Neutron Scattering

and which lead to the scattering cross section
dE _ 1 N
d~( Q ) Y~b V
DaD(rn)+bHaH-
(rn)+b0(1-aD(rn-)_ - 6H-(rn)))e'Q'~ >
s 1
which after some calculation leads to the form
z
according to.
The partial structure factors are given as :
(bD - bo ~TD(rr)+(bx - bo)6x(Ei)+ b, o, e iQr; 2 > (14.26)
-0-
and, fmally, to a sum of partial structure factors weighted with conesponding contrast factors
d~(Q)=V [4bDS DD +24bD4b .S DH +4bHS 1 (14.27)
5
D(H) D(H)
D D
SDD = (PnZ ZP(Q)+ (1) Zn2 Z Z W(Q) (14.28)
SHH =(1- ~D )nZZP(Q)+
~D Zn2ZZW(Q) (14.29)
H
S De = (D(1 - (D~2Z2 W(Q) (14.30)
H D
and fmally one delivers the following scattering law
dl(Q)= V
~bD-bH) Z q)(1-d)nZ Z P(Q)+(br oiy -b [ o)Z nZ Z P(Q)+n 2 Z Z W(Q) ] } (14.31)
5
For this systems the Babinet principal is not valid as it contains polymers and solvent
molecules . If one matches the scattering length of the solvents and the averaged one of the
polymers (broiy =d)bD +( 1- ~)bH) according to broiy =b o (,,zero" contrast), the second term
in Eq .(14 .31) does not contribute to the scattering and, consequently, one again determines
the form factor of a single chain according to
(Q) = c -1)(1-1) VP(Q)K (14.32)
ddY--
144 1