Polymer Physics

Tgx¼TgðlinearÞþKxr (6.78)

or

Tgx¼TgðlinearÞþ

Kx

Mc

(6.79)

HereKxis constant, andMcis the average molecular weight of the network

chains.

5. Other external factors like heating rates, tension, pressure, frequency, etc.

6.3.4 Fluid Transition

The rubber-fluid transition is associated with the change in the global mobility of
molecules. This transition is practically important to the molding of polymer
materials, for it is a prerequisite condition of permanent deformation. In
1979–1981, Boyer suggested thatTfcorresponds to a dynamic transition called as
Tll(a liquid-liquid transition aboveTg), reflecting the frozen and de-frozen of the
whole polymer chain (Boyer 1979 , 1980 , 1981 ). From the molecular weight
dependence curve illustrated in Fig.6.3, one may see thatTf appears as an
extrapolation from glass transition temperatures of small molecules. The properties
ofTllare quite similar toTg:

1.Tllappears as general to non-crystalline polymers and their copolymers;

2. The chains are more rigid,Tllbecomes higher; the interchain interactions are
   stronger,Tllbecomes higher as well;


3. When the molecular weight is large, the molecular weight dependence of
   Tllbecomes saturated, as

T¼ð 1 : 2  0 : 05 ÞTg (6.80)

4.Tllhas the equivalent-free-volume phenomenon, as well as of viscosity;

5. When the molecular weight is not large,

Tll¼Tllð1Þ

K

MN

(6.81)

Normally, polydisperse samples display not obvious but broadened
Tlltransition;
6.Tll transition will be hindered by the crosslink of polymers or by high
crystallinity;

7. The dependence on the measuring methods, exhibiting the thermodynamic
   characters of the third-order phase transition, while the glass transition exhibits
   the thermodynamic characters of the second-order phase transition.

118 6 Polymer Deformation