The equation of state of polymers. Part III: Relation with the compensation law

Jacques Rault

doi:10.1140/epje/i2017-11565-9

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2024 Impact factor 2.2

Soft Matter and Biological Physics

Eur. Phys. J. E (2017) 40: 82
https://doi.org/10.1140/epje/i2017-11565-9

Regular Article

The equation of state of polymers. Part III: Relation with the compensation law

Jacques Rault^*

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

^* e-mail: jacques.rault@yahoo.fr

Received: 14 April 2017
Accepted: 21 August 2017
Published online: 29 September 2017

Abstract

The properties of amorphous polymers and of organic compounds under pressure are interpreted in the framework of the modified Van der Walls Equation of State (mVW-EOS) the Vogel-Fulcher-Tamann (VFT) law and of the compensation law. We have shown recently that polymers and organic compounds in amorphous liquid and crystalline states verify the mVW-EOS which depends on three parameters, $P^{\ast}$ $V^{\ast}$ and $T^{\ast}$ . In this paper we compare the characteristic pressure $P^{\ast}$ of the mVW-EOS to the various pressures $P_{X}= \Delta H_{X}/\Delta V_{X}$ deduced from thermodynamic and kinetic properties of polymers in the liquid and solid states. $\Delta H_{X}$ and $\Delta V_{X}$ are: a) the enthalpy and volume change at the melting and glass transitions (the glass being isotropic or oriented and annealed below $T_{g}$ at various aging conditions); b) the activation parameters of individual $\beta$ and cooperative $\alpha$ motions in crystalline liquid and amorphous polymers studied by dielectric or mechanical spectroscopy; and c) the activation parameters of amorphous (solid and liquid) polymers submitted to a deformation depending on the time frequency temperature and strain rate. For a same material, whatever its state and whatever the experimental properties analyzed (dielectric and mechanical relaxation, viscosity, auto-diffusion, yielding under hydrostatic pressure), we demonstrate that $P_{X}=P^{\ast}=1/\gamma\kappa$ , ( $\gamma$ Grüneisen parameter, $\kappa$ compressibility). In all polymers and organic compounds (and water), these pressures, weakly dependent on T and P near $T_{g}$ and $T_{m}$ at low pressure are characteristic of the H-H inter-molecular interactions. It is shown that the two empirical Lawson and Keyes relations of the compensation law can be deduced from the mVW-EOS.