Polymer Physics

All those theories above consider the homogeneous freezing process of glass
transition in the liquid. In fact, fluctuations generate nano-scale heterogeneity in the
dynamic distribution of molecules, which contains the fast-moving liquid phase and
the slow-moving solid phase. There might be a critical temperature for the equiva-
lence in free energy between the solid phase and the liquid phase. Below this
temperature, there occurs first-order liquid–solid phase transition; while above
this temperature, there exists the inhomogeneous fluctuation. With the decrease
of temperature, the solid phase generated by dynamic fluctuations becomes large
enough to resist the load of the external stress and could not relax down in time,
then comes the glass transition (Fischer et al. 2002 ; Tanaka et al. 2010 ).

6.3.3 Chemical-Structure Dependence of Glass Transition

The factors of chemical structures that are related to polymer glass transition
behaviors can be classified into two categories, separately corresponding to the
intrinsic and extrinsic levels described in Chap. 2.
The first category is the dominant factor for the glass transition temperatures:

1. When polymer chains are more rigid, the values ofTgare higher;


2. When inter-chain interactions are stronger, the values ofTgare higher.

So far, how to make a feasible and unified interpretation to the structural
dependence of glass transition temperatures above is still a big challenge.
The second category contains the subsidiary factor for the glass transition
temperatures:

1. Molecular weight. In the high molar mass region, the glass transition appears
   insensitive to the molecular weight of polymers, as illustrated in Fig.6.3. In the
   low molar mass region, the chain ends contain high mobility; then there are the
   excess free volumey. According to the equivalence phenomenon of free volume,
   one obtains

af½Tgð1ÞTgŠ¼

2 ryNa

MN

(6.70)

whereNais the Avogadro constant,ris the density,MNis the number-average
molecular weight. Therefore,

Tg¼Tgð1Þ

K

MN

(6.71)

whereKis a polymer-specific constant. This equation is known as Flory-Fox
equation (Fox and Flory 1950 ).

116 6 Polymer Deformation