Dynamic properties of the melt

The discussion of the last subsection and of the experimental investigations on the structmal properties of glasses we mentioned in the introduction showed that no sharp distinction between the fluid and the glassy state exists on structural grounds. A distinction between these two states can, however. 

In the Kohlrausch-Wilhams—Watts equation the exponent /3k typically ranges between 0.3 and 0.8 for structural glasses and is often found to be temperature-independent, which means that the structural relaxation time Tie carries the whole temperature dependence in the Kohlrausch formula. A plot of the correlation function versus the reduced variable i/tic 

To what extent the schematic model systems A and B for a polymer melt show this typical relaxation behavior will be addressed in this subsection, by calculating various structural correlation functions that probe the dynamical changes of the melt on different length scales (Section 6.3.2.1). From these correlation functions it is possible to extract relaxation times the temperature dependence of which can be studied and compared to that of transport coefficients, such as the diffusion coefficient. This will be done in Section 6.3.2.2. The final paragraph of this subsection then deals with the calculation of the incoherent intermediate scattering function and its quantitative interpretation in the framework of the idealized mode coupling theory (MCT).  

In order to investigate the slowing down of the dynamics on the length scale of the average chain s size one can calculate the auto-correlation function of the polymer s end-to-end distance or of the radius of gyration, which might be defined in the following way  

16 Scaling plot of the auto-correlation functions (Rjj (/) (a) and RQ](i) (b) versus different temperatures, obtained by a simulation of the 2d version of model A. TTie front (left) part refers to = 0.4 and back (right) part to = 0.8. The chain length is N= 10. 

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