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Polymer Processing 619

flow is generated. The device can be operated by either
applying a constant squeeze rate or a constant force. The
device is very useful for making viscosity measurements
5
on fluids with high viscosity (e.g., η> 10 Pa sec) such as
composite materials containing long-fiber reinforcement
or propellants.

F. Effect of Molar Mass on Viscosity
Molar mass (M) has a significant effect on the rheological
properties of polymer melts and hence on their processing
performance. At low molar mass, i.e., below some critical
molar mass (M c ), for flexible chain polymers η 0 depends
on M w , while above M c , η 0 depends on M w to the 3.4 to
3.6 power for most flexible linear polymer chains:

M w for M w < M c
η 0 ∝ 3.4 . (21)
M
w for M w > M c
The 3.4 power dependence has been observed experimen-
FIGURE 11 Rheotens apparatus for estimating uniaxial exten-
tally and predicted theoretically. Furthermore, the primary
sional viscosity. [From Baird, D. G., and Collias, D. I. (1998). “Poly-
mer Processing: Principles and Design,” Wiley, New York.] normal stress difference coefficient in the limit as the shear
rate goes to zero, 1,0 , is observed to be proportional to
M w raised to the 7.0 power, i.e.:
shear and shear-free flows is the squeezing-flow rheome- 2 7.0
1,0 ∝ η ∝ M . (22)
ter shown in Fig. 12. For small gaps and no slip at the 0 w
walls, the kinematics are primarily that of shear flow. For For branched polymers the dependence of η 0 on M w can
large gaps and in the presence of lubrication at the inter- be to higher or lower powers than 3.4 to 3.6 depending on
face between the plates and polymer, biaxial extensional the molecular weight between branch points. For rodlike

FIGURE 12 Squeezing-flow rheometer showing displacement of parallel disks. [From Baird, D. G., and Collias, D. I.
(1998). “Polymer Processing: Principles and Design,” Wiley, New York.]