fraction of polymers is lower, the interpenetrated chains in the unit volume become
fewer, hence a largerpis required to accommodate 21 interpenetrated chains,
resulting in a larger value ofMe. The plateau modulus of polymer melt is
E 0 Me^1 p^3 ðlw^2 Þ^3 (6.6)This relationship implies that when polymer chains are more rigid, or the
attractive interactions between chains are stronger, the rubbery plateau modulus
of their bulk phase should be larger.
Ueberreiter suggested to treat the rubber state of polymers as a liquid containing
crosslinking structures, as illustrated in Fig.6.5(Ueberreiter 1943 ). This idea
implies that the rubber-fluid transition of linear polymers might be an extrapolation
of glass transition temperatures from small molecules, both originated from inter-
molecular interactions, although the entanglement effect is an intermolecular inter-
action unique to long-chain polymers. Meanwhile, the glass-rubber transition
temperatures of linear polymers are not so sensitive to the molar mass, implying
its origin from intramolecular interactions. Therefore, this analogue might shade
light to the molecular nature of glass transition of polymers. The rubber-glass
transition of polymers involves the restrictions of chain mobility from both the
intramolecular semi-flexibility and the intermolecular interactions, with the length
scale much smaller than the chain entanglement, thus it happens in the temperature
region much lower than the rubber-fluid transition temperatures.
6.2 Relaxation of Polymer Deformation
6.2.1 Relaxation Via Molecular Motions
Large-scale deformation of polymers is realized by the integration of monomer
motions that is driven by the external forces. After the external force has been
removed, part of the deformation recovers quickly, while the rest may remain
Fig. 6.5 Illustration of
structured liquid proposed by
Ueberreiter, reflecting two
kinds of glass transitions
separately for small
molecules and for polymers
6.2 Relaxation of Polymer Deformation 97