Neutron Scattering

This incoherent approximation does not reveal e .g . symmetry related cancellations, but
displays a major feature of the corresponding dynamic structure factor, namely the relative
suppression of the inelastic contributions from local jump processes at the maximum of the
structure factor . Fig .15 .3 displays the situation for polybutadiene . There a ß-process
corresponding to a jump length of d = 1 .5Â has been found . The corresponding inelastic
dynamic structure factor is strongly reduced at the position of the flrst peak, while it
contributes strongly at higher Q. Fig .15 .3 suggests a Q selectivity for thé différent relaxation
processes : at thé structure factor maximum local jump processes should not contribute and thé
relaxation due to flow should dominate . On thé other hand at larger Q, in particular in thé
minimum ofthé structure factor, thé secondary relaxation should reveal itself.
0 .5
0
Figure 15 .3 : Static structure factor S(Q) and normalized inelastic contribution S" to
S(Q)
S(Q,ca)IS(Q) for PB .
We now assume that thé a- and thé ß-relaxation are statistically independent. Then, in real
space thé joint correlation function is given by a convolution of thé corresponding functions
for both separated processes . In Q-space this convolution becomes a product and we may
write thé total scattering function as a product of thé structure factor due to thé a- and ß-
processes .
15-6