Deviant points

The existence of an isokinetic relationship supports (but does not prove) a claim that a single mechanism operates along the series. If certain members deviate from the correlation to a significant extent, this observation is a suggestion (that bears further checking) that a new mechanism has come into play. The deviant point(s) will likely lie above the isokinetic line, since a new mechanism wins out because it is faster than the normal one (and of course the rate constant records the sum of the contributions from all of the operative pathways). 

Fig. 4 Correlation of constants for transition state stabilization (pKxs) and substrate binding (pKs) for the cleavage of meta- and para-substituted phenyl acetates by /3-CD. The substituents are alkyl groups and the four halogens. The two deviant points are for longish p-alkyl groups (n-butyl and n-pentyl). Data from Tables A5.2...

The metal-solvent interaction is expected to depend on the donicity of the solvent the higher the donor number of the solvent the stronger the solvent-metal interaction should be. Hence, a correlation between the contact potential difference A>// (a = 0) and the donor number of the solvent should be observed. However, this correlation for the Hg electrode is rather poor, with the most deviant point having been found for water, that is, for the case of the strongest dipole-dipole interaction in the bulk. The correlation is better when acceptor numbers of solvents are taken into account. ... 

Figures Reaction of substituted phenoxide ions with a 4-nitrophenyl triazinef The significance of the deviant points is discussed in Chapters 6 and 7...

Even though the data of Problems 7 and 8 fit a linear Equation (except for the deviant points) they can be forced to fit the Equation for the quasi-symmetric method (Equations 11 or 12) to yield a value for Ap of 0.1 units (with an uncertainty of 0.1). Indicate how this value affects the conclusions that can be drawn regarding the concertedness or otherwise of the displacement reaction. Compare the Ap with that for the pyridinolysis of N-triazinyl-pyridinium ions." ... 

A prerequisite that the mechanism in a series should be the same is a linear free-energy correlation if a member of the series takes a different pathway then the alternative mechanism will be more favourable, will predominate over the normal and will be diagnosed as a positive deviant point. An example of this behaviour is the demonstration that general acid catalysis by primary amines of the iodination of acetone differs from that by carboxylic acids (Fig. 24) [3a] simple proton transfer is identified with the carboxylic acid catalysis and it is thought that amines utihse Schiff s base formation (Eqn. 116) leading to a more favourable path. 

Fig. 26. Dependence of hydrolysis of acyl-a-chymotrypsins (t 3) on the reaction of hydroxide ion with the corresponding ethyl esters [11 la]. Deviant points 1, 3-phenylpropionyl 2, 3-(4 -hydroxyphenyl)pro-pionyt 3, 3-(3 -indolyl)propionyl.

A problem which occasionally arises in non-linear free-energy correlations is whether an observed rate constant lower than that extrapolated for a given series is always the result of a change in mechanism (Fig. 32). The low rate constant could result from a change in mechanism provided a change in rate-limiting step had occurred prior to the value of the parameter corresponding to the deviant point (Fig. 32). 

Fig. 2. Chain stiffhess, a, as a function of polymer chain area, nm. ( ) theta solvent conditions (0) non-theta solvent conditions (A) deviant points. The solid line is a least-squares fit to alt but the deviant points. From ref 5.

Fig. 4. EquivaieiU Biagg spacings for amorphous peaks of ciystallizable polymers as a functioii of the cross-sectional area of the crystalline chain conformation. Linear least-squares lines are shown. +) deviant points. From ref 24. 

Fig. 21. Log AH a - log area per chain for the values in Table A-VII-1. The equation for the bottom line without the high deviant points is AH = A . (Points 2,5,7", 8, 12 , and 12" not included in the correlation.) Dashed line shows slope from a plot of log - log A...

Schwartz, L. M. 1985. Rejection of a deviant point from a straight-line regression. Anal. Chim. Acta 178 355-359. 

Regardless of the temperature-measuring deviee to be used, on-site eali-bration of the entire measurement system is desirable. Usually, a two-point eheek ean be made by employing frozen and boiling water. At the very least, all deviees ean be eheeked at a eommon temperature, preferably in the midrange of expeeted temperatures so that any deviant deviees ean be disearded. This eheek is partieularly desirable for low-head maehines where the temperature rise will be slight. 

In another case, one of the core members lost his job as a result of being taken to a psychiatric hospital in an LSD panic attack. Becker has pointed out that such a crisis can often be the first step in a frankly deviant career (Becker, 1963). However, this young man simply got himself another job, in which such an item on his record would not cause him trouble. It is also of considerable interest that this panic attack occurred away from the group, when he took LSD with some friends he was introducing to the drug. 

A related isomerization is that of the trans-1,2- to 1,1-disubstituted alkenes. The only series for which there is sufficient data are for the methyl, n-alkyl substituents. The slope of equation 11 is 1.01 and so the enthalpies of isomerization are nearly constant, although there is some scatter in the data. The point representing the C5 isomers is deviant in the plot, again suggestive of the unreliability of the enthalpy of formation of... 

These observations can be put on a more chemical basis by examining the variation of AHpp with the atomic hydrogen-to-carbon ratio (Figure 4). Here, the clustering of exinite properties is even more prominent. The single deviant exinite point comes from a very different organic matter type—alginite, rath-... 

In this reaction, partial rate factors (relative to reaction at the 2-position) were determined (Table 6.11) (72JOC2615), and if the points for the C02Et substituents are excluded (5-C02Et is particularly deviant), a very good correlation with cr+ is obtained (p = -6.7), and again the effects of... 

We find that the first periodic selection happens at about 100 hr, with 100-200 hr between subsequent ones. It can range from as early as 50 hr, if there is a common mutation which is strongly selected such as lactose constitutive mutations in lactose-limited chemostats,17 to as late as about 120 hr. We sample for about 100 hr and then eliminate deviant final points (those that significantly increase the variance) to eliminate frequency changes caused by periodic selection. It is this limitation of the time over which selection can be measured that limits the resolution of the measurement of the selection coefficient to about 0.002/hr. 

On the other hand, the products under conditions 2 and 4 in Table I show considerable discrepancy from what would be considered a normal distribution of equilibrium products. Although the data were taken at a point when there seemed to be little change occurring in the system, it can still be argued that equilibrium was not achieved in these examples. Later work with lithium cryptate, one of the deviants in Table I, indicates agreement in the distributions of D4, D5, and Dg reported by earlier workers (26). Unfortunately, no data were given for Wp in that publication. 

Considerable scatter in the neighborhood of the critical point is a result of the difficulty of measurement and the deviation amplifying effect of the function A (Pr) for Pr near unity. In the case of smoothed data, a smoothing j3c which departs from Equation 11 will lead to a singularity in A at the critical point. Similarly, deviant critical properties Pc and Vc will lead to a singularity in A at the critical point (for a detailed discussion, see Thompson (20)). 

Mixtures that have a maximum in the Px curve exhibit positive deviations from ideal-solution behavior that is, the activity coefficients are greater than unity. Such mixtures are called positive deviants and their azeotropes are called positive azeotropes. Since such mixtures have minima in their Tx curves, those same azeotropes are also called minimum boiling-point azeotropes. Positive deviants usually occur when attractive intermolecular forces between molecules of the same species are stronger than those between molecules of different species. 

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