reaction. To investigate the effect of a particular substituent in different reactions, the values for the various reactions of the logarithms of the partial rate factors for the substituent were plotted against the p+ values of the reactions. This procedure should show more readily whether the effect of a substituent depends on the reaction, in which case deviations from a hnear relationship would occur. It was concluded that any variation in substituent effects was random, and not a function of electron demand by the electrophile. ... 

The difference in 5 values for two substances (P,Q) measured against a standard substance is approximately equal to 1000 times the natural logarithm of their fractionation factor (app). 

The Chauvenet tables relate the number of measurements to p values and assess the probability that the unusual value may be real or may be ignored. In the present example, the tables show that p = 1.73 for 6 measurements. Since the calculated value (1.80) is greater than 1.73, the result may be rejected. 

If the fractions of triads could be measured, they either would or would not lie on a single vertical line in Fig. 7.9. If they did occur at a single value of p, this would not only give the value of p (which could be obtained from the fraction of one kind of triad), but would also prove the statistics assumed. If the fractions were not consistent with a single p value, higher-order Markov statistics are indicated. 

Fig. 8. Sedimentation equipment performance where the particles have a A5 value of 1.0 g/cm and a viscosity, p., value of 1 mPa-s(=cP). The value of is twice the settling velocity at G = 1, and Q = overflow discharge rate in measurements given.

The numerical values of the terms a and p are defined by specifying the ionization of benzoic acids as the standard reaction to which the reaction constant p = 1 is assigned. The substituent constant, a, can then be determined for a series of substituent groups by measurement of the acid dissociation constant of the substituted benzoic acids. The a values so defined are used in the correlation of other reaction series, and the p values of the reactions are thus determined. The relationship between Eqs. (4.12) and (4.14) is evident when the Hammett equation is expressed in terms of fiee energy. For the standard reaction, o%K/Kq = ap. Thus,... 

Another example of enhanced sensitivity to substituent effects in the gas phase can be seen in a comparison of the gas-phase basicity for a series of substituted acetophenones and methyl benzoates. It was foimd that scnsitivtiy of the free energy to substituent changes was about four times that in solution, as measured by the comparison of A( for each substituent. The gas-phase data for both series were correlated by the Yukawa-Tsuno equation. For both series, the p value was about 12. However, the parameter r" ", which reflects the contribution of extra resonance effects, was greater in the acetophenone series than in the methyl benzoate series. This can be attributed to the substantial resonance stabilization provided by the methoxy group in the esters, which diminishes the extent of conjugation with the substituents. 

The acidity of various substituted acetophenones has been measured in DMSO. Would you expect the p value for a Hammett correlation to be positive or negative Would you expect the best correlation with a, or [Pg.442]

Next we turn to the magnitudes of the p constants. Evidently if p = 0, there is no substituent effect on reactivity. Moreover because p = -I-1.000 by definition for the aqueous ionization of benzoic acids, we have a scale calibration of sorts. Wiberg gives examples of p as a measure of the extent of charge development in the transition state. McLennan" has pointed out that p values must first be adjusted for the transmission factor before they can be taken as measures of charge devel-... 

Instead of the definition in Eq. (7-82), the selectivity is often written as log k,). Another way to consider a selectivity-reactivity relationship is to compare the relative effects of a series of substituents on a pair of reactions. This is what is done when Hammett plots are made for a pair of reactions and their p values are compared. The slope of an LEER is a function of the sensitivity of the process being correlated to structural or solvent changes. Thus, in a family of closely related LFERs, the one with the steepest slope is the most selective, and the one with the smallest slope is the least selective.Moreover, the intercept (or some arbitrarily selected abscissa value, usually log fco for fhe reference substituent) should be a measure of reactivity in each reaction series. Thus, a correlation should exist between the slopes (selectivity) and intercepts (reactivity) of a family of related LFERs. It has been suggested that the slopes and intercepts should be linearly related, but the conditions required for linearity are seldom met, and it is instead common to find only a rough correlation, indicative of normal selectivity-reactivity behavior. The Br nsted slopes, p, for the halogenation of a series of carbonyl compounds catalyzed by carboxylate ions show a smooth but nonlinear correlation with log... 

Closely related to water solubility as a polarity measure is the partition coefficient of a substance between water and an immiscible organic solvent. Most commonly the organic solvent is selected to be n-octanol, and the symbol P is given to the octanol/water partition coefficient. Then log P is a quantitative measure of hydro-phobicity and, therefore, of nonpolarity. Table 8-3 gives log P values for many of... 

C 0.5012 mol 2 at 15°C). It is clearly unwise to associate a pH meter reading too closely with pH unless under very controlled conditions, and still less sensible to relate the reading to the actual hydrogen-ion concentration in solution. For further discussion of pH mea.surements, see Pure Appl. Chem. 57, 531-42 (1985) Definition of pH Scales, Standard Reference Values, Measurement of pH and Related Terminology. Also C E News, Oct. 20. 1997. p. 6. 

Few other reactions of series of substituted pyridines have been investigated extensively. Dondoni, Modena, and Todesco have measured the rate of N-oxidation of a limited series of pyridines and found a good correlation with normal u-values with a p-value of — 2.23. The A-alkylation of pyridines with alkyl iodides in nitrobenzene has been studied by Brown and Cahn and by Clarke and Rothwell. Unfortunately, the only data available are for the parent compound and for alkyl derivatives, and, since the a-values for the various alkyl groups in a given position are substantially constant, this leaves a correlation of only three independent points. However, the rates of A-alkylation of the j8- and y-alkyl derivatives are so nearly equal that it appears as if no correlation existed. Clarke and Rothwell have also studied the alkylation with allyl bromide in nitromethane at various temperatures, and in this case a more extensive series is available. The authors state that no overall Hammett correlation is obtained however, the j8-substituted derivatives fall on one straight line and the y-derivatives on another one with a different slope. The data are shown in Fig. 2. The line for the j8-compounds, p = — 2.53 0.31, r = 0.95, is seen not to be very good the line for the y-derivatives, p = — 1.42 0.06, r = 0.99, is much more satisfactory. It does not seem likely that the discrepancy is due to the intervention of resonance effects, since in this case one would expect the correlation for the y-derivatives to be poorer than that for the j8-analogs. More extensive studies with a wider variety of substituents would seem very desirable. 

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