physical meanings: one is the potential energy differenceDebetweentransand
gaucheconformations, and the other is the potential energy barrierDEfor the
transition from thetranstogaucheconformations. The thermodynamic equilibrium
based on the energy potentialDedefinesthe static flexibilityof polymer chains. We
know that the thermodynamic distributions in three conformation states are related
to the capability of local thermal fluctuations, which is at the energy level of 1kT.
WhenkT>>De, the statest,g+,g-will occur with almost the same probabilities,
and polymer chains will exhibit random coils with a high flexibility. WhenkT<<
De, thetransconformation will be dominant, and polymer chains will exhibit the
fully extended conformation with a high rigidity. The extended chains mainly exist
in the ordered states, so the static semi-flexibility facilitates the ordering of polymer
chains. On the other hand, the transition kinetics based on the activation energyDE
definesthe dynamic flexibilityof polymer chains. WhenkT>>DE, it is easy for
polymer chains to change their conformation, so they are in the fluid state. When
kT<<DE, polymer chains are unable to change their conformation, so they are in
the solid state, either in the glass states or in the crystalline state. Therefore, the
chain semi-flexibility provides an intra-molecular source of the activation energy to
the glass transition of polymers.
For a flexible polymer chain, if the internal rotation of each bond along the
backbone chain has three possible rotational isomerism states, 1,000 such bonds on
one chain imply that the random coil could have as many as 31,000 10477 ways to
arrange all the micro-conformations. Although compared to the real polymer chain
this chain is not very long, we could not count out one-by-one the astronomical
figures of conformations. Therefore, if we want to learn the conformational
properties and their variation laws, we have to employ the statistical method
introduced in the next chapter.
In practice, not all the combinations of three representative internal rotation
states can be accepted along the real polymer chain. For polyethylene chains, there
exists the so-called “pentane effect” (Flory 1993 ). We know that the summation of
two van der Waals radii of carbon atoms is 3.0 A ̊. Two consecutivegauche
conformations,g+g+org-g-, bring the end-to-end distance of the pentane segment
to 3.6 A ̊. Thus, these two chain ends interleave with each other, which can be
acceptable. However, the conformationg+g-org-g+bring the end distance to 2.5 A ̊,
Fig. 2.3 (a) Illustration of the overlapping,gaucheandtranspositions of polyethylene. (b) The
potential energy curve of the internal rotation of polyethylene
2.2 Semi-Flexibility of Polymer Chains 19