Motion in solids

This Schrodinger equation forms the basis for our thinking about bond stretching and angle bending vibrations as well as collective phonon motions in solids... 

Heidemann, A., A. Magerl, M. Prager, D. Richter and T. Springer, eds, 1987, Quantum Aspects of Molecular Motions in Solids. 

Kashiwabra, H., Shimada, S., Hori, Y. and Sakaguchi, M. ESR Application to Polymer Physics — Molecular Motion in Solid Matrix in which Free Radicals are Trapped. Vol. 82, pp. 141 -207. 

Fig. 10. Correlation times for the tetrahedral jump motion in solid HMT obtained from 2H line shape analysis and 2H spin alignment...

Springer T (1972) Quasielastic neutron scattering for the investigation of diffusive motions in solids and liquids. Springer, Berlin Heidelberg New York... 

Since about 1960 nuclear magnetic resonance (NMR) spectroscopy has become an important tool for the study of chain configuration, sequence distribution and microstructure of polymers. Its use started from early broad-line studies of the one-set of molecular motion in solid polymers and passed through the solution studies of proton NMR, to the application of the more difficult but more powerful carbon-13 NMR methods to both liquids and solids. 

An instructive illustration of the effect of molecular motion in solids is the proton resonance from solid cyclohexane, studied by Andrew and Eades 101). Figure 10 illustrates their results on the variation of the second moment of the resonance with temperature. The second moment below 150°K is consistent with a Dsi molecular symmetry, tetrahedral bond angles, a C—C bond distance of 1.54 A and C—H bond distance of 1.10 A. This is ascertained by application of Van Vleck s formula, Equation (17), to calculate the inter- and intramolecular contribution to the second moment. Calculation of the intermolecular contribution was made on the basis of the x-ray determined structure of the solid. 

Molecular motion in solids has been the object of many studies in the field of physical chemistry of polymers , but dynamic processes in molecular crystals of organic and inorganic compounds are less well investigated. In fact, the average chemist is not aware of the fact that processes like internal rotation or ring inversion proceed in solids quite often with barriers which are not very different from those found for these types of internal motion in the liquid state. Thus, for the equatorial axial ring inversion of fluorocyclohexane values of 42.4 and 43.9 kJ mol have been measured in the liquid and the solid, respectively. The familiar thermal ellipsoids of individual atoms obtained from X-ray studies are qualitative indicators of molecular motion in the crystal, but a more quantitative study of such processes is only possible after appropriate solid state NMR techniques are applied. 

Polymers, Photochemistry and Molecular Motion in Solid Amorphous... 

Disordering Chain Motions in Solid State Poly(Tetrafluoroethylene)... 

We have been interested in the nature of cooperative motions in polymers for some time and have used carbon-13 nuclear magnetic resonance for examining main-chain motions in solids (22-27). Carbon-13 nmr with cross-polarization and magic-angle... 

A classical dynamics model is used to investigate nuclear motion in solids due to bombardment by energetic atoms and ions. Of interest are the mechanisms of ejection and cluster formation both of elemental species such as Nin and Arn and molecular species where we have predicted intact ejection of benzene-CgHg, pyridine-Cs N, napthalene-CigHg, bipheny 1-0 2 10 an[Pg.43]

Important examples of chemical interest include particles that move in the central held on a circular orbit (V constant) particles in a hollow sphere V = 0) spherically oscillating particles (V = kr2), and an electron on a hydrogen atom (V = 1 /47re0r). The circular orbit is used to model molecular rotation, the hollow sphere to study electrons in an atomic valence state and the three-dimensional harmonic oscillator in the analysis of vibrational spectra. Constant potential in a non-central held dehnes the motion of a free particle in a rectangular potential box, used to simulate electronic motion in solids. 

These methods for studying molecular motion in solids are well understood and have been well documented in the literature prior to the review period. Therefore, it is not the intention of this review to discuss the underlying principles of these experiments in detail. However, there have been experimental and theoretical advances in all of these areas and these are discussed in Sections 2-4. 

Relaxation time measurements have long been used to characterize molecular motions in solids. All nuclear spin relaxation processes are mediated by fluctuating nuclear spin interactions, with the fluctuations (generally) arising... 

---