Reptation model dynamic structure factor

Like the dynamic structure factor for local reptation it develops a plateau region, the height of which depends on Qd. Figure 20 displays S(Q,t) as a function of the Rouse variable Q2/ 2X/Wt for different values of Qd. Clear deviations from the dynamic structure factor of the Rouse model can be seen even for Qd = 7. This aspect agrees well with computer simulations by Kremer et al. [54, 55] who found such deviations in the Q-regime 2.9 V Qd < 6.7. 

Fig. 3.16 Scaling presentation of the dynamic structure factor from a M =36,000 PE melt at 509 K as a function of the Rouse scaling variable. The solid lines are a fit with the reptation model (Eq. 3.39). The Q-values are from above Q=0.05,0.077,0.115,0.145 A The horizontal dashed lines display the prediction of the Debye-Waller factor estimate for the confinement size (see text)...

From Fig. 3.17 and Fig. 3.18 it is apparent that these data clearly favour the reptation model. The reptation model is the only model for which the dynamic structure factor has been calculated and which is in quantitative agreement with these results. We observe that the models of Ronca [63] (see Fig.3.17) and des Cloizeaux [66] (see Fig. 3.18) produce a plateau which is too flat. On the other hand, the model of Chaterjee and Loring relaxes too quickly and does not form a plateau (see Fig. 3 in [65]). 

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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