Neutron Scattering

By means of neutron scattering two different correlation functions may be accessed . In the
case of coherent scattering, all partial waves emanating from different scattering centres are
capable of interference - the Fourier transform of the pair correlation function of a single
chain is measured . In contrast incoherent scattering, where the interferences from partial
waves of different scatterers are destructive, measures the self conelation function . The self
correlation function leads directly to the mean square displacement of the diffusiog segments .
In Gaussian approximation for t < ZR we have
~- 2
kBT e 4 \v2
C 12L"o
in the case of coherent scattering, which observes the pair correlation function, interferences
from scattering waves emanating for various segments complicate the scattering function .
With Eq.[15 .14] we obtain
S(Q, t) =1exp [ -Q 2 DRt] 1 exp {-1In-ml Q2~2
N 6
2 R2 Q 2 1
7 2 p2
for small Q (QRE < 1) the second and third terms are negligible and S(Q t)
centre ofmass diffusion of the chain .
describes the
S(Q,t)=N exp (-DRt) (15 .18)
For QRE > 1 and t < ZR the internal relaxations dominate . Converting the sums in Eq .[15 .17]
to integrals and aller some algebra de Gennes has derived an expression for the dynamic
structure factor.
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