Polymer Physics

from the interfaces, rigid amorphous near the interfaces, and the crystalline) will
facilitate a better understanding to their mechanical properties.
Glass transition phenomenon depends on the methods of measurement.

1. Using dilatometer and thermal mechanical analysis (TMA), one can measure the
   volume of polymers as a function of temperature, as illustrated in Fig.6.14. The
   step change in the slopes of the volume-temperature curve, i.e., the coefficients of
   thermal expansion, determines the glass transition temperature of the polymer.

a¼

1

V

dV

dTP

j (6.49)

Below the glass transition temperature, the molecular motions are frozen.

Therefore, the corresponding volume dependence on temperature becomes less

dramatically, compared to that in the liquid state.

2. Using differential scanning calorimetry (DSC), one can measure the heat flow
   rate curve of polymer solid changing with the temperatures, as demonstrated in
   Fig.6.15a. Heating (cooling) rates are constant,

q¼

dT

dt

(6.50)

Therefore, the heat capacity

Cp¼

dH

dT

¼

dH

dt

1

q

(6.51)

The heat capacity exhibits a step change at the glass transition temperature.

Below the glass transition temperature, the motion and re-orientation of

molecules are restricted, appearing as the depression of the heat capacity.

With the decrease of heating (or cooling) rates, the glass transition temperature

decreases. This behavior reflects the dynamic nature of glass transition, because

the heating (or cooling) rates determine how much time available to relax any

Fig. 6.14 Illustration of (a) polymer volume and (b) thermal expansion coefficient as a function
of temperature, displaying the glass transition phenomenon

110 6 Polymer Deformation