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Encyclopedia of Physical Science and Technology EN012c-593 July 26, 2001 15:56

Polymer Processing 613

The IV is obtained from measurements of the viscosity of
a dilute polymer solution relative to the viscosity of the
solvent. Typically, it measured at a specific polymer con-
centration. The IV is directly related to the intrinsic vis-
cosity, which is obtained by the extrapolation of solution
viscosities to zero polymer concentration. Well-known
relations between the intrinsic viscosity and the molar
mass of a polymer exist (this relation is referred to as the
Mark–Houwink relation). For polymers such as those pro-
duced by means of addition reactions, the melt index (MI)
FIGURE 2 Steady simple shear flow with shear rate equal to V /b.
is used to categorize the molar mass. The measurement of
MI is discussed in the rheology section.
Another factor affecting processing is whether the chain between force, F, divided by the area of the plates, A, and
is linear or branched. Branching refers to arms that extend the velocity divided by the separation distance, b, is given
from the main backbone of a chain. These branches may as follows:
be long or short depending on whether the molar mass
F V
of the branch, M, is greater than the critical molar mass = µ . (1)
A b
for entanglements, M c , or less than M c . Branching may be
quite dense, in which every chain contains many branches, The constant of proportionality, µ, is called the viscosity
or sparse, in which not every chain contains a branch. of the fluid. F is the force required to keep the top plate
The branching architecture can be described as random, moving with a constant velocity. The force per unit area
comb, star, or H. Random branching involves irregular acting in the x direction on a fluid surface at constant y
spacing of the branches along the backbone as well as the by the fluid in the region of lesser y is the shear stress,
branches. Combs are systems in which the branches pro- τ yx . Because the velocity of the fluid particles varies in a
trude from one side of the chain. Star-branched polymers linear manner with respect to the y coordinate, it is clear
consist of three or four arms emanating from a central that V /b = d v x /dy, which is the derivative of the velocity
point. H-branched polymers consist of multiple branches withrespecttothedistance y.Equation(1)canberewritten
at the end of the chains. The processing behavior as well as:
as the mechanical properties of a polymer are dependent
τ yx = −µ(d v x /dy). (2)
on the branching architecture.
The thermal conditions for processing are determined This states that the shear force per unit area is propor-
by two important thermal transition temperatures. These tional to the negative of the local velocity gradient and
temperatures are the glass transition temperature, T g , and is known as Newton’s law of viscosity. Fluids that obey
the melting point, T m . For amorphous polymers that ex- this simple linear relationship are termed Newtonian flu-
hibit no crystallinity, the T g determines where it becomes ids. From Eq. (2) we can determine the dimensions of
deformable and, hence, processible. For semicrystalline viscosity, which are mass/unit length/unit time. For the
polymers, T m determinestheprimarytemperatureatwhich Syst` eme International (SI), the units of viscosity are Pa
the polymer will flow and become processible. Some sec (or kg/m/s), whereas for the CGS system they are the
2
semicrystalline polymers can be processed to limit the Poise (dyn/cm /sec or g/cm/sec).
formation of crystallinity and thereby behave somewhat The flow behavior of most thermoplastics does not fol-
like an amorphous polymer. Temperature T g is associated low Newton’s law of viscosity. To quantitatively describe
with an increase in free volume, which allows mobility the viscous behavior of polymeric fluids, Newton’s law of
of the polymer chains. Hence, one must be above T g to viscosity is generalized as follows:
process amorphous polymers.
τ yx = −η d v x /dy, (3)
where η can be expressed as a function of either d v x /dy or
τ yx . Some typical responses of polymeric fluids are shown
II. RHEOLOGY OF POLYMER MELTS
in Fig. 3, where τ yx is plotted versus the velocity gradient.
For a pseudoplastic fluid, the slope of the line decreases
A. Purely Viscous Behavior
with increasing magnitude of dv x /dy, or in essence the
When a simple fluid, such as water, is placed between the viscosity decreases. Some polymeric fluids (in some cases
two plates, as shown in Fig. 2, in which the top plate is polymer blends and filled polymers) exhibit a yield stress,
moved to the right with constant velocity, V , the relation which is the stress that must be overcome before flow