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

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.

Graphical abstract