Subgroup motion

Luminescence of Probe Molecules. These studies permit evaluation of polymer properties. In particular, measurement of the relative Intensities of fluorescence of a probe molecule polarized parallel to and perpendicular to the plane of linearly polarized exciting radiation as a function of orientation of a solid sample yields Information concerning the ordering of polymer chains. In solution, similar polarization studies yield Information on the rotational relaxation of chains and the viscosity of the microenvironment of the probe molecule. More recently, the study of luminescence Intensity of probe molecules as a function of temperature has been used as a method of studying transition temperatures and freeing of subgroup motion in polymers. 

We discuss under this heading the use of fluorescence polarization methods to study the order In polymers, particularly In drawn fibrous materials and, by association, the use of such ordered systems to study fundamental details of the luminescence of probe molecules, the use of polarization methods to study rotational motion In polymers In solution, and the temperature dependence of luminescence as a probe of subgroup motion. 

Molecular subgroups of molecules in a crystal can sometimes move rather independently in the vibrational (or rotational) mode. If those motions become strongly... 

Let us re-examine the notion of a point defect in this context. If a molecular subgroup of a molecule is imperfect, this damaged molecule constitutes a point defect in the crystal, although the defect has no immediate influence on the molecule s translational mobility. Point defects that induce (translational) motion are vacancies or interstitials. We can infer from the form of the Lenard-Jones potential that vacan-... 

The foregoing discussion allows to state the theorem The full isometric group JP( ) is a proper or improper subgroup ofthe symmetry group ft of the rotation internal motion hamiltonian H = T + V... 

Altmann remarked that, in free space, the Euclidean operations are not of physical interest. Therefore the Euclidean operations will be 2issimilated with the identity. Besides, he stated that the discrete symmetry operations are purely changes of labelling, especifically they are not motions of atoms. The Schrodinger subgroup may be then assimilated with the symmetry point group of the molecule in a fixed configuration. 

Notice that the full NRG s of this series of molecular systems may not be written as a semi-direct product of a restricted NRG for the internal motions and a symmetry point subgroup for the external rotation, as Altmann presented [10], because of the coupling between both motions. The full NRG s, however, possess the same group structure as the Longuet-Higgins Molecular Symmetry Group, in all the cases. 

The symmetric PFs molecule is a clear example where the Schrodinger Supergroup cannot be factorized into two subgroups, as expected by the Alt-mann s theory. In this case, the internal rotations around a single atoms induce overall rotations of the molecule as a whole, i.e. the internal and external motions are not separable. 

Since the two motions do not depend anymore on the rotation sense of each other, the double switch operator of (26) may be written as a product of two simple switch operators (15-a) acting independently on each single motion. As a result the switch subgroup takes the particular form ... 

The local full NRG appears then as a direct product of two subgroups the restricted NRG corresponding to the internal motions, and a switch subgroup, Ul, corresponding to the external rotation, in accordance with equation (20) ... 

The local full NRG appears then as a direct product of two subgroups the restricted NRG corresponding to the internal motions, and a single switch subgroup, Uf, which corresponds to the external rotation. The restricted NRG is found to be smaller than the full NRG and the external rotation one isomor-pic to the symmetry point group of the molecule, Cs, in its most symmetric configuration. As a result, it may be written as in the case of phenol ... 

Different spectral domains reflect motions of individual subgroups of a molecule. Assignments can be made by comparison with the IR and Raman spectra of simple bases, nucleosides, nucleotides, and polymers (Tsuboi, 1969). Isotopic substitution by N or 0, which causes selective absorption shifts, has also been employed (Miles, 1964 Tsuboi et ah, 1968). 

The experimental and theoretical investigation of higher order vibrational motion and relaxation in solids should now advance quite rapidly as, in fact, there are no lack of suitable problems and the methods to tackle them. We note in this context, and in anticipation of the section on vibrational energy propagation, that the existance of polariton bound states has been inferred from the production of additional gaps in the phonon-polariton dispersion curves of ionic crystals having a molecular subgroup. ... 

In a one-component gas it is conceptually still possible to label a certain subset of particles with 1 and the complement, 2. The resulting motion of the conceptually labeled subgroup of particles is called self-diffusion. Diffusion in a two-component system is called mutual diffusion. 

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