Viscosity in amorphous polymers
An amorphous polymer in the solid state is hard and brittle. Under an applied heat the polymer will first transform to a soft leathery state before forming into a viscous liquid.
The transition from the solid state to the soft leathery state occurs at the Glass Transition Temperature, Tg, of the polymer. However, there is no sharp transition in viscosity at this temperature.
All polymers with some level of an amorphous phase exhibit a Tg.
After Engineering Materials: Properties and Selection, K. G. Budinski, 8th Edition, Pearson Education International.
Specific volume in amorphous polymers
An amorphous polymer never melts in the way that a semi-crystalline polymer does. Instead it becomes progressively less viscous (more runny) as it is heated above Tg.
When an amorphous polymer cools from its liquid state, it slowly contracts based on the coefficient of thermal expansion. The viscosity increases at a constant proportional rate.
Below Tg the rate of contraction falls below the rate that the viscosity increases due to structural rearrangement of the molecular chains into the glassy amorphous state.
After Engineering Materials: Properties and Selection, K. G. Budinski, 8th Edition, Pearson Education International.