Neutron Scattering

Having obtained very good agreement between experiment and simulation, the simulations
which contain complete information about the atomic trajectories may be further exploited, in
order to rationalize the origin for the discrepancies with the Rouse model . A nuinber of
deviations evolve .
1 . According to the Rouse model the mode correlators (Eq.[15 .13] should decay in a single
exponential fashion . A direct evaluation from the atomic trajectories shows that the 3
contributing Rouse modes decay with stretched exponentials displaying stretching
exponents ß of (1 :,6 = 0.96 and 2,3 :iß = 0.86)
2 . A detailed scrutiny of the Gaussian assumption (sec e .g . (Eq .[15 .16] and [15 .17]) reveals
that for t < rR deviations occur .
3 . While the Rouse model predicts a linear time evolution of the mean squared centre of
mass coordinate (Eq.[15 .17]), within the time window of the simulation (t < 9ns) a
sublinear diffusion in form of a stretched exponential with the stretching exponent of
,8 = 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 < zR =
2ns .
The prediction of a time dependent centre of mass diffusion coefficient bas recently been
corroborated by NSE-experiments on short chain polybutadienes . Fig . 15 .16 displays the mean
square centre of mass displacement from simulation compared to the saine quantity obtained
from the dynamic structure factor at various Q-values . Both the simulation as well as the
experimental data consistently lead to a weaker than linear time dependence of the mean
square centre of mass displacement .
The overall picture emerging from this combined simulational and experimental effort is, that
for chains, which should be ideal Rouse chains, the model is capable of quantitatively
describing the behaviour only on time scales of the Order of the Rouse time or larger and
therefore on length scales of the Order of the radius of gyration of the chains or larger and in
the regime, where the chains actually show Fickian diffusion . The self diffusion behaviour for
times smaller than the Rouse time and the relaxation ofthe intemal modes of the chains show
15- 2 1