NSE Experiments on Entanglement Formation

An experimental test of the scaling model requires a selective variation of the two scaling variables of the model, i.e. the lateral chain distance and the chain stiffness. The Kuhn length /K depends on temperature via the characteristic ratio Cw the lateral chain distance s can be varied via the volume fraction 4 . 

On saturated PB (PEB-2 Mw = 73 200 g/mol Mw/Mn = 1.02), the dependence on contour length density was studied by diluting the melt with the short oligomer n-C19D40 [60], Thus, a concentration range 0.25 1 was 

Boothroyd et al. [74] recently determined the temperature dependence of the Kuhn length for polyethylene with the aid of small-angle neutron scattering. In the temperature range between 100 and 200°C, dlnC /dT = - 1.1 x 10 3 K 1 

In the temperature range between 400 and 550 K, NSE spectra on the same undiluted polyethylene melt were recorded. These data were analyzed with respect to the entanglement distance. The result for the temperature-dependent entanglement distance d(T) is shown in Fig. 30. An increase in the tube diameter from about 38 to 44 A with rising temperature is found. 

Since both the temperature dependence of the characteristic ratio and that of the density are known, the prediction of the scaling model for the temperature dependence of the tube diameter can be calculated using Eq. (53) the exponent a = 2.2 is known from the measurement of the -dependence. The solid line in Fig. 30 represents this prediction. The predicted temperature coefficient 0.67 + 0.1 x 10-3 K-1 differs from the measured value of 1.2 + 0.1 x 10-3 K-1. The discrepancy between the two values appears to be beyond the error bounds. Apparently, the scaling model, which covers only geometrical relations, is not in a position to simultaneously describe the dependences of the entanglement distance on the volume fraction or the flexibility. This may suggest that collective dynamic processes could also be responsible for the formation of the localization tube in addition to the purely geometric interactions. 

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