Chemistry Reference
In-Depth Information
It is easily shown that both equations should extrapolate to a common inter-
cept equal to [
k
1
should equal 0.5. The usual calculation proce-
dure involves a double extrapolation of
Eqs. (3-89) and (3-90)
on the same plot,
as shown in
Fig. 3.8
. This data-handling method is generally satisfactory.
Sometimes experimental results do not conform to the above expectations. This is
because the real relationships are actually of the form
η
] and that
k
H
1
k
0
H
½η
c
2
1
2
c
3
c
2
ðη=η
0
2
1
Þ 5 ½η 1
k
H
½η
1
1
?
(3-91)
and
k
0
1
½η
c
2
1
ln
2
c
3
c
2
ðη=η
0
Þ 5 ½η 2
k
1
½η
2
2
?
(3-92)
and the preceding equations are truncated versions of these latter virial expres-
sions in concentration. No two-parameter solution such as
Eq. (3-89) or (3-90)
is
universally valid, because it forces a real curvilinear relation into a rectilinear
form. The power series expressions may be solved directly by nonlinear regres-
sion analysis
[11]
, but this is seldom necessary unless it is desired to obtain very
accurate values of [
] and the slope constants
k
H
and
k
1
.
The term
k
H
in
Eq. (3-89)
is called “Huggins constant.” Its magnitude can be
related to the breadth of the molecular weight distribution or branching of the sol-
ute. Unfortunately, the range of
k
H
is not large (a typical value is 0.33) and it is
not determined very accurately because
Eq. (3-89)
fits a chord to the curve of
Eq. (3-91)
, and the slope of this chord is affected by the concentration range in
which the curve is used.
A useful initial concentration for solution viscometry of most synthetic poly-
mers is about 1 g/100 cm
3
solvent. High-molecular-weight species may require
lower concentrations to produce a linear plot of
c
2
1
(
η
η
/
η
0
2
1) against
c
(
Fig. 3.8
),
1
η
η
0
C
( — -1)
1
η
η
0
[
η
]
n (—-)
C
C
FIGURE 3.8
Double extrapolation for graphical estimation of intrinsic viscosity.
