Multiple internal rotations theory

Howartht17b)has used the theory of Internal Librational Motion to successfully predict the field dependent relaxation behavior of the 1,2-decanediol (DD), PBMA, and PHMA systems (using our published experimental data). We have utilized together multiple internal rotations (MIR) and distributions of correlation times. These methods individually have been successful in predicting relaxation behavior at one field. However, only the distribution theory predicts the observed field dependence for the carbons at or near sites of motional restriction, yet still having apparent correlation times <10 <-)sec. Our interest in the study of concerted motions along these alkyl chains has led us to combine the two approaches in the treatment of 13C relaxation parameters. 

While use of multiple internal rotations does allow prediction of the Tp s at any one field better than a single correlation time theory, it still does not predict a Tp field dependence. 

Table XII. Calculated Carbon-13 T] s and NOEF s Using the Theory of Multiple Internal Rotations Both With and Without a Distribution of Correlation Times for Overall Motion.

Stone applied the theory of Longuet-Higgins to deduce the character tables for the multiple internal rotation in neopentane and in octahedral hexa-ammonium metallic complexes [6]. Dalton examined the use of the permutation-inversion groups for determining statistical weights and selection rules for radiative processes in non-rigid systems [7]. Many applications of the Molecular Symmetry Groups have been reviewed later by Bunker [8,9]. 

The advances in time resolved techniques have fostered a reexamination of theories of the rotational motions of molecules in liquids. Models considered include the anisotropic motion of unsymmetrical fluorophores the internal motions of probes relative to the overall movement with respect to their surroundings, the restricted motion of molecules within membranes (e.g., wobbling within a cone), and the segmental motion of synthetic macromolecules [8]. Analyses of these models point to experimental situations in which the anisotropy can show both multi-exponential and none-exponential decay. Current experimental techniques are capable in principle of distinguishing between these different models. It should be emphasized, however, that to extract a single average rotational correlation time demands the same precision of data and analysis as fluorescence decay experiments which exhibit dual exponential decays. Multiple or non-exponential anisotropy experiments are thus near the limits of present capabilities, and generally demand favourable combinations of fluorescence and rotational diffusion times [48]. 

In-depth treatments of the topic are available in several books [1-6] and in a large number of review articles. The monograph by Dong [6], for example, focuses on aspects like the dynamics of nuclear spins, orientational order, molecular field theories, nuclear spin relaxation theory, director fluctuation and spin relaxation, rotational and translational dynamics, internal dynamics of flexible mesogens, and multiple-quantum and two-dimensional NMR, topics that will be touched upon very briefly here. Re-... 

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