Line Shapes and Widths

The line-widths of e.s.r. absorptions in solution may be as narrow as a few milligauss (Hausser, 1964) in this respect, solution studies have a considerable advantage over studies in viscous media or glasses, where lines are broadened by anisotropic interactions. Carrington (1963) has discussed some of the factors affecting line-shape and width in solution. 

From the analysis of the ESR line shape and width using the model of motional narrowing, one obtains the following results for the dynamics of the quasi-one-dimensional triplet excitons in DBN ... 

In most cases, the line shape and width are a consequence of the dipolar interaction between the nuclear moments which leads to the second moment of the resonance. This has been discussed in sections 1.2.3. For a given resonance lineshape, the second moment M2 and linewidth are related [Abragam (1961)]. 

FIGURE 4.4 Line shapes. Lorentzian (broken lines) and Gaussian (solid lines) line shapes and their first derivatives are given. The outermost vertical lines delimit full width at half height (FWHH) of the absorption lines. 

Treating vibrational excitations in lattice systems of adsorbed molecules in terms of bound harmonic oscillators (as presented in Chapter III and also in Appendix 1) provides only a general notion of basic spectroscopic characteristics of an adsorbate, viz. spectral line frequencies and integral intensities. This approach, however, fails to account for line shapes and manipulates spectral lines as shapeless infinitely narrow and infinitely high images described by the Dirac -functions. In simplest cases, the shape of symmetric spectral lines can be characterized by their maximum positions and full width at half maximum (FWHM). These parameters are very sensitive to various perturbations and changes in temperature and can therefore provide additional evidence on the state of an adsorbate and its binding to a surface. 

Two samples of the same phosphor crystal have quite different thicknesses, so that one of them has a peak optical density of 3 at a frequency of vo. while the other one has a peak optical density of 0.2 at vq. Assume a half width at half maximum of Av = IGHz and a peak wavelength of 600 nm, and draw the absorption spectra (optical density versus frequency) for both samples. Then show the absorbance and transmittance spectra that you expect to obtain for both samples and compare them with the corresponding absorption spectra. (To be more precise, you can suppose that both bands have a Lorentzian profile, and use expression (1.8), or a Gaussian line shape, and then use expression (1.9).)... 

If a S> 1, collective effects play an important role and the light scattering is no longer caused by individual electrons but by electron density fluctuations 280), Jn this case the spectrum shows a central line at Xq and two narrow lines located symmetrically about Xq, at a distance governed by the electron plasma frequency. The linewidth is smaller than in the case X < 1 and is determined rather by the thermal motion of the ions, not that of the electrons. The line shape depends on the ratio of electron to ion temperatures. Therefore, a measurement of the shape and width of this central line allows, under certain assumptions, a direct determination of the ion temperature. 

There are many more solvent effects on spectroscopic quantities, that cannot be even briefly discussed here, and more specialized works on solvent effects should be consulted. These solvent effects include effects on the line shape and particularly line width of the nuclear magnetic resonance signals and their spin-spin coupling constants, solvent effects on electron spin resonance (ESR) spectra, on circular dichroism (CD) and optical rotatory dispersion (ORD), on vibrational line shapes in both the infrared and the UV/visible spectral ranges, among others. 

When the ESR spectrum has been analyzed into spectral components assigned to particular radicals, the individual spectra are simulated, taking into consideration (1) g value, (2) hyperfine splitting, (3) line shape and (4) line width. These simulated spectra are then summed, corresponding to the percentages of individual radicals, to produce a spectrum similar to that obtained experimentally. The application of ESR to the study of radiation degradation of polymers is extremely valuable and the techniques described above have been used extensively in the present work. 

In eqn. (2), AH°m is the EPR line width in the limit of such dilution that one can neglect the dipole-dipole interaction and A is a coefficient depending on the EPR line shape and on the character of the spatial distribution of the spin-labelled molecules. In the case of random spatial distribution according to theoretical calculations A = 35 GM 1 for the Gaussian EPR line shape and A = 56GM-1 for the Lorentzian EPR line shape. 

Electron spin relaxation in aqueous solutions of Gd3+ chelates is too rapid to be observed at room temperature by the usual pulsed EPR methods, and must be studied by continuous wave (cw) techniques. Two EPR approaches have been used to study relaxation studies of the line shape of the cw EPR resonance of Gd3+ compounds in aqueous solution, and more direct measurement of Tle making use of Longitudinally Detected EPR (LODEPR) [70]. Currently, LODESR is available only at X-band, and the frequency dependence of relaxation is studied by following the frequency dependence of the cw EPR line shape, and especially of the peak-to-peak line width of the first derivative spectrum (ABpp). 

The sum must be made over all spin pairs in the proton-rich solid. In the absence of large-amplitude molecular motion this Hamiltonian describes a line shape of width of up to 100 kHz. In the presence of molecular motion the angular part of Equation 13.1 becomes time-dependent, and the partial averaging of this term results in reduced linewidths. In polymers the geometry of main-chain motion is limited by the structure of the polymer chain, and is inherently anisotropic. As a general rule, as the measurement temperature is increased the motion tends to become more isotropic in nature as the free volume increases, and the extent of averaging of the dipolar Hamiltonian increases. This... 

The fast beam separated oscillatory field technique (SOF) provides a method through which one can obtain a series of lines whose widths are less than the natural line width with a good understanding of the factors which determine the line shape and the line center. This paper summarizes a separated oscillatory field measurement of the Lamb shift in hydrogen.[1]... 

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