Amorphous polymers exhibit two distinctly different types of mechanical behavior. Some, like polymethyl methacrylate and polystyrene are hard, rigid, glassy plastics at room temperature while others like polybutadiene and polyethyl acrylate are soft, flexible, rubbery materials at room temperature.

There is a temperature, or range of temperatures, below which an amorphous polymer is in a glassy state and above which it is rubbery. This temperature is called the glass transition temperature, Tg, and it characterizes the amorphous phase. It is especially useful since all polymers are amorphous to some degree, they all have a Tg.

Molecular Motions in Amorphous Polymers

The molecular motions occuring inside an amorphous polymer influence the glass transition temperature. The important motions are:

1. Translation motion of entire molecules (permits flow)
2. Cooperative wriggling and jumping of segments of molecules
   (permits flexing and uncoiling leading to elasticity)
3. Motions of a few atoms along the main chain or side groups on the main chain
4. Vibrations of atoms about equilibrium position

The glass transition temperature is the temperature at which there is only enough energy for motions (3) and (4) to occur. Below the glass transition temperature processes (1) and (2) are frozen out. This makes the the material is "glassy" below Tg and "rubbery" above Tg.

Factors Influencing Glass Transition Temperature

In general the glass transition temperature depends on five other factors which are:

1. Free volume of the polymer vf, which is the volume of the polymer mass not actually occupied by the molecules themselves. The higher vf is the more room the molecules have to move around and the lower Tg is. For all polymers the ratio of the free volume vs the total volume (vf/v) is about 0.025 at Tg.
2. The attractive forces between the molecules. The more strongly the molecules are bound together , the more thermal energy must be applied to produce motion.
3. The internal mobility of the chains, or their freedom to rotate about the bonds.
4. The stiffness of the chains. Stiff chains cannot easily coil and fold, causing Tg to be higher for polymers with stiff chains. Polymers with parallel bonds in the backbone, like polyimides, and polymers with highly aromatic backbones have extremely stiff chains and thus high Tg's.
5. The chain length. The glass transition temperature varies according to the relation:
   Tg = Tinf - C/x
   where C is a polymer specific constant, Tinf is the asymptotic value of the glass transition temperature for a chain of length infinity and x is the length of the chain. This relationship shows that shorter chains can move easier than longer chains. For most commercial polymers Tg ~ Tinf, since x is quite long.

Determination of the Glass Transition Temperature

The most common method used to determine Tg is to observe the variation of a thermodynamic property with T. Tg determined in this manner will vary somewhat depending on the rate of cooling or heating, which reflects the fact that long entangled polymer chains cannot repsond instantaneously to changes in temperature.

At the glass transition temperature a thermodynamic property will exhibit a discontinuity with termperature, thus it is classified as a second order thermodynamic transition.