The ESR linewidth

The linewidth, or lineshape, is the third aspect of the ESR spectrum important in any study of radicals. The two most frequently encountered lineshapes observed are the Lorentzian and Gaussian. The Gaussian line-shape is observed when the line is the superposition of a large number of unresolved individual components, such a line being referred to as inho-mogeneously broadened. More important is the Lorentzian lineshape which is often observed for radicals in solution, when complications due to unresolved hyperfine splittings do not occur. The Lorentzian lineshape may be defined by 

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When excess of ZnTPP (1.0 X 10 3 M) is used for the oxidation with Ru(bpy)33+ (5.0 X 10 4 M) at 233 K, the ESR linewidth becomes broader than the spectrum obtained in the equimolar condition (Fig. 13.2c). The computer simulation spectrum with a broader linewidth is shown in Fig. 13.2d. The line broadening results... 

In isotropic three-dimensional conventional metals 2e Tle and the linewidth has a temperature dependence which is similar to that of the resistivity [13]. The dominant process leading to the spin-lattice relaxation rate, l/Tle, comes from the modulation of spin-orbit interactions by phonons. Elliot [14] has shown that in this case, the ESR linewidth, AHpp, is... 

In Fig. 23 we show the ESR linewidths AHpp for the six compounds discussed above. The larger widths of (TMTSF)2X salts, compared to the (ET) Re04 derivatives, is due to the larger spin-orbit coupling in Se than in S. Apart from this, the linewidths show the following features. 

Fig. 23. A comparison of the ESR linewidths of various (TMTSF)2X, X = monovalent anion, and ET Re04 salts.

Several formalisms have been applied to relaxation in exchanging radicals. Principal among these are modifications of the classical Bloch equations (8, l ) and the more rigorous quantum mechanical theory of Redfield al. (8 - IJ ). When applied in their simplest form, as in the present case for K3, both approaches lead to the same result. Since the theory has been elegantly described by many authors (8 - 12 ), only those details which pertain to the particular example of K3 will be presented here. Secular terms contribute to the ESR linewidth (r) and transverse relaxation time (T ) by an amount... 

ESR is very useful in the study of dynamic properties of membrane components because of its high sensitivity and favorable time scale. Early ESR studies of short-range lateral diffusion in membranes were based on Heisenberg exchange (HE) effects of nitroxide spin-label line width. The HE contribution to the ESR linewidth is given for nitroxides by = )dDNACf, where d is the encounter dis-... 

We note a very interesting manifestation of the strong chelating agent-cation interaction, i.e. the ESR linewidths observed for Chel Na+C10H8" in the presence of excess Ci0H8. We consider two processes which can broaden the ESR lines, anion-neutral molecule electron transfer... 

Photooxidation of the reaction center not only produces an optical absorbance change, but results in an ESR signal as well. This ESR signal has a kinetic behavior identical to the 700 nm bleaching and has therefore been assigned to the cation of the photoactive chlorophyll. The ESR linewidth of the cation of the photoactive chlorophyll a is narrowed by... 

Spin delocalization in the two pentachlorophenyl rings is high, as shown by the value of the esr linewidth (4.0 G) (which reflects multiple couplings with chlorines) about three times that in the radical PTM- (1.4 G) and similar to that of the radical PPF- (4.7 G)). 

Figure 6.2. The temperature dependence of the H NMR peak-to-peak linewidth AWpp in irans-PA [21,22] x. after [21], The other symbols (2,0 G) O (1,5 G) O (1.3 G) (1.0 G) are taken from [22], where the figures in the parentheses mean the ESR linewidth AWpp at 50 MHz and 300 K. It is remarkable that A//pp is practically independent of the magnitudes of the second moments A/2. The curious behaviour of x symbols was interpreted by the motional narrowing due to chain rotation around the chain axis [21], So far, no successful follow-up of this data has been reported [2,20,22,30],...

Figure 6.3. The temperature dependence of the second moment M2 in trans-PA 9 [28] [2] A [32] were obtained by the pulse techniques. The first two data at 200 K are the same data, but analyzed with different fitting functions to estimate M-. ffl [20] O (1.3 G) (1,0 G) A (0.5 G) [22] A [30] were taken by cw-NMR for different batches of irans-PA, where the figures in the parentheses mean the ESR linewidth AWpp at 50 MHz and 300 K. The solid curves indicate eAH, where e = O.I2l, 0.133, 0.141 and 0.165 from bottom to top. For the Gaussian lineshape, M2 = 0.25 A// Z holds.

Figure 6.4. The second moment M2 versus the ESR linewidth (taken at 50 MHz) at 300 and 78 K in irans-PA [22], The second moment M2 increases with increasing ESR linewidth. It is expected that the intrinsic second moment of the irans-isomer is realized at the minimum of the ESR linewidth, see text for details.

The above conclusions on the magnitude of the isotropic part (25-32% for the second moment of H NMR and 50% for both the ESR linewidth and TTc in (roni -NT-PA) imply that the concentration of the neutral soliton in the amorphous part is higher by 7/3, more than twice that in the crystalline region. 

Good evidence for the rapid motion and trapping of the soliton is demonstrated by a DNP experiment as shown in Figure 6.30 [146,173]. The dynamic nuclear polarization (DNP) experiments are carried out at 9 GHz between 1.5 and 300 K in cis [143,174] and irons PA [143,145,146,173,174]. At room temperature the pure Overhauser effect (OE) was observed in a -irans-PA without air or oxygen but a mixed solid state effect (SSE) together with OE was found in c/s-rich PA without air [143,174] and al -lrans-PA with air [146]. In particular, below 150 K, the mixed effect was observed, even in a -trans-PA without air [145,173], The OE is characteristic of dynamic interaction between nuclear spins and electron spins, with rapid motion, On the other hand, the SSE is of the static interaction between them. In other words, observation of the pure OE is clear evidence for the electron spin for motion with an inverse of the correlation time comparable with or larger than Wj,. At 300 K, the pure OE observed in all-/ra s-PA, is consistent with the conclusions for the neutral soliton to diffuse rapidly compared with 1/We as concluded from the ESR linewidth narrowed by motion [53] and the proton NMR 7Y ] [143] as a function of frequency over a broad range. 

Other problems to be resolved, revealed by further exijerimental. studies, are (1) that the temperature dependence of ll NMR T/, yields a temperature variation of the diffusion rate that is inconsistent with the motional narrowing of the ESR linewidth and the DNP results (2) that C NMR does not follow (14) [ 148,150,152,181 ] and (3) that a variety of ESR measurements gave conclusions inconsistent with each other both qualitatively and quantitatively [160, 161,164,165,186]. 

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