Hole, heat capacity theory

Also plotted in Fig. 1.2 is the experimental heat capacity of the liquid (at omi-stant pressure) In simple cases, such as polyethylene, the heat capacity of the liquid state could be understood by introducing a heat capacity contribution for the excess volume (hole theory) and by assuming that the torsional skeletal vibration can be treated as a hindered rotator A more general treatment makes use of a separation of the partition function into the vibrational part (approximated for heat capacity by the spectrum of the solid), a conformational part (approximated by the usual conformational statistics) and an external or configurational part. 

The simplest model to represent the glass transition is based on the hole theory which was developed by Frenkel and Eyring some 60 years ago and is described in more detail in Sect. 6.1.3 (see also Sect. 4.4.6). The equilibrium number of holes at T is N and each contributes an energy e, to the enthalpy. As given on Fig. 6.5, the hole contribution to the vibrational heat capacity Cp and its kinetics is represented by ... 

The kinetic theory defines Tg as the temperature at which the relaxation time for the segmental motions in the main polymer chain is of the same order of magnitude as the time scale of the experiment. The kinetic theory is concerned with the rate of approach to equilibrium of the system, taking the respective motions of the holes and molecules into account. The kinetic theory provides quantitative information about the heat capacities below and above the glass transition temperature and explains the 6 to 7°C shift in the glass transition per decade of time scale of the experiment. 

The glass transitions were detected between 249 to 261° K. No time dependent studies of the glass transition have been made. The magnitude of the heat capacity jump was found in good agreement with the hole theory as predicted by Wunderlich (1960) assuming 2 beads per... 

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