Dynamic structure factors reptating chain

The simplest case of comb polymer is the H-shaped structure in which two side arms of equal length are grafted onto each end of a linear cross-bar [6]. In this case the backbones may reptate, but the reptation time is proportional to the square of Mj, rather than the cube, because the drag is dominated by the dumb-bell-like frictional branch points at the chain ends [45,46]. In this case the dependence on is not a signature of Rouse motion - the relaxation spectrum itself exhibits a characteristic reptation form. The dynamic structure factor would also point to entangled rather than free motion. 

Obviously, if found experimentally, the exponent -2 is only a sign of reptation motion but not a sufficient condition for it. Thus, in order to prove that reptation is a really dominant mode of chain motion in polymer concentrates, we have to test it not only with self-diffusion but also with other physical properties which reflect the local motion of polymer chains. One such property is the (coherent) dynamic structure factor 5(fc, r) (see Section 3.2 of Chapter 4 for its definition). In fact, it was predicted theoretically [45-47] that the k dependence of its decay with r in the range of k defined by... 

Figire 39 Dynamic structure factor of a center-labeled 25 kg moL PE chain (red symbols) compared to a fully labeled chain (green symbols) of the same overall molecular weight. Ovalues (in nm ) 0.5 (squares), 0.96 (circles), 1.15 (triangles). Lines for center-labeled chain, pure reptation model (eqn [64], red) forfully labeled 25 kg mol chain (green) CLF was considered. From Zamponi, M. Monkenbusch, M. Willner, L etal. Europhys. Lett 2005, 72,1039-1044. ... 

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