Rouse Model Computer Simulation and NSE

In order to learn more about the Rouse model and its limits a detailed quantitative comparison was recently performed of molecular dynamics (MD) computer simulations on a 100 C-atom PE chain with NSE experiments on PE chains of similar molecular weight [52]. Both the experiment and the simulation were carried out at T=509 K. Simulations were imdertaken,both for an explicit (EA) as well as for an united (l/A) atom model. In the latter the H-atoms are not explicitly taken into account but reinserted when calculating the dynamic structure factor. The potential parameters for the MD-simulation were either based on quantum chemical calculations or taken from literature. No adjusting 

Having obtained a very good agreement between experiment and simulation, the simulations containing the complete information about the atomic trajectories may be further exploited in order to rationalize the origin of the discrepancies with the Rouse model. A number of deviations from Rouse behaviour evolve. 

According to the Rouse model the mode correlators (Eq. 3.14) should decay in a single exponential fashion. A direct evaluation from the atomic trajectories shows that the three major contributing Rouse modes decay with stretched exponentials displaying stretching exponents jSof (1 13=0.96 and 2,3 jS=0.86). We note, however, that there is no evidence for the extreme stretching of in- 

A detailed scrutiny of the Gaussian approximation (Eq. 2.7) reveals that for KTr deviations occur. This was studied later in more detail for the case of polybutadiene (PB) [55]. These simulations demonstrated that the deviations from the Gaussian approximation relate to intermolecular correlations that are not included in any of the analytical models at hand. 

While the Rouse model predicts a linear time evolution of the mean-square centre of mass coordinate (Eq. 3.14), within the time window of the simulation t 9 ns) a sublinear diffusion in form of a stretched exponential with a stretching exponent of (3=0,83 is found. A detailed inspection of the time-dependent mean-squared amplitudes reveals that the sublinear diffusion mainly originates from motions at short times t i =2 ns. 

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