Basic HTML Version
223
η
[ ]
=
2.5
v
h
=
10
3
πξ
3
R
G
3
N
Avo
M
This equation shows – for randomly coiled chains – that a change in R
G
leads
to a very large change in intrinsic viscosity. For example, a 2-fold reduction in
R
G
leads to a 8-fold reduction in
[η]
. This can happen if a randomly coiled
polyelectrolyte (e.g. alginate or chitosan) is transferred from low ionic strength
(expanded) to high ionic strength (contracted):
Since, for random coils, the relation between R
G
and M is given by:
R
G
∝
M
0.5
−
0.6
(
θ
-solvent - good solvent)
it follows by substituting for R
G
that (still for random coils only):
η
[ ]
=
KM
0.5
−
0.8
Note the constant K is different for different systems, and different from the
constants used in analogous equations for R
G
(R
G
= KM
b
).
6.1.6. The Mark-‐Houwink-‐Sakurada
(MHS) equation
The very famous - and much used – MHS equation incorporates all three
basic shapes of macromolecules in solution:
η
[ ]
=
KM
a
log(
η
[ ]
)
=
log
K
+
a
log
M
Solid spheres (e.g. globular proteins): a = 0
Rigid rods: a = 1.8
Random coils (
θ
-solvent): a = 0.5
Random coils (good solvent): a = 0.8