Motion description

The simplest motional description is isotropic tumbling characterized by a single exponential correlation time ( ). This model has been successfully employed to interpret carbon-13 relaxation in a few cases, notably the methylene carbons in polyisobutylene among the well studied systems ( ). However, this model is unable to account for relaxation in many macromolecular systems, for instance polystyrene (6) and poly(phenylene oxide)(7,... 

The failure of this model led to the application of motional descriptions involving several correlation times. The simplest of these, a two correlation time model, was developed by Woessner ( ) and suggested for macromolecular systems by Allerhand, Dodrell, and Glushko ( ). The model considers two motions modulating the dipole-dipole interaction anisotropic Internal rotation about an axis which also undergoes overall rotatory diffusion. This model can successfully account for the carbon-13 Ti and NOE values observed for the methyl carbons in PIB ( ). The methyl group is... 

The shift in the two tensors is expected to be effective for carbohydrate molecules bearing a number of polar groups and hydrogen-bonding centers. Hence, serious difficulty for quantitative analysis may arise if the molecule does not contain three or more nonequivalent C—H vectors that relax predominantly via the overall motion. If this fact is ignored, qualitative treatment may lead to an erroneous motional description. Thus, one should be very cautious in interpreting the relaxation data for overall motion, especially when discrepancies well outside the experimental error are observed for the T, values. When the relaxation times are nearly similar and within the experimental error, isotropic motion may be considered as a first approximation to the problem. 

Table I, which lists a number of mono-, oligo-, and polysaccharides and derivatives whose motional descriptions are available based on qualitative arguments, summarizes the experimental conditions and types of measurements used to obtain those descriptions. Table II deals specifically with those carbohydrates for which a quantitative treatment and dynamic modeling have been undertaken. In naming the compounds listed in Tables I and II, IUPAC rules are used for monosaccharide and less complex oligosaccharide molecules. However, empirical names are used for unusual oligosaccharides involving a complex aglycon substituent and polysaccharides. The gross motional features of a number of the compounds in Table I have been discussed in references 6-8, and will be mentioned here only if necessary for further clarification or for comparison with quantitative results.

The three bond jump segmental motion description can also be combined with a description of restricted anisotropic rotational diffusion (13-14). In this case, the composite spectral density equation is... 

Treatments using a Browni in motion description begin with Berne cmd Pecora [16], who treat a solution of dilute, nonirderacting Browni ln p ud icles, for which from the Centred Limit Theorem the probability distribution for the displcicements of a particle is... 

As the first point, the dynamics of the phenyl group in the poly-formal can be considered. Motional descriptions from the two segmental models can be compared as they have been before for the polycarbonates ( 5). In the three bond jump model the primary parameter is the harmonic mean correlation time, and in the... 

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