Exner relationship

The kinetics of oxidation of aniline by sodium perborate catalysed by the meso-tetraphenylporphyriniron(III) chloride reveal that the catalyst is slowly degraded. The retardation in the rate with increasing H+ ions suggests that the protonated aniline is less reactive. Sodium perborate oxidation of several meta- and puru-substituted anilines complies with isokinetic and Exner relationships but not to any of the linear free energy relationships. The solvent interaction has a major role in governing the reactivity. ... 

Figure 3.13. Simple relationships between properties and microstriictural geometry (a) hardness of some metals as a function of grain-boundary density (b) coercivity of the cobalt phase in tungsten earbide/coball hard metals as a function of interface density (after Exner 1996).

It was not until the 1970s that the statistics of the isokinetic relationship was satisfactorily worked out.Exner first took this approach Let k, and 2 be the rate constants for a member of a reaction series at temperatures T, and T2, with T2 > T, and let k° and k° be the corresponding values for the reference member of the series. Then Eqs. (7-76) and (7-77) are easily derived for the reaction series. 

Obviously for this method to work the ratio T1IT2 must be appreciably smaller than unity. Provided this condition is met, this method is a simple and reliable way to test for an isokinetic relationship or to detect deviations from such a relationship. Exner shows examples of systems plotted both as log 2 vs. log and as AH vs. A5, demonstrating the inadequacy of the latter plot. Exner has also developed a statistical analysis of the Petersen method this analysis yields p and an uncertainty estimate of p. Exner has applied his statistical methods to 100 reaction series, finding that 78 of them follow approximately valid isokinetic relationships. 

Earlier analyses making use of AH vs. AS plots generated many p values in the experimentally accessible range, and at least some of these are probably artifacts resulting from the error correlation in this type of plot. Exner s treatment yields p values that may be positive or negative and that are often experimentally inaccessible. Some authors have associated isokinetic relationships and p values with specific chemical phenomena, particularly solvation effects and solvent structure, but skepticism seems justified in view of the treatments of Exner and Krug et al. At the present time an isokinetic relationship should not be claimed solely on the basis of a plot of AH vs. A5, but should be examined by the Exner or Krug methods. 

Hammett discovered linear relationships between two sets of equilibrium or rate constants of substituted benzene derivatives (reviews Hammett 1937, 1940, 1970, Johnson 1973, Exner 1988, and others see Scheme 7-1). 

Exner, O. In Advances in Linear Free Energy Relationships, Chapman, N. B. Shorter, J., Eds. Plenum Press London, 1972 pp 1-69. 

O. Exner, in Advances in Linear Free Energy Relationships (Eds. N. B. Chapman and J. Shorter), Chap. 1, Plenum Press, London, 1972. 

The interactive properties of the derivatives of benzene vary widely, depending upon the nature of the substituent and its influence upon the aromatic ring. The effects of substituents have been categorized and quantified through the introduction of first the Hammett and then the Taft constants, which were obtained through the analysis of linear free-energy relationships (Exner 1988). The electrostatic potentials of benzene derivatives provide another means of ascertaining how the substituents affect the interactive behavior of the aromatic systems (Murray, Paulsen, and Politzer 1994). 

Exner, 0. In "Advances in Linear Free Energy Relationships". Chapman, N.B. and Shorter, J. 

Exner O (1972) In Chapman NB, Shorter J (eds) Advances in linear free energy relationships. Plenum, London... 

MII O. Exner, in Advances in Linear Free Energy Relationships (N. B. 

Confirmation of these expected relationships have been obtained by Ohaudesaignes G.R. OXLVii. 104j4j, 1908), Perrin, Exner, and others. 

Extensive theoretical analyses of the compensatory enthalpy-entropy relationship were first carried out by Leffler and later by Leffler and Grunwald, Exner, and Li. The empirical linear relationship between the thermodynamic or activation parameters AH and AS) directly leads to Eq. 11, where the proportional coefficient p, or the slope of the straight line in Figure 9, has a dimension of temperature. Merging Eq. 11 into the differential form of the Gibbs-Helmholtz Eq. 12 gives Eq. 13 ... 

Good et al. (15,30,140) have also considered these problems and extended Exner s approach in a reassessment of the validity of previously reported relationships between the energies and entropies of activation for the fluidity of certain aqueous solutions. These workers show, for the particular systems considered, that the relationship is nonlinear. Good et al. (30,140) emphasize the necessity, in the general statistical analysis, of distinguishing between two alternative objectives, which are... 

The high quality (r = —0.987) of the linear correlation in Fig. 2 a, for which Eq. (1) is given in the caption, is quite surprising for several reasons. In particular, because free enthalpies of activation AG are correlated with strain enthalpies Hs despite the fact that there is neither an isoentropic (AS = const.)41) nor an isokinetic relationship (AH aAS ) 41) within this series. Indeed AS varies from 13 to 26 entropy units14). In a kind of Exner test42) it was shown, however, that the order of decreasing AG (T) values is independent of temperature and therefore significant for structural interpretation 14). 

Exner O, "Additive Physical Properties, 1. General Relationships and Problems of Statistical Nature", Collection Czechoslov. Chem. Commun., 1966, Vol 31. 

In a broader context, LFER and similar approaches are subsets of correlation analyses. Exner defines correlation analysis as a mathematical treatment starting from experimental data and seeking empirical relationships which can subsequently be interpreted theoretically. Although certainly not restricted to chemistry, correlation analysis has been developed extensively in physical organic chemistry. In addition to LFER, LSER, QSAR, and QSPR involve empirical models and, hence, fall in the category of correlation analysis. 

O. Exner, Correlation Analysis of Chemical Data, Plenum Press, New York, 1988, pp. 99-111 O. Exner, The Enthalpy-Entropy Relationship, Progr. Phys. Org. Chem., 1973,10,411. 

---