Breathing modes

Different motions of a molecule will have different frequencies. As a general rule of thumb, bond stretches are the highest energy vibrations. Bond bends are somewhat lower energy vibrations and torsional motions are even lower. The lowest frequencies are usually torsions between substantial pieces of large molecules and breathing modes in very large molecules. 

Three /3-CH modes corresponding to in-plane C—H deformations are also observed (Table 22) and are probably best depicted as in (27), (28) and (29), although those for pyrrole will be modified as a result of interaction with the in-plane N—H deformation. The skeletal ring breathing mode (30) observed at ca. 1137 cm for 2-substituted pyrroles and... 

The two terms correspond to different polarization of phonons. The cosine term corresponds to displacements along the rotation axis or the direction tp = 0. The sine contribution arises from the phonons polarized along the line tp = The interaction (6.29) does not change the symmetry of the (p potential, and, in this respect, it is symmetric coupling, as defined in sections 2.3 and 2.5. Nonetheless, the role of the cosine and sine couplings is different. The former ( breathing modes ) just modulate the barrier (6.22), while the latter ( shaking modes ) displace the potential. 

In order to adapt that expression to the problem at hand, we note that interaction matrix elements for shaking and breathing modes are different. Namely, the matrix element AfiV, symmetry index (A or E), is very small for even I + I, while the cosine matrix element, M - = is minor for odd I + I [Wurger 1989]. At low temperatures, when only / = / is accessible, the shaking... 

At 186 cm a strong line is seen in Fig. 23. This feature is identified with the Alp radial breathing mode and depends only on the nanotube diameter. The linewidth and lineshape is due to contributions from nanotubes of different... 

This leaves only ions in the vibrational ground state, in the v2 = 1 bending-mode vibration at 0.3126 eV, and in the v, = 1 breathing mode vibration at 0.394 eV (see Lie and Frye 47 or Oka and Jagod6). Since the argon density in these experiments is quite high ( 5 x 1015cm-3), v > 1 ions would be destroyed in less than 1 (is. This is an important point, since Smith and Spanel s proposed reconciliation of theory and experiment rests on the assumption that vibrationally excited ions dominate the plasma. 

Because of the spherical shape of the PS-PI micelles, the equation of motion for the local displacement u(r, t) of the normal or breathing modes, where all the radical shells or layers move in phase, is given by the radical part of... 

Fig. 69.oNSE spectra of 2% diblock copolymer (d-PS and h-PI blocks) in deuterated n-decane. The Q/A-1 values are 0.026, V 0.032, 0.038, x 0.051, O 0.064, A 0.089, O 0.115. Experimental data and theoretical dynamic structure for breathing modes are compared (solid lines). (Reprinted with permission from [174]. Copyright 1993 The American Physical Society, Maryland)... 

Modified CNTs feature various spectral changes depending on the methods and the location of modifications. These changes include variations in band frequencies, width, and intensities. For example, aryldiazonium salts [139] were used to modify individual sodium dodecyl sulphate (SDS) coated SWNTs with aryl group. The Raman spectrum of functionalized (SDS-free) SWNTs shows a disorder mode much higher than pristine SWNT the radial breathing modes are nearly unobservable. 

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