Chemistry Reference
In-Depth Information
molecular sizes, the greater is the disparity between averages. The ratio of this disparity,
M
w
/
M
n
is a
measure of
polymeric dispersity
.A
monodisperse
polymer has a ratio of:
M
w
=M
n
¼
1
In all synthetic polymers and in many naturally occurring ones the weight average molecular
weight is greater than the number average molecular weight. Such polymers are
polydisperse
.
Two samples of the same polymer equal in weight average molecular weight may exhibit different
physical properties, if they differ in themolecular weight distributions.Molecular weight distribution can
affect elongation, relaxation modulus, tensile strength, and tenacity of the materials [
65
]. An additional
average molecular weight that is obtained with the aid of ultracentrifugation is referred to as sedimenta-
tion average molecular weight, or Z-average molecular weight,
M
z
This was more often used in the past,
particularly with naturally occurring polymeric materials. It is not used, however, as much today.
.
X
N
i
X
3
2
M
z
¼
M
i
M
i
N
i
In solutions of polymers the viscosities are more affected by the long chains than by the short ones.
A correlation of the viscosity of the solution to the size of the chains or to molecular weight of the
solute, allows an expression of a
viscosity average
molecular weight:
.
1
=b
X
N
i
X
M
i
bþ
1
M
¼
M
i
N
i
where,
b
is a constant., usually less than unity. When
b ¼
1, then
M
Z
becomes equal to
M
w
. Actually,
though, the values of
M
are usually within 20% of the weight average molecular weights. For
polydisperse polymers
M
n
.
Most of the methods for determining the molecular weights and sizes of polymers (with the
exception of small-angle neutron scattering) require dissolving the polymers in proper solvents first.
The measurements are then carried out on dilute solutions.
Solution viscosities of linear polymers relate empirically to their molecular weights. This is used in
various ways in industry to designate the size of polymers. The values are obtained by measuring the
efflux time
M
w
is larger than
M
and
M
in turn is larger than
t
o
of pure
solvent. Typical viscometers, like those designed by Ubbelohde, Cannon-Fenske, (shown in Fig.
1.3
),
and other similar ones are utilized and measurements are carried out in constant temperature baths.
The viscosity is expressed in following ways:
t
of a polymer solution through a capillary. It is then related to the efflux time
Common name
Symbol
Definitions
1. Relative viscosity
rel
/
o
¼ t
/
t
o
2. Specific viscosity
sp
(
o
)/
o
¼
rel
1
/
(
t t
o
)/
t
o
3. Reduced viscosity
red
sp
=C ¼
rel
1
=CZ
4. Inherent viscosity
i
ln
rel
/
C
5. Intrinsic viscosity
[
]
c
!
0
(
sp
/
C
)
c ¼
0
¼
(
i
)
c ¼
0
2.7.2 Methods for Measuring Molecular Weights of Polymers
To determine the intrinsic viscosity, both inherent and reduced viscosities are plotted against concen-
tration (
C
) on the same graph paper and extrapolated to zero. If the intercepts coincide then this is taken
