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103
•
monomers have a volume, and often charges (in polyelectrolytes), the
latter leading to attraction or repulsion
Each of these is treated separately (Textbook chapter 6.1.2 – 6.1.6), but
finally will be incorporated into the model, which in the end looks like this:
r
2
=
α
2
C
∞
nl
2
n
→ ∞
2.2.7. The
characteristic
ratio
(C
∞
): A
stiffness parameter
The term C
∞
is called the characteristic ratio, and combines the effects of both
fixed bond angles between monomers, and restricted rotation around bonds.
See Equations 6.8 and 6.11 in textbook.
C
∞
is hence a stiffness parameter characteristic for each polymer. It depends
only on the chemistry of the polymer.
Examples:
•
Pullulan (Fig. 4.22, 7.12c)
C
∞
= 4.3
32
•
Cereal mixed
β
-1,3/
β
-1,4 glucans,
C
∞
= 13-14
33
•
Alginates (I =
∞
):
C
∞
= 47
The larger C
∞
, the more stiff and extended chain (at constant M).
2.2.8. Excluded volume effects and
θ
-‐conditions
The term α
2
refers to the excluded volume effect. The fact that monomers do
have a finite volume and sometimes equally charged monomers results in a
general electrostatic expansion of the chain (α
2
>1). The excluded volume
effect is also slightly dependent on the chain length:
α
∝
n
0-0.1
, or α
∝
M
0-0.1
32 Buliga, Gregory S.; Brant, David A.. Temperature and molecular weight dependence of the unperturbed dimensions of aqueous pullulan.
Int. J. Biol. Macromol. (1987), 9(2), 71-6.
33 Gómez et al. (1997) Carbohydr. Polym. 32, 17-22