Inhomogeneous linewidth

If inhomogeneous broadening of the EPR linewidth is primarily due to unresolved hyperfine couplings (hfc), at higher frequencies the g-an iso (ropy will dominate over the hyperfine interactions, i.e., the condition (Ag/gIS0H0) > AHhk must be fulfilled. 

For systems in which the inhomogeneities in the local magnetic field exceed the linewidth as determined by the uncertainty principle, still... 

FIGURE 4.2 Linewidth increase with temperature for an S = 1/2 system. The linewidth of a feature in the low-spin heme spectrum from cytochrome a in bovine heart cytochrome oxidase has been fit as a convolution of a constant component from inhomogeneous broadening and a temperature-dependent component from homogeneous broadening (Hagen 2006). (Reproduced by permission of The Royal Society of Chemistry.)... 

This chapter considers the distribution of spin Hamiltonian parameters and their relation to conformational distribution of biomolecular structure. Distribution of a g-value or g-strain leads to an inhomogeneous broadening of the resonance line. Just like the g-value, also the linewidth, W, in general, turns out to be anisotropic, and this has important consequences for powder patterns, that is, for the shape of EPR spectra from randomly oriented molecules. A statistical theory of g-strain is developed, and it is subsequently found that a special case of this theory (the case of full correlation between strain parameters) turns out to properly describe broadening in bioEPR. The possible cause and nature of strain in paramagnetic proteins is discussed. 

As a starting point let us be faithful to the history of the subject and try a simple physical model due to (Johnston and Hecht, 1965) if the inhomogeneous EPR line reflects a distribution in g-values, then the anisotropy in the linewidth should be scalable to the anisotropy in the g-value. In other words, the analytical expression for g-anisotropy in terms of direction cosines, between B and the... 

An alternative model (Venable 1967) proposes that the main cause of inhomogeneous broadening is unresolved superhyperfine interactions and, therefore, that the linewidth expression should be equivalent to the Equation 5.12 for the angular dependence of first-order hyperfine splitting ... 

The last mentioned dynamical capability of lasers is in its infancy. It is possible in principle to make optical measurements which are analogous to coherent NMR measurements, and thereby to observe homogeneous linewidths in inhomogeneously broadened systems, to measure optical or vibrational Ti and T2 relaxation times directly, and to observe quantum recurrences. 

Besides a poorly resolved triplet structure in the EPR spectrum of 57Fe enriched two-iron ferredoxins266 at gz, no hf interactions are observed in all these iron-sulfur clusters. The distribution of principal axes of the g tensors gives rise to an inhomogeneous, field-dependent EPR linewidth, and obscures the resolution of ligand hfs265. This distribution, whose origin is not completely established, does not, however, prevent application of the ENDOR technique. 

Figure 34 shows spectra of TA and SOL from a 24-year-old male volunteer recorded at 1.5 T (a) and 3.0 T (b). Besides the clearly improved SNR, which is elevated by a factor of 1.7 to 1.8 at 3.0 T, distinct differences can be observed for the two magnetic field strengths In both muscles, IMCL and EMCL are clearly better separated at 3.0 T as the methylene resonance of IMCL shows smaller natural linewidths (in ppm). However, EMCL signals remain with a broad lineshape in TA as well as in SOL, since the lineshape is dominated by susceptibility induced static field inhomogeneities. Crs and TMA signals are... 

The convenient NMR observables depend on the characteristics of the system studied, but generally the protons of the liquid are readily detected. The apparent NMR linewidths are often determined by the magnetic susceptibility inhomogeneities in the sample and do not directly reflect the dynamics of the liquid. This report will focus largely on theoretical approaches to understand the spin-lattice relaxation rate constants for both classes of microporous materials. The magnetic held dependence of the spin-lattice relaxation rate constant generally provides a useful dynamical characterization of the liquid and often a structural characterization of the confining media. 

Line broadening due to inhomogeneity in the static magnetic field. Ho, as well as in the rf pulse Hj, can contribute to the observed resonance. However, studies of standard sairples, of known natural linewidths, enable the contributions from this source to be determined. In the present case these causes contribute only a few percent, i.e., a few Hz, to the total linewidth and are thus inconsequential to the present problem. Before discussing the different motional contributions to the linewidth. 

It is again apparent from these results that the resonant line is inhomogeneous since the symmetry, linewidth at half-height, and peak maxima change with the position and strength of the irradiation. ... 

On the other hand, Schaefer ( ) has shown from selective saturation experiments of amorphous cis polyisoprene, crystalline trans polyisoprene, as well as carbon black filled cis polyisoprene, that the resonant lines are homogeneous. The linewidths in these cases are thus not caused by inhomogeneous broadening resulting from equivalent nuclei being subject to differing local magnetic fields. The results for these systems are thus contrary in part to what has been found here. 

Recently, an ESR spectrum from Aujj at 4.4 K, with g= 1.9204 and linewidth 67 mT, has been reported [54]. The intensity of the signal followed the Curie-Weiss law, and the g-value and linewidth were independent of temperature. If the linewidth were determined by the electronic spin-spin relaxation time Tj, it would be expected to increase with temperature, so its temperature-independence suggests inhomogeneous broadening by unresolved hyperfine coupling to P and Au nuclei. Similar behaviour has been found in rhodium carbonyl clusters [18]. 

Multiple-pulse measurements were performed on both the LP and HP samples at 20° and — 80° C, and when no differences were noted, lower temperature measurements were performed only on the LP sample. Multiple-pulse spectra for the LP sample are illustrated in Figure 4 together with the eight-pulse spectrum of the reference used for the low-temperature measurements, Ca(OH)2. The lineshapes observed are quite broad, and the line center is a function of temperature. The line width was separated into three contributions by performing three related multiple-pulse measurements (I). These indicated that the main contributions to the linewidth came from both relaxation and second-order dipolar effects. The maximum possible field inhomogeneity Hamiltonian is estimated to be less than 16 ppm by this means, which indicates that the com-... 

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