Tube dilation by orientational ordering

The local equilibrium approximation breaks down if the frequency of the external field becomes comparable with the characteristic time of the fluctuation Xe — e lD o. The motion of the polymer in such a short time-scale can be treated by eqn (9.66) or a rotation model limited in a cone-like region. Both treatments gives qualitatively similar results e.g., af (to) and Koc((o) approach zero as with the relaxation time 

Recent studies have been reviewed by Moscicki.  

Here we calculate the rotational diffusion constant for the case when the orientational distribution of the surrounding polymer is not isotropic. The number N(r), which is given by the sum of eqn (9.11) over the entire surface, is written as 

First we calculate ( 1),. For a slender tube, the surface area is mostly on the long side of the tube and s is perpendicular to u, then is written as 

We evaluate (i4( )). for small e. To that end we expand A(u) with respect to the small vector t - Ji 

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