A universal modified van der Waals equation of state. Part I: Polymer and mineral glass formers

摘要

PVT data of glass formers (minerals and polymers) published in the literature are re-analyzed. All the polymer glass formers (PS, PVAc, PVME, PMMA, POMS, PBMA, PVC, PE, PP, PMPS, PMTS, PPG) present two main properties which have never been noted: a) the isobars P(V) have a fan structure characterized by the two parameters T-* and V-*; b) the isotherms verify the principle of temperature-pressure superposition for P < P (*). From these properties we show that the Equation Of State (EOS) can be put on a modified van der Waals form (VW-EOS), (V - V (*)) = (V0 - V (*))P (*)/(P + P (*)) . The characteristic pressure P-* and the covolume V-* are T and P independent. In polymer glass formers P-* and V-* have same values in the alpha (melt) and beta (glass) domains. The characteristic temperatures T (*) deduced from the Fan Structure of the Isobar (FSIb) above and below T (g) are different. The characteristic temperature T (*)(alpha) of the melt state is found near the Vogel temperature T (0) for linear polymers and more than 100 K below T (0) for atactic polymers (with pendent groups). This difference in atactic polymers (and in some low molecular weight compounds) is explained by the importance of the beta motions due to the pendent groups. The independence of T (0) on P is discussed. A modified VFT equation (analogous to the compensation law and Meyer-Neldel rule) giving the relaxation time tau of the alpha motions as a function of P and T is proposed. The fan structure of the isotherm log tau versus P is explained. It is shown that organic non-polymeric liquids (C6H12, C6H14, DHIQ, OTP, Glycerol, Salol, PDE, DGEBA), mineral glass (SiO2, Se, GeSe4, GeSe2, GeO2, As2O3 and two metallic glasses (LaCe and CaAl alloys) verify this VW-EOS with similar accuracy. The relation P (*) = B (0)/gamma (B) among the characteristic pressure P (*), the zero-pressure modulus B (0) and the Slatter-Gruneisen anharmonicity parameter gamma (B) deduced from the VW-EOS, is observed in all the glass formers.