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

708 Polymers, Mechanical Behavior

V. TIME AND TEMPERATURE WITH
RESPECT TO MOLECULAR
CONSIDERATIONS

To interrelate the variables of temperature and time (rate of
deformation), we must focus on the types of materials we
are discussing, that is, systems composed of macromole-
cular chains. As mentioned earlier, the length-to-diameter
FIGURE 13 General plot of log modulus versus rate (or log rate)
ratio, or aspect ratio, of linear polymers is considerable
of deformation for many amorphous polymeric materials.
and is much greater by far than the typical strands of
spaghetti that are often used as an analogy for linear poly-
denoted. In Fig. 13 a mirror image of the behavior given mers. Besides this large mismatch in aspect ratio, there is
in Fig. 11 is observed, where rate of deformation was as- another major discrepancy in the common comparison of
sumed constant and the temperature was then varied. In macromolecules with spaghetti. This concerns the lack of
fact, since rate can be viewed as frequency (i.e., recip- mobility or motion of a spaghetti strand. A more suitable
rocal time), this clearly shows that time and temperature analogy, and one that is consistent with developments in
are strongly interrelated, and we will have to address this the theories of reptation for the flow of polymer melts (vis-
important fact. Before we do so, it is important to point cous flow), compares linear polymers with long, stringy
out that the variable of pressure may be used to influence earthworms. Though somewhat crude and simplistic, this
the stress–strain or modulus behavior at a constant tem- analogy has some merit in terms of the discussions that fol-
perature and deformation rate. As indicated in Fig. 14, for low. In particular, long, stringy earthworms have many of
a process in which the temperature and rate are constant, the same response characteristics as polymer molecules.
an increase in the hydrostatic pressure will tend to pro- For example, placing them in liquid nitrogen would in-
mote higher modulus behavior in general. These remarks deed produce a more “glasslike material” whereas placing
are meant to be general, for there are some specific ef- them on a hot stove would tend to create a much higher
fects of pressure that can be taken into account, such as its degree of motion (at least for a short time!) within their
influence on the melting point (T m ), T g , etc. Also, some- backbones similar to the effect of thermal energy (kT ) on
times increased pressure can promote a higher strain to macromolecules. In fact, let us be so simplistic as to con-
break. In brief, however, the effects of hydrostatic pressure sider stress–strain experiments carried out on entangled
on the general mechanical property behavior of polymers worms if indeed they could be mounted into a suitable
are not particularly important except in cases involving mechanical testing device. There is little doubt that, at
high hydrostatic pressure, for example, in deep oceanic a constant deformation rate, the variable of temperature
applications. (in the framework indicated above) would lead to stress–
strain curves that would have the general characteristics
given by the same temperature function as indicated ear-
lier in Fig. 10. The cause of the lower modulus and higher
strain behavior, in general, simply arises from the fact that
within the time scale of the experiment (constant loading
rate) the worms would have sufficient time to respond to
the imposed stress, thereby allowing some disentangle-
ment and sliding of one backbone by another. The seg-
mental friction would lead to a viscous dissipation, that
is, loss of mechanical energy. However, as the temper-
ature decreased and the backbone motion of the worms
also decreased (an analogy with less thermal Brownian
motion), there would be less chance for disentangling
in the same time-scale, and hence the general entangle-
ment network character would provide a higher mod-
ulus behavior similar to that noted for macromolecular
FIGURE 14 Plot of stress versus strain for polypropylene being systems.
measured at ambient temperature but at different hydrostatic pres-
sures. [Reprinted with permission from Nielson, L. E. (1974). “Me- As can be imagined, varying the chemical structure of
chanical Properties of Polymers and Composites,” Vol. 2, Dekker, a polymer can alter its conformational freedom or back-
New York. Copyright 1974 Marcel Dekker.] bone flexibility thereby influencing the average molecular