Nature of the Glass Transition and the Glassy State

The thermodynamic properties of amorphous phases of linear molecular chains are obtained from statistical mechanics by means of a form of the quasi-lattice theory which allows for chain stiffness and the variation of volume with temperature. A second-order transition is predicted for these systems. This second-order transition has all the qualitative features of the glass transition observed experimentally. It occurs at a temperature which is an increasing function of both chain stiffness and chain length and a decreasing function of free volume. The molecular ``relaxation times'' are shown to increase rapidly as the second-order transition temperature is approached from above. To permit quantitative application of the theory and determine the relationship between the second-order transition and the glass transition observed in ``slow'' experiments these two transitions are tentatively identified. By this means quantitative predictions are made concerning the variations of (1) glass temperature with molecular weight, (2) volume with temperature, (3) volume with molecular weight, (4) volume at the glass temperature with the glass temperature for various molecular weights of the same polymer, (5) specific heat vs temperature, and (6) glass temperature with mole fraction of low-molecular weight solvent, since extensive experimental results are available for these properties. These and other theoretical predictions are found to be in excellent agreement with the experimental results.