Weber-Helfand model, motion

FIG. 7.—Hall-Weber-Helfand (HWH) motional model. A[Pg.81]

To apply the models to the interpretation of the data, the approach developed for the polycarbonates will be followed. The phenyl proton Tj s are interpreted first in terms of segmental motion. For these protons, the dipole-dipole interaction is parallel to the chain backbone and therefore relaxed only by segmental motion. In the three bond jump model the parameters tjj and m are adjusted to account for phenyl proton data, and in the Weber-Helfand model the parameters tq and tj are adjusted. Table II contains the three bond jump parameters, and Table III, the Weber-Helfand model parameters. Both models can simulate the data within 10% which is equivalent to the experimental error. 

Table III Phenyl Group Motion Simulation Parameters Weber-Helfand Model Using the...

Weber-Helfand model the primary parameter is the correlation time for cooperative backbone transitions, X]. At the lower temperatures studied, xq plays an increasing role in the Weber-Helfand model but xj is still the major factor. This is an interesting point in itself since cooperative transitions were also found to predominate when the Weber-Helfand model was applied to the polycarbonates. Here in the polyformal, single bond conformational transitions do play a larger role and this can be seen in the three bond jump model as well by the drop of m to 1 at lower temperatures. Since xj and x are both measures of the time scale for cooperative motions, it is interesting to note that the Arrhenius summaries of the two correlation times in Tables II and III are very similar. This similarity, taken together with the domination of cooperative transitions in the Interpretations, supports the utility of both models though the Weber-Helfand model is developed from a more detailed analysis of chain motion. 

Weber and Helfand (8) characterize segmental motion in terms of a correlation time for single conformational transitions, tq, and a correlation time for cooperative conformational transitions, tj. This model has been applied to nuclear spin relaxation before (5) and the form of the spectral density for a composite segmental motion and anisotropic internal rotation is written... 

The anisotropy of segmental motion exhibited in Fig. 19 may arise, as noted above, either from the intramolecular or from the intermoleoilar ccmstraint to the rotational motion. The anisotropy d orioitational condadon decay was indeed noted already by Weber and Helfand [47] in their Brownian dynamics simulation of polyethylene of infinite chain length. Their orioitational time-correlation function of the chord vector ( = 0°) decayed much more slowly than those of either the bisector vector ( = 0°, = 0°) or the out-of-plane vector ( = 0°, = 90°). What they modeled was a phantom chain having no... 

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