| Abstract: | A crystalline-state theory recently developed by Midha and Nanda is commented on and applied to the isobars of polyethylene, poly(vinylidene fluoride), and poly(chlorotrifluoroethylene) at atmospheric pressure, and to an isotherm of polyethylene. Satisfactory agreement with experiment results. This includes the volume change at the melting point Tm and the volume difference ΔV between crystal and melt below Tm, when crystal and the earlier liquid-state theory are combined. A similar agreement is noted with respect to the results at high pressure. The scaling parameters obtained indicate the approximate role of melt temperature and volume as reducing quantities. An inverse proportionality between Tm and αl, the expansivity of the melt at Tm, derived much earlier for low-molecular-weight solids, is recovered with an identical numerical coefficient. The thermodynamic functions of polyethylene are investigated in both phases. For this purpose contributions of internal harmonic modes are considered within the framework of the equivalent s-mer model. One or, at most, two average frequencies are adequate to represent the temperature dependence of the excess free energy and entropy over the value at absolute zero, when the external contributions are included for the crystal. A similar representation of the hard modes can be adopted for the melt. However, the free energy of segmental disorientation computed either from a constant entropy for the s-mer or a rotational isomeric state model for the isolated chain does not appear to be an adequate representation over a sufficient temperature range. An additional temperature-dependent term in the entropy and free energy is introduced and tentatively attributed to a volume- and temperature-dependent short-range ordering. Good agreement with experiment, including the entropy and temperature of fusion, ensues. |
