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142
µ
i
−
µ
i
0
=
RT
ln
X
i
for all
i
(ideal solutions) (Eq. 10.37)
(Some textbooks use this equation to define the ideal solution)
3.2.6. Second virial
coefficient
(A
2
)
The general equation (again):
µ
1
−
µ
1
0
= −
RTV
1
0
c
2
1
M
+
A
2
c
2
+
A
3
c
2
3
+ ⋅ ⋅ ⋅
⎛
⎝⎜
⎞
⎠⎟
A
2
expresses, as we have seen, the deviation from thermodynamic ideality.
For dilute solutions of biopolymers this term consists of two parts: The
excluded volume term and the Donnan term. The latter is only relevant for
polyelectrolytes.
A
2
≈ A
2
(excluded volume) + A
2
(Donnan)
The excluded volume effect arises from the fact that two polymer chains
cannot occupy the same volume. For example, the centers of two spheres
with radius R cannot be closer than 2R, each sphere thus having an excluded
volume of 4/3
π
(2R)
3
(See also textbook fig. 10.2-10.4)
Because of the size of the polymers this terms becomes important, even in
dilute solutions. Conversely, determining A
2
provides information about the
polymer.