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221
η
[ ]
≈
η
sp
c
=
2.5
v
h
c
: concentration
v
h
: specific hydrodynamic volume (volume of 1 g spheres)
Since
v
h
c
=
φ
(volume fraction), the equation also reads:
η
sp
=
2.5
φ
In other words,
[η]
is independent of the size (radius, molecular weight) of the
spheres, just the concentration and hydrodynamic volume. In other words:
η
[ ]
=
KM
0
=
K
(constant) for solid spheres
For this reason, globular proteins have intrinsic viscosities close to 2.5 ml/g,
irrespective of their molecular weights, since most of them turn out to have
hydrodynamic volumes close to 2.5 ml/g, including bound water molecules
(hydration layer, which adds to the volume).
The situation changes, however, when going to rigid rods and flexible chains.
6.1.4.
Intrinsic viscosity of
rigid
rods
The general expression for rigid rods is:
η
sp
=
νφ
=
ν
(
v
h
c
)
ν
: A form factor which depends on the molecular weight:
ν
∝
M
1.8
(see textbook chapter 11.1.3. for more detailed explanation)
It follows that for rigid rods the intrinsic viscosity depends strongly on the
molecular weight:
η
[ ]
=
KM
1.8
=
for rigid rods
Compare this expression to the analogous expression for the radius of
gyration (R
G
). The strong dependence on the molecular weight (exponent 1.8)
means, for example, that if the molecular weight of a rod-like polymer is