Homogeneous line widths

If dye molecules are embedded into an amorphous matrix, preferably transparent polymers, greatly and inbornogenously broadened spectral lines are observed. This broadening is caused by the energetic interaction of the dye molecules with the locally different environment in the polymer matrix. The ratio of the homogenous initial line width of the dye molecule T to the inhomogenous line width of the dye in the polymer T ranges from 1 10 to 1 10 . ... 

From XRD line widths, it was noted that the crystal size increased as the S concentration increased, although values were not given. A simple but useful characterization technique to quantify film thickness homogeneity was used here. The transmittance of a focused light spot scanned across the sample showed excellent homogeneity. 

FIGURE 1.15. Electrohydrodynamic pattern replication, (a) double-hexagonal pattern, (b) the word nano , (c) 140 nm wide and 140 nm high lines. In (b) the line width was s300 nm. The larger columns stem from a secondary (much slower) instability of the homogeneous (not stmctured) film. Adapted from [30] and [38]. 

Equation (7.22) is at the heart of spectroscopy. The positions of the absorption lines reflect the energy levels of the excited complex and the widths provide information about the lifetime and therefore about the coupling to the continuum states. The latter requires, however, that the measured widths are the true homogeneous line widths, i.e., unadulterated by poor resolution and/or thermal broadening, for example. Each resonance has a characteristic width. In Chapters 9 and 10 we will discuss how the final fragment distributions reflect the initial state in the complex and details of the fragmentation mechanism. 

The data from Table 3.7 make it possible to make a few estimates. Let us consider a concrete example. If the length of the resonator is L = 2 m, the Doppler contour, say of a K2 molecule in the BlTlu state, contains about 11 axial modes, the distance between them being Au>i = ttc/L m 4 108 s-1. If we assume that the width of the Bennet dip is equal to the homogeneous line width, rBen T = 0.86 108s 1 (see... 

As we saw in Section 2.5, NMR lines from small molecules in the liquid phase often have a natural line width of less than 1 Hz (frequently a small fraction of a hertz), and as will be seen later, lines separated by 1 Hz or less must sometimes be resolved to obtain information of chemical interest. For proton NMR, rf frequencies of 200—800 MHz are usually used hence a resolution of the order of 10 9 is often required. In addition to careful fabrication of the magnet, three approaches are used to obtain adequate homogeneity over the sample volume, as follows ... 

Equations (6) and (7) predict a transition whose width will be small if the NC sample is monodisperse (i.e., all particles have the same a value). However, even samples with a narrow size distribution show transition line widths of —30 nm FWHM (full width half maximum), which is significantly broader than expected. This line broadening is due to both homogeneous broadening related to phonon excitations in the NC and inhomogeneous broadening due to interactions with the surrounding environment. ... 

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