Neutron Scattering

2
P(Q) = 1 ~exp(-Ii - j'6 Q2 ) (14 .7)
z ;;
and alter some calculation one gets the well known Debye formula
with x = R g
2 Q 2 .
PDebye(Db) (Q) -2[x - 1 + exp(-x) ] (14 .8)
x
In Figure14 .3 the form factor according to Debye's formula has been plotted.
0.8
a
0.6
0.4
0.2
0.0
0 2 4 6 8 10
x = (RgQ)2
Figure 14.3 : Debyeformfactor ofa linear chain
The Symbol beside Eq .(14 .6) represents the form factor of a linear chain determined
exclusively by intramolecular phase factors . Such symbols should help to make transparent
the meaning of scattering laws ofmore complex polymers .
There are expressions for the form factor in Eq.(14 .6) being approximately valid in the
regions of small and large scattering vector if compared with the inverse size of the polymer ;
they have a much simpler form and can easily be used for the analysis of the scattering data.
So in the region of small Q, e.g . Q« 1/Rg one finds
PDb -1-3 Rg Q2 or the Zimm approximation : Ppb -1 + 3Rg Q2 (14.9)
as depicted in Figure 14 .4a. From this plot one gets the radius ofgyration and the scattering in
forward direction according to Eq .(14 .9), delivering the polymer molar volume and volume
14-5