Chemistry Reference
In-Depth Information
molecules. This last dependence permits estimation of an average molecular
weight from solution
vis
cosity. The average molecular weight that is measured is
the viscosity average
M
v
, which differs fr
om
those described so far in this text.
Before viscosity data are used to calculate
M
v
of the solute, it is necessary, how-
ever, to eliminate the effects of solvent viscosity and polymer concentration. The
methods whereby this is achieved are described in this section.
The procedures
ou
tlined below do not remove the effects of polymer
solvent
interactions, and so
M
v
of a particular polymer sample will depend to some extent
on the solvent used in the solution viscosity measurements (
Section 3.3.1
).
Solution viscosity measurements require very little investment in apparatus
and can be carried out quite rapidly with certain shortcuts described in
Section 3.3.4
. As a result, this is the most widely used method for measuring a
polymer molecular weight average. Solution viscosities are also used, without
explicit estimation of molecular weights, for quality control of some commercial
polymers, including poly(vinyl chloride) and poly(ethylene terephthalate).
We first consider briefly why a polymer solution would be expected to have a
higher viscosity than the liquid in which it is dissolved. We think initially of a
suspension of solid particles in a liquid. The particles are wetted by the fluid, and
the suspension is so dilute that the disturbance of the flow pattern of the suspend-
ing medium by one particle does not overlap with that caused by another.
Consider now the flow of the fluid alone through a tube which is very large com-
pared to the dimensions of a suspended particle. If the fluid wets the tube wall its
velocity profile will be that shown in
Fig. 3.6a
. Since the walls are wetted, liquid
on the walls is stationary while the flow rate is greatest at the center of the tube.
The flow velocity
v
increases from the wall to the center of the tube. The differ-
ence in velocities of adjacent layers of liquid (velocity gradient
5
dv/dr
) is great-
est at the wall and zero in the center of the tube.
When one layer of fluid moves faster than the neighboring layer, it experi-
ences a retarding force
F
due to intermolecular attractions between the materials
Radial position, r
Tube
wall
(a)
(b)
FIGURE 3.6
(a) Variation of the velocity of laminar flow with respect to the distance r from the center of
a tube. (b) Sphere suspended in a flowing liquid.
