Page 122 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Molecular Weight of Polymers 85

We will now turn our attention from the viscosity of dilute solutions and look at the viscosity of
melted polymers. The viscosity of melted polymers is important in transferring resins and in poly-
mer processing such as determining the correct conditions to have a specifi c flow rate for injection

processing and in determining the optimum conditions to get the necessary dimensions of extruded
shapes. Fillers, plasticizers, temperature, solvents, and molecular weight are just some of the vari-

ables that influence the viscosity of polymer melts. Here we will look at the dependence of melt
viscosity on polymer molecular weight. Polymer melts have viscosities on the order of 10,000 MPas
(1 centiposes is equal to 0.001 Pa/s).
For largely linear polymers, such as polystyrene, where particularly bulky side chains are not
present the viscosity or the flow is mainly dependent on the chain length. In most polymers, the melt

viscosity-chain length relationship has two distinct regions where the region division occurs when
the chain length reaches some length called the critical entanglement chain length, Z, (or simply
critical chain length) where intermolecular entanglement occurs. This intermolecular entanglement
causes the individual chains in the melt to act as being much more massive because of the entangle-

ment. Thus, the resistance to flow is a combination of the friction and entanglement between chains
as they slide past one another. Below the critical entanglement length, where only the friction part is
important, the melt viscosity, η, is related to the weight average molecular weight by
η = KM 1.0 (3.41)
w
1
And above the critical chain length, where both the friction and entanglement are important, the
relationship is
η = KM 3.4 (3.42)
h
w
where K is a constant for the precritical entanglement chain length and K is for the situation above
l h
Z and where both K values are temperature dependant. The first power dependence is due to the

simple increase in molecular weight as chain length increases, but the 3.4 power relationship is due
to a complex relationship between chain movement as related to entanglement and diffusion and
chain length.
The critical chain length is often the onset of “strength” related properties and is generally con-
sidered the lower end for useful mechanical properties. The Z value for polymers varies but is typi-
cally between about 200 and 1,000 units in length. For instance, the Z value for polystyrene is about
700; for polyisobutylene about 600; for poly(decamethylene sebacate) about 300; for poly(methyl
methacrylate) about 200; and for poly(dimethyl siloxane) about 1,000.
A number of techniques have been developed to measure melt viscosity. Some of these are
listed in Table 3.8. Rotational viscometers are of varied structures. The Couette cup and bob vis-
cometer consists of a stationary inner cylinder, the bob, and an outer cylinder, cup that is rotated.

TABLE 3.8
Viscosity Measuring Techniques and Their Usual Range
Technique Typical Range (Poise)
Capillary pipette 0.01–1,000
Falling sphere 1–100,000
Parallel plate 10,000–10 9
Falling coaxial cylinder 100,000–10 11
Stress relaxation 1,000–10 10
Rotating cylinder 1–10 12
Tensile creep 100,000–greater than 10 12

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