Biomedical Engineering Reference
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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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