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144
A
2
c
2
1
M
⇒
µ
1
−
µ
1
0
= −
RTV
1
0
c
2
1
M
In this case the A
2
c
2
term does not contribute significantly to
µ
1
-
µ
1
0
.
High A
2
obviously means that
A
2
c
2
1
M
⇒
µ
1
−
µ
1
0
= −
RTV
1
0
c
2
(
A
2
c
2
)
In this case the A
2
c
2
term does contribute significantly to
µ
1
-
µ
1
0
. The effect of
A
2
is consequently dependent on c
2.
In practice: High values are in the range 10
-3
(ml mol g
-2
) or higher
3.2.8. A
2
:
Important
link
to
chain
statistics
In Section 2.2.8 we introduced the concept ‘excluded volume’ for monomers in
a single chain, leading to the intramolecular excluded volume factor (α
2
) which
influences the radius of gyration and the average end-to-end distance:
We further introduced the influence of intramolecular forces on
α
, leading to:
θ-conditions: α = 1 (excluded volume cancelled by weak attractive forces)
Good solvent:
α > 1 (excluded volume dominates)
Bad solvent:
α < 1 (attractive forces outweigh excluded volume)
The argument leading to the
θ
-condition (balance between intramolecular
excluded volume and weak attractive forces) can be applied also for the entire
molecules (intermolecular attractive forces and excluded volume):
θ-solvent:
A
2
= 0
Good solvent:
A
2
> 0
Bad solvent:
A
2
< 0
r
2
=
α
2
C
∞
nl
2