ESR line

SWCNTs have been produced by carbon arc discharge and laser ablation of graphite rods. In each case, a small amount of transition metals is added to the carbon target as a catalyst. Therefore the ferromagnetic catalysts resided in the sample. The residual catalyst particles are responsible for a very broad ESR line near g=2 with a linewidth about 400 G, which obscures the expected conduction electron response from SWCNTs. 

The XRD peaks characteristic of Co and Ni disappeared after the treatment, as did the broad ESR line, successfully leaving only the narrow asymmetric line with 26 G linewidth as shown in Fig. 8 [40]. The g-value of the narrow line is =2.002 0.001. The narrow ESR line shows Dysonian at all temperatures in the range of 4-300 K. Furthermore, the ESR intensity is quite independent of T and thus the density of conduction electrons is invariant as a function of temperature as shown in Fig. 9. These show that the material is highly metallic, even at low 7. 

An ESRI system can be built with small modifications of commercial spectrometers by, for example, gradient coils fixed on the poles of the spectrometer magnet, regulated direct current (DC) power supplies, and required computer connections [40,53,55]. Gradients can be applied in the three spatial dimensions, and a spectral dimension can be added by the method of stepped gradients. The spectral dimension is important when the spatial variation of ESR line shapes (as a function of sample depth) is of interest this situation will be described below, in the ESRI studies of heterophasic polymers. In most systems, the software for image reconstruction in ESRI experiments must be developed in-house. 

Simulation programs for the ESR line shapes of peroxy radicals for specific models of dynamics have been developed for the study of oxidative degradation of polymers due to ionizing radiation [66]. The motional mechanism of the peroxy radicals, ROO, was deduced by simulation of the temperature dependence of the spectra, and a correlation between dynamics and reactivity has been established. In general, peroxy radicals at the chain ends are less stable and more reactive. This approach has been extended to protiated polymers, for instance polyethylene and polypropylene (PP) [67],... 

Figure 1.10 Effect of increasing microwave power on intensity and shape of an ESR line. Power increases from top to bottom of the figure. Units are relative values of Bx.

Figure 1.12 Effect of 100 kHz modulation on an ESR line of decreasing width. The x-axis is magnetic field, in Gauss, relative to the center of the line.

Figure 1.13 Effect of field changing (modulation/line width) on relative amplitude (left-hand axis) and observed width (right-hand axis) of an ESR line.

Things get a little more complicated when a spin 1 nucleus like 14N is added to the picture, but the same technique works again for the determination of the relative intensities of the ESR lines. Consider, for example, the relative intensities of the hyperfine lines arising from the pyrazine anion radical, whose spectrum is shown in Figure 2.3. Like that of the naphthalene anion radical, the spectrum observed for the pyrazine anion radical2 consists of 25 well-resolved... 

Figure 2.4 Derivation of the relative intensities of the 25 ESR lines of the pyrazine anion radical. See Section 2.5 for details of the method.

ESR line widths can provide a measure of the effective size of a paramagnetic molecule or ion - useful information when there is a suspicion that a radical has polymerized. 

ESR line widths are also sensitive to processes that modulate the g-value or hyperfine coupling constants or limit the lifetime of the electron spin state. The effects are closely analogous to those observed in NMR spectra of dynamical systems. However, since ESR line widths are typically on the order of 0.1-10 G... 

Thus, if the lifetime of a spin state is 81, the energy level is broadened by an amount H/81, with consequences for ESR line widths. Ward and Weissman1 added some unreduced naphthalene to a solution of the radical anion, and, from the observed broadening, computed 81, and from 8/ the rate constant for the electron transfer reaction ... 

Fig. 13. Theoretically calculated shape of the asymmetric ESR line based upon the Lorentzian form of the individual lines. Reprinted from (37) with permission of Plenum Press.

The reciprocal of the frequency can be defined as the rotational correlation time, tc, which represents the approximate time required for reorientation by random thermal tumbling. For values of tc < 5 x 10"9 s, an approximate theoretical solution for the linewidths of the three nitroxide ESR lines is given by (17) ... 

Esr line broadening. When one of the couples if uncharged, the electrostatic work term is approximately zero. Structural differences between the two species are also likely to be small (X small). The effect of solvent is contained in Using Eqns. (5.23) and (5.25)-(5.27), a plot of log A .xch vs (Dop -ZJ " ) should be linear with negative slope. 

The stochastic Liouville equation, in the form relevant for the ESR line shape calculation, can be written in a form reminiscent of the Redfield equation in the superoperator formulation, Eq. (19) (70-73) ... 

In many systems ESR line widths of Cu(ll) depend on the microwave frequency. It was shown in some early papers that lines are broader at Q-band (35 GHz)" and narrower at S-band" 7 compared with those at X-band. This was our initial motivation for... 

The formation of crystalline fulleride salts at the electrode occurs when less polar solvents and bulky cations are used for the electrosynthesis. The first fulleride salt was synthesized by Wudl by bulk electrolysis of in o-dichlorobenzene with tetraphenylphosphonium chloride as supporting electrolyte [39, 80]. This black microcrystalline material with the composition (Ph4P )3(Cgg )(Cr)2 exhibits an ESR line with a g-value of 1.9991 and a line width of 45 G at room temperature. Single crystals of the slightly different salts (Ph4P )2(Cgg )(Cr) and (Ph4P )2(C50 )(Br ) could be obtained by electrocrystallization and their crystal structure was determined [82, 83]. Magnetic measurements showed the presence of unpaired spins. 

The ENDOR technique refers to electron-nuclear double resonance. This consists of the effect on a partially saturated ESR line of simultaneously irradiating the sample with a radiofrequency to induce nuclear resonance transitions of hyperfine coupled nuclei. It may enable one to obtain information about signs of coupling constants. ELDOR is the technique corresponding to electron-electron double resonance. Such techniques, coupled with TRIPLE resonance, have been utilized and well described in a discussion of pyridine and 4,4-bipyridyl radical anion ESR spectra measured in sodium/liquid ammonia (80JMR<41)17). 

Because of the inherent non-planar structure of helicenes it seemed of interest to examine the spin distribution in helicene radical anions. For the mono anion of hexahelicene a set of 8 hyperfine splitting constants (hfsc s) and 38 = 6561 ESR lines can be expected. Such a spectrum will be poorly resolved. Indeed, it was not possible to determine hfsc s from the ESR-spectrum of hexahelicene 132). Using the ENDOR technique which reduces the amount of lines the eight hfsc s could be deduced, however, and the relative signs could be determined l33) by the triple resonance technique. 

The system used for amplification and detection of an ESR signal is such that the first derivative of the absorption line is recorded. The shape of an ESR line in solution is usually Lorentzian [Equation (3.86)]. The Lorentzian shape resembles a Gaussian (except that it falls off more slowly). Differentiation of the Gaussian shape (3.89) gives — 2cd(v — v0)exp[-d(v - v0)2], which has the form of the u=l harmonic-oscillator function [(1.133) and (1.137)] with x — y v0. Thus the first-derivative of an absorption resembles Fig. 1.1b with the origin at v0. (See also Problem 8.22.)... 

The multiplet hyperfine pattern of ESR lines in organic radicals is most frequently due to electron-proton interactions, but other nuclei with nonzero spin may also cause hyperfine structure. Weak satellite lines arising from interactions between the unpaired electron and C13 nuclei are sometimes observed C13 has and the analysis is straightforward. Nitrogen-containing radicals may show hyperfine splittings due to N14, which has 7 1. The possible Mj values are 1, 0, and -1, so that an electron... 

---