Molecular 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. 

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... 

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... 

Analysis of molecular motion in solids using NMR spectroscopy has been a developing field during the past decades. In this context, 2H NMR is the most used approach but recently a number of other quadrupolar nuclei have been studied. This includes spin-1 as well as half-integer quadrupolar nuclei such as 7Li and 23Na. 

As already mentioned, the lack of molecular motion in solids gives rise to broad resonances and the received spectral pattern consist of overlapped lines, hiding the valuable analytical information available from the isotropic chemical shifts. In principle, there are three line broadening mechanisms, described in the following (13). 

Einstein s theory of specific heat leads to the same result. This theory connects the molecular motion in solid bodies with Planck s theory of radiation, and has been confirmed in the main by the experimental researches of Nernst and his collaborators in the last few years. Einstein assumes that the heat motion in solid bodies consists of vibrations of the atoms about a point of equihbrium, as distinct from the translational motion of the molecules which we assume for gases. The energy of these vibrations—and this is the characteristic feature of the theory, and also of Planck s theory of radiation—is always an integral multiple of a quantity of energy e, which, in turn, is the product of a universal constant (. e. a constant independent of the nature of the substance) and the frequency i/ (number of vibrations R,... 

Polymers, Photochemistry and Molecular Motion in Solid Amorphous (Guillet). Primary Processes and Energy Transfer Consistent Terms and Deflnitions... 

Unfortunately, the usefulness of NMR for the investigation of chemical problems was strictly limited to liquid samples, so solid samples first had to be dissolved or melted. This is because of the anisotropic nuclear interactions which strongly depend on molecular orientation, and are therefore averaged by molecular motion. In liquids, the molecules reorient randomly very quickly a water molecule requires ca. 10 s for complete reorientation. Although certain solids have sufficient molecular motion for their NMR spectra to be obtainable without resorting to special techniques, in the general case of a true solid, there is no such motion, and conventional NMR, instead of sharp spectral lines, yields a broad hump which conceals most information of interest to chemists. For example, the width of the H NMR resonance in the spectrum of water is ca. 0.1 Hz, while the line from a static sample of ice is ca. 100 kHz wide, i.e., a million times broader. Andrew et al. [ 12], and independently Lowe [ 13], had the idea of substituting the insufficient molecular motion in solids for the macroscopic rotation of the sample. 

Relevant reviews published in Annual Reports on NMR Spectroscopy have encompassed recent developments in dipolar recoupling under MAS conditions, characterization of porous media using NMR methods, NMR studies of molecular motions in solids," recent progress in solid-state NMR of low y nuclei and Co NMR. ... 

If the orientation dependence of the resonance frequency of a spin 5 is determined by just one interaction, it can be exploited for use as a protractor to measure angles of molecular orientation. In powders and materials with partial molecular orientation, the orientation angles and, therefore, the resonance frequencies are distributed over a range of values. This leads to the so-called wideline spectra. From the lineshape, the orientational distribution function of the molecules can be obtained. These lineshapes need to be discriminated from temperature-dependent changes of the lineshape which result from slow molecular reorientation on the timescale of the inverse width of the wideline spectrum. The lineshapes of wideline spectra, therefore, provide information about molecular order as well as about the type and the timescale of slow molecular motion in solids [Sch9, Spil]. 

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