Neutron Spin Echo Results on Chain Confinement

Neutron Spin Echo Results on Chain Confinement 

In Fig. 3.16 dynamic structure factor data from a A =36 kg/mol PE melt are displayed as a function of the Rouse variable VWt (Eq. 3.25) [4]. In Fig. 3.6 the scaled data followed a common master curve but here they spht into different branches which come close together only at small values of the scahng variable. This splitting is a consequence of the existing dynamic length scale, which invalidates the Rouse scaling properties. We note that this length is of purely dynamic character and cannot be observed in static equilibrium experiments. 

In the spirit of Eq. 3.39 and neglecting the ongoing decay of Schain(Q 0 due to local reptation, from the heights of the achieved plateaus we may obtain a first estimate for the amount of confinement. Identifying the plateau levels with a Debye-Waller factor describing the confinement we get d=44 A, a value that is a lower estimate for the true tube diameter since S ° (Q,t) is not fully relaxed. The horizontal bars in Fig. 3.16 are the predictions from this Debye-Waller factor estimate. 

First detailed studies of the dynamic structure factor of highly entangled polymer melts were reported at the beginning of the 90 s. At that time the attainable Fourier times were limited to about 40 ns. On this time scale, NSE has already played a crucial role in helping to understand the dynamics of polymeric systems [49, 50, 72, 73]. At that time the existence of an entanglement length scale in a linear polymer was been proven [72]. However, with the available time resolution, it was not possible to separate the predictions of the different confinement models addressed above. 

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]). 

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