McConnell’s relation

A-2) Stereo-structure of free radical can be obtained from McConnell s relation [1]. This is the dependence of the isotropic hfs interaction, on dihedral angle, 0, shown in Fig. 7.1 as an example in the case of polyethylene end radical. 

In this equation, Ao is a small constant. B is also a constant. We can determine the twisted structure of the radical by evaluating the angle 0 from the experimental value of A. McConnell s relation can be explained by hyper-conjugation, which allows some spin density to be located in the fl-hydrogen Is orbital. The -hydrogen is bonded to Cp which is bonded to (C<, ) having an unpaired electron. 

The hyperfine structure of the ESR spectrum is used to identify trapped radicals. This is due to the interaction of unpaired electrons with magnetic moments of the nuclei surrounding unpaired electrons localized at the radical site. Hyperfine interaction is described by two terms. One is the isotropic interaction, a, originating from the contact interaction of the wave functions of electron- and nuclear spins, and the other is the anisotropic interaction, D, originating from the magnetic dipole-dipole interaction. The total hyperfine interaction, a -f D, is therefore essentially anisotropic and can also be expressed in the form of a tensor A. As in the case of g-tensor, A can be described by three principal values. A, Aj, and A3, corresponding to the principal axes in a proper molecular coordinate system. The magnitude of the isotropic term of hyperfine interaction depends on an overlap of the wave packets of the unpaired electrons and nuclei in the case of the hyperfine interaction of an unpaired electron with a P-proton (see Fig. 2.2), McConnell s relation [Eq. (2.3)] has been derived... 

The materials were y-irradiated up to ca. 1 Mrad at 77 K at about 10" Pa, and the ESR spectra of the alkyl radicals trapped in the polyethylene chain of the respective materials were recorded. The temperature dependence of hyperfine splitting due to p protons will mainly be discussed based on McConnell s relation (Eq. (2.2)). After... 

An exception to this rule arises in the ESR spectra of radicals with small hyperfine parameters in solids. In that case the interplay between the Zeeman and anisotropic hyperfine interaction may give rise to satellite peaks for some radical orientations (S. M. Blinder, J. Chem. Phys., 1960, 33, 748 H. Sternlicht,./. Chem. Phys., 1960, 33, 1128). Such effects have been observed in organic free radicals (H. M. McConnell, C. Heller, T. Cole and R. W. Fessenden, J. Am. Chem. Soc., 1959, 82, 766) but are assumed to be negligible for the analysis of powder spectra (see Chapter 4) where A is often large or the resolution is insufficient to reveal subtle spectral features. The nuclear Zeeman interaction does, however, play a central role in electron-nuclear double resonance experiments and related methods [Appendix 2 and Section 2.6 (Chapter 2)]. 

A second steady-state method involves the analysis of the broadening of the nuclear magnetic resonance spectra of phospholipids in bilayers containing low concentrations of spin-labeled phospholipids. A theoretical analysis of the relation between this line broadening and diffusion rates has been given by Brulet and McConnell.3 [In this paper (6) is not correct the subsequent equations are nonetheless correct. For an alternative derivation, see Brulet.2] In this paper it is shown that a number of measurements of nuclear relaxation rates T71 of nuclei in phospholipids are consistent with lateral diffusion constants in the range 10 7 to 10 R cm2/s. 

Eldridge, J.C., R.F. McConnell, L.T. Wetzel, and M.O. Tisdel (1998). Appearance of mammary tumors in atrazine-treated female rats probable mode of action involving strain-related control of ovulation and estrous cycling, Chapter 32. In L.G.Ballantine, J.E. McFarland, and D.S. Hackett, eds., Triazine Herbicides Risk Assessment. ACS Symposium Series 683. Washington, DC American Chemical Society, pp. 414—423. 

We shall demonstrate this for Arnold s EPR-spectroscopic scale (ax, Table 3) [36, 39], which relates the radical substituent constant ((7rad) to the benzylic a spin densities (p) according to Eq. (17), in which px and p refer to the substituted and unsubstituted benzyl radicals. Since the a hyperfine coupling constants (a) are linearily related to the spin densities by the McConnell equation [36,38], that is, ax oc px (cf. Section III.B), the coupling constants may be used instead of the spin densities [Eq. (18)]. According to Eq. (8) (pA = pB for the symmetrically substituted cases), the D value is proportional to the square of the spin density and a trAD scale may be defined by taking the square root of the ratio of the D values instead... 

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