Biomedical Engineering Reference
In-Depth Information
Sphere
Radius R
Radius 2 R
U ( r )
0
2 R
r
Hard core interaction
1. 2
I 1 ( q )
S ( q )
1
0.8
0.6
0.4
0.2
I ( q )
0
0
2
4
6
qR
Scattered intensity for a suspension of hard spheres of radius R at a volume fraction ϕ = 12.5%. Two
spheres interact through a hard core interaction potential. The scattered intensity I(q) and the two
contributions - the form factor I 1 (q) and the structure factor S(q) - are shown separately.
Figure 2.3
seen, the scattered intensity normalized by concentration displays a distinct peak with
progressively increasing particle volume fraction.
2.2.4
Polymer solutions
When dealing with polymer solutions one has to distinguish between dilute solutions and
semi-dilute solutions or gels. In dilute solutions, inter-particle interference effects should
be taken into account. Then the total intensity scattered is given by the well-known Zimm
equation, valid for very dilute solutions (c < 1%):
h
i
;
2
I
ð
q
Þ¼
KcM I 1 ð
q
Þ
2 A 2 cMI 1 ð
q
Þ
ð
2
:
10
Þ
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