Chemistry Reference
In-Depth Information
Section 2.4.1 gives an outline of the Flory-Huggins theory of polymer solutions
and introduces the Y-solvent as a solvent that gives as close to ideal behaviour
as can be obtained, defines the solution dimension (the radius of gyration, R
g
)
and the value of concentration, c*, below which our solution is dilute. At
polymer concentrations of c
o
c*, the vescosity of the solution is given by
Z
¼
Z
0
1
þ½
Z
c
þ
k
H
c
2
þ
ð
3
:
69
Þ
The value of the intrinsic viscosity is used to calculate the molecular weight as
described in Section 5.6.1 using the Mark-Howink equation
½
Z
¼
KM
n
ð
3
:
70
Þ
where K and n are constants that can be obtained from the literature for a
particular polymer-solvent-temperature combination.
38
Frequently, the units
used for the polymer concentration are g/dL and not the current S.I. system.
Hence, the values for the intrinsic viscosity have units of dL/g.
In a Y-solvent a polymer coil is as close to the random-coil configuration as
possible as the polymer-segment-solvent-molecule interactions are minimised.
In this case, (3.71) becomes
½
Z
Y
¼
K
Y
M
0
:
5
ð
3
:
71
Þ
where K
Y
is related to the size of the unperturbed coil:
3
2
R
2
M
K
Y
¼
F
ð
3
:
72
Þ
F is known as the Flory-Fox parameter and substitution of eqn (3.72) in eqn
(3.71) gives
½
Z
Y
¼
F
R
3
ð
3
:
73
Þ
M
In non-theta solvents we can use an experimentally determined value of F as an
indicator of the degree of chain expansion.
The Huggins coefficient indicates the strength of the pairwise interaction of
the polymer molecules. It can be useful to express the Huggins coefficient as
k
H
¼½
Z
2
k
0
H
ð
3
:
74
Þ
In eqn (3.69) a value of k
0
H
: 1 indicates that the interaction is just hydrodynamic
with no interactions from van der Waals' or electrostatic forces. Attractive
interactions, such as those found with self-associating polymers, result in much
larger values. With polyelectrolytes, the repulsive interactions between the charges
on the polymer produce an expansion of the chain (the tertiary electroviscous
effect) so that the details of the chemical environment need to be known and
specified when comparing data. For example, if we consider a common polyelec-
trolyte such as poly(acrylic acid), the dimensions in solution are a function of both
pH and salt concentration. In addition, ion type can be important. Calcium ions
bind strongly to carboxyl groups and can form ion bridges with poly(acrylic acid)
leading to multimolecular associations at low polymer concentration and gel
