Biomedical Engineering Reference
In-Depth Information
1
1.0
2
1
I
1
(
q
)
2
Φ
= 0.02
3
Φ
= 0.04
4
0.8
3
0.6
Φ
= 0.06
4
0.4
0.2
0
0
1
2
3
qR
4
5
6
Figure 2.4
Total intensity normalized by the particle concentration for a dilute suspension of hard spheres at
various volume fractions indicated in the figure. The volume fractions are smaller than in
Figure 2.3
. A peak in scattered intensity appears with increasing volume fraction.
ξ
Definition of the correlation length
ξ
in a semi-dilute solution.
Figure 2.5
where K is a constant related to the scattering technique, c is the concentration of chains,
M is the molar mass (or
cient and I
1
(q) is the
normalized scattering function of a single chain. When the second virial coef
'
weight
'
), A
2
is the second virial coef
cient is
zero, the total intensity is proportional to concentration; when it is positive, the polymer is
in a good solvent and the intensity divided by concentration decreases with increasing
concentration, with the converse for poor solvents when A
2
<0.
As the polymer concentration increases, a new parameter describes the structure: the
correlation length
, shown schematically in
Figure 2.5
. The correlation length decreases
with polymer concentration according to a scaling law:
ξ
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