Intra- and InterSegment Spin Interactions Dispersion Region III

Intra- and Intersegment Spin Interactions (Dispersion Region iii) 

A schematic representation of the situation one is dealing with in this context is shown in Fig. 37. We consider the representative segments kon chain a and I on chain p. The internuclear vector, 7ki t), fluctuates because of self-diffusive displacements Rrei t) of segment I relative to segment k. That is, the origin of the reference frame is considered to be fixed at segment k. 

The average correlation function for the intersegment dipolar interaction can be expressed as [154] 

The correlation function in Eq. 171 can be approximated by the following consideration. For relative displacements R t) (see Fig. 37) much larger than the initial internuclear distance ro=rki (0), the distance and polar angle variation leads to total loss of any correlation to the initial distance vector, whereas the correlation is completely retained in the opposite limit. That is, 

The time dependence of the mean squared segment displacement in the laboratory frame was derived on the relevant time scale as low-mode-number, short-time limits of the renormalized and twice renormalized Rouse models as and (R ,(f)) oc (limit (II)trr) respectively 

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