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143
The contributions from the excluded volume for the basic shapes can be
determined (no proof given):
2
2
2
3
-5
2
2
2
2
2
2
2
2
2
(
)
(
) ( .10.63)
2
4 16
(
)
Typically 3 10
3
(
)
Typically
Avo
Avo
N u
A general
u excluded volume per macromolecule Eq
M
v
R N
A compact spheres
ml mol g
M M
L v
A rods
d M
π
−
=
=
= =
⋅
⋅
⋅
=
-3
2
3 3
-4
2
2
2
2
1 10
16
(
)
Typically 1-5 10
3
Avo
G
ml mol g
N
A random coils
R
ml mol g
M
π
γ
−
−
⋅
⋅
⋅
=
⋅
⋅
⋅
The contribution from Donnan effect (polyelectrolytes), which may in fact
dominate, turns out to be:
2
2
2
1
1
(
)
( .10.133)
4
, . .
BX
BX
z
A Donnan
Eq
M C
C molar concentration of added salt BX e g NaCl
⎛ ⎞
=
⎜ ⎟
⎝ ⎠
=
The Donnan effect will be discussed and explained in more detail in Section
3.4.
3.2.7. A
2
: High or
low?
Biopolymer scientists often refer to ‘high’ or ‘low’ A
2
values. What does it
mean? These are of course relative terms, and need to be considered in
terms of the general equation:
µ
1
−
µ
1
0
= −
RTV
1
0
c
2
1
M
+
A
2
c
2
+ ⋅ ⋅ ⋅
⎛
⎝⎜
⎞
⎠⎟
Low A
2
means that the term A
2
c
2
is much less than 1/M and can be ignored: