Eur. Phys. J. E (2014) 37: 113
https://doi.org/10.1140/epje/i2014-14113-3

Regular Article

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

Laboratoire de Physique des Solides, Université de Paris-Sud, 91405, Orsay, France

^* e-mail: rault@lps.u-psud.fr

Received: 11 February 2014
Revised: 6 June 2014
Accepted: 17 September 2014
Published online: 20 November 2014

Abstract

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 α (melt) and β (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 ^*(α) 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 β 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 τ of the α motions as a function of P and T is proposed. The fan structure of the isotherm logτ 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/γ _B among the characteristic pressure P ^*, the zero-pressure modulus B ₀ and the Slatter-Grüneisen anharmonicity parameter γ _B deduced from the VW-EOS, is observed in all the glass formers.