Neutron Scattering

S (Q,t) = 12 fdu exp ~ -u_ (S2Rt) vz h )1
(u (nRt)-vz
Q Y 0
(15 .19)
h(y) = - i A cos(xy) (1-exp(- x2»
0
We observe that in spite of the complicated functional form S(Q t),
function, only depends on one variable, the Rouse variable .
like the self correlation
(~ t) v2 - Qz 3kRT f Z t -
R
6 N ;0 6
YVt (15 .20)
Since there is no length scale in the problem, for différent momentum transfers the dynamic
structure factors are predicted to collapse to one master cuive, if they are represented as a
function ofthe Rouse variable .
15 .3 .2 Neutron spin echo results
The self correlation function of a Rouse chain was first obseved on polydimethylsiloxane
(PDMS) . Since a straight forward study of the incoherent scattering by NSE is vey difficult -
due to spin flip scattering a severe loss of polarization occurs leading to vey weak signals -
the measurements of the self correlation fonction were performed on high molecular weight
deuterated PDMS chains which contained short protonated labels at random positions . In such
a sanple the scattering essentially originates from the contrast between the protonated
sequence and a deuterated environnent and therefore is coherent. On the other hand the
sequences are randonly distributed, so that there is no constructive interference of partial
waves arising from différent sequences . Under these conditions the scattering experiments
measures the self correlation fonction .
In Fig .15 .10 the corresponding NSE spectra are plotted against the scaling variable of the
Rouse model . The results for the different momentum transfers follow a common straight
line . In Gaussian approximation for the case of the self correlation function the scattering
function directly measures the mean square segment displacement, which according to
Eq .[15 .15] obeys a square root law in time . This behaviour may be directly read off fron
Fig .15 .10 .
15- 16