Echo Attenuation by Reptation

In the short gradient pulse limit of the fringe-field NMR diffusometry technique, which is of particular interest in context with slowly diffusing polymers (see Fig. 3), the effective diffusion time is given by twA=r2- Under this prerequisite the stimulated-echo attenuation factor can be analyzed according to 

The ensemble averages indicated by the brackets refer to displacements along the field gradient direction. The subscripts of the ensemble averages indicate displacements R in general, displacements R relative to the center-of-mass by segment diffusion (Hmits (I)de, (H)de (1H)de) displacements of the center-of-mass Rc (Hmit (IV)de) respectively. 

Attenuation by center-of-mass diffusion (limit (IV)de) is described by the standard expression given in Eqs. 13 or 26 

Rouse displacement dynamics is anticipated on a length scale up to the tube diameter. That is, the chain connectivity constraint and excluded-volume interactions are ignored for this limit. In the frame of this model, these restraints are taken into account only outside the tube but not inside. 

A further inconsistency refers to the treatment of shear stress relaxation. The Doi/Edwards tube cannot exist without long-living intermolecular correlations pertaining to a time scale of the order Nevertheless, 

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