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Encyclopedia of Physical Science and Technology EN012c-598 July 26, 2001 15:59

Polymers, Mechanical Behavior 709

weight between entanglements with neighboring chains. different in their values of M wc . The first two are of rel-
To help clarify this issue, the reader will note that atively low M wc , this is due to the fact these chains are
Table I provides a listing of the critical molecular weight very flexible and therefore can easily entangle with neigh-
between entanglements (often determined from melt rhe- boring chains. However, in the case of polystyrene, it has
ological measurements) for many of the common poly- large bulky phenyl groups on alternate backbone carbons
mers. As a comparison, one notices that the first three en- and therefore makes the conformational freedom of that
tries, polyethylene, polpropylene, and polystyrene, which chain more restricted thereby leading, as the usual case,
all possess the same carbon–carbon backone, are quite to a distinctly higher value of M wc . The reader might look
over the other entries in Table I to note the wide variability
that occurs between different chemical structures for these
TABLE I Critical Weight Average Molecular Weight
between Entanglements (M wc ) a linear polymers.
On the basis of the above remarks, an additional con-
Polymer (M wc )
cept can be introduced. It is based on the definition of the
Polyethylene 3800 Deborah number D e , which is a ratio of two times and
Polypropylene 7000 therefore is dimensionless. For our purposes this can be
Polystyrene 35,000 defined as
Poly(vinyl chloride) 6250
molecular response or relaxation time
Poly(vinyl acetate) 24,500 D e = . (19)
experimental or observation time
Poly(vinyl alcohol) 5300
Polyacrylamide 9100 In Eq. (19) the numerator refers to a general characteristic
Poly(a-methyl styrene) 40,800 time or relaxation time over which the molecular system
Polyisobutylene 15,200 in question can respond. For example, this would mean
Poly(methyl acrylate) 24,100 that molecular movement is possible in this time-scale,
Poly(ethyl acrylate) 31,300 and therefore the material would appear somewhat liquid-
Poly(methyl methacrylate) 31,000 like if the time-scale of the experiment were appropriate.
Poly(n-butyl methacrylate) 60,400 The denominator concerns the time frame over which the
Poly(n-hexyl methacrylate) 91,900 observation occurs, that is, the experimental window or
Poly(n-octyl methacrylate) 114,000 observation time. In brief, if the Deborah number is greater
Poly(2-ethylbutyl methacrylate) 42,800 than unity, this means that the molecular response time is
Poly(dimethyl siloxane) 24,500 longer than the experimental time, and hence the material
Poly(ethylene oxide) 4400 will behave or appear more as a rigid solid. When the Deb-
Poly(propylene oxide) 7700 orah number is less than unity, however, this means that
Poly(tetramethylene oxide) 2500 the molecular response time is less than the experimental
Cis-polyisoprene 7700 time frame, and hence relaxation or flow may be observed
Hydrogenated polyisoprene 4000 in this period. The exact value of the Deborah number
Cis, trans, vinyl-polybutadiene 4500 is of relatively little concern here. In general terms, if it
Cis-polybutadiene 5900 is large the material is more “solid-like,” whereas as the
1,2-Polybutadiene 12,700 number becomes less than unity the behavior of the ma-
Hydrogenated 1,2-polybutadiene 26,700 terial becomes more liquid-like. Temperature influences
Poly(ε-caprolactam) nylon 6 5000 the Deborah number for a given experimental time frame
Poly(hexamethylene adipamide) nylon 66 4700 by affecting the numerator. Specifically, as temperature
Poly(decamethylene succinate) 4600 increases, the molecular response time decreases and the
Poly(decamethylene adipate) 4400 Deborah number therefore decreases. Some exceptions
Poly(decamethylene sebacate) 4500 to this can occur in polymeric materials. For example, a
Poly(diethylene adipate) 4800 material raised to a higher temperature may first become
Poly(ethylene terephthalate) 3300 somewhat liquid-like, but then due to the higher tempera-
Poly(carbonate of bisphenol A) 4900 ture, which may promote crystallization in selective sys-
Poly(ester carbonate of 1-bisphenol A and 4800 tems, the presence of developing crystals may begin to
2-terephthalic acid) increase the relaxation time due to the restrictions placed
Poly(ester of bisphenol A and diphenyl sulfone) 7100 on molecular mobility. One can also change the Deborah
number by changing the experimental time frame. The ap-
From Zhang, Y. H., and Carreau, P. J. (1991). J. Appl. Polym.
propriate variable here is deformation rate, be it in shear
Sci. 42, 1965.
a
Generally determined from melt rheological measurements. or elongation. Although the rate of deformation carries