motion of the whole chain via entanglement and hence drives molten polymers into
the rubber state. The ability of polymers to make permanent deformation has been
drastically reduced, and the highly elastic deformation begins. Second, the occur-
rence of the rubber-glass transition freezes the motion of chain segments, driving
the rubbery polymers into the glass state. Consequently, the chain conformation is
unable to make a large-scale elastic deformation. Finally, the cooling freezes
sequentially the motions of chain repeating units and side groups in thesecondary
transitions.
The occurrence of various characteristic states of dynamic responses is related
not only to the molar mass, but also to the crystallinity and the degree of cross-
linking. Large molar mass is the prerequisite condition of the rubber state, while
high crystallinity and high degree of cross-linking will suppress the rubber state. As
illustrated in Fig.6.2, an evident rubber state occurs only for non-crystalline or
semi-crystalline linear polymers with the large enough molar mass. Moreover,
semi-crystalline polymers will reach the fluid state above their melting points.
The polymers with low degree of cross-linking will not be able to enter the fluid
state. The high degree of cross-linking even eliminates the rubber state. Similarly,
the high crystallinity makes polymers directly change from the crystalline solid to
the viscous fluid around their melting points.
Since the rubber state is a characteristic property of the mechanical response of
polymers, the occurrence of such a state can sometimes be used to evidence the
existence of high polymers. We can define the average molar mass between entan-
glement pointsMe, corresponding to the number of bonds ne. BelowMe,the
molecules can be regarded as short-chain polymers, while aboveMe, the molecules
can be treated as long-chain polymers. As illustrated in Fig.6.3,TfandTgwill merge
together in the region of low molar mass. Such a separation of molar mass implies
that an interaction mechanism between polymer chains, similar to the crosslink of
Fig. 6.1 Illustration of the characteristic deformation of non-crystalline linear polymers as a
function of temperature under a small external stress. The characteristic glass, rubber and fluid
states are separated by the glass-rubber transitionTgand the rubber-fluid transitionTf, respectively.
Thedashed linesare drawn to guide the eyes
94 6 Polymer Deformation