Equilibrium state, amorphous solids, glass transition

In 1931 Simon reported that small molecules in their amorphous solid state are not in thermodynamic equilibrium at temperatures below their glass transition u. Such materials are in fact supercooled liquids whose volume, enthalpy, and entropy are greater than they would be in the equilibrium glass. (See Fig. 1). 

The tables in Chapter 6 provide speeifie volumes neither at or below the melting transition of semieiystalline materials nor at or below the glass transition of amorphous samples, since PVT data of solid polymer samples are non-equihbrium data and depend on sample history and experimental procedure (which will not be diseussed here). Therefore, only equilibrium data for the liquid/molten state are tabulated. Their common accuracy (standard deviation) is about 0.001 cm /g in specific volume, 0.1 K in temperature and 0.005 P in pressure (1995ZOL). 

Some transitions that are only known for macromolecules, however, will not be mentioned at all since they are covered elsewhere in this Encyclopedia (see, eg. Gel Point). Also we shall not be concerned here with the transformations from the molten state to the solid state of polymeric materials, since this is the subject of separate treatments (see Crystallization Kinetics Glass Transition Viscoelasticity). Unlike other materials, polymers in the solid state rarely reach full thermal equilibrium. Of course, all amorphous materials can be considered as frozen fluids (see Glass Transition) Rather perfect crystals exist for metals, oxides, semiconductors etc, whereas polymers typically are semicrystalline, where amorphous regions alternate with crystalline lamellae, and the detailed structure and properties are history-dependent (see Semicrystalline Polymers). Such out-of-equilibrium aspects are out of the scope of the present article, which rather emphasizes general facts of the statistical thermodynamics (qv) of phase transitions and their applications to polymers in fluid phases. 

Polyterephthalates. The molecular motion and their connection to the thermal parameters for the three most common members of the homologous series of polyterephthalates is summarized in Fig. 6.40. The number of vibrations and the derived 0-temperatures allows the calculation of a vibrational heat capacity of the solid state, as outlined in Sect. 2.3.7. The changes within the 0-temperatures are practically within the error hmit. The specific heat capacities of the polyterephthalates are, as a result, also almost the same. The transition parameters are extrapolated to the equilibrium crystals and the fuUy amorphous glasses. Their values show regular changes with chemical stracture. All thermal properties are next related to the vibrational baselines computed from the parameters of Fig. 6.40. 

---