The modified van der Waals equation of state

Abstract

PVT data of crystallizable materials (CM), minerals, alkali, alkali halides, metals, mineral oxides and hydroxides, rare gas, water, organic compounds and polymers, published in the literature are reanalyzed. It is shown that all these materials under pressure verify the modified van der Waals equation of state (mVW-EOS), discussed recently [J. Rault, Eur. Phys. J. E 40, 82 (2017)]. The characteristic parameters P*V* of this EOS depend only on the nature of the material and not on its state (liquid, glassy, solid of different structure) and whatever are its conductivity and magnetic properties (insulator, conductor, superconductor, paramagnetic, ferromagnetic). This EOS explains the following properties: (a) the fan structure of the isobars V(T), and of the tangents to the isotherms V(P); (b) the superposition principle of the isotherms V(P); (c) the αB rule: the constancy of the thermal pressure coefficient (dP/dT)V = αB, product of the thermal expansion coefficient α and the bulk modulus B; (d) its relation with the Slater conjecture: (dP/dT)V ~ dP/dTm in crystallized materials, Tm being the melting temperature. The characteristic pressure P* (T and V independent) is compared with the various pressures: (i) Pcoh = Ecoh/V, the cohesive energy density; (ii) PLm = Lm/ΔVm, Lm and ΔVm being the enthalpy and volume jumps at the melting, respectively; (iii) PD = ΔHa/DVa, ratio of the activation parameters of the autodiffusion coefficient; (iv) PX = X∕X′, X being the bulk modulus B, shear modulus G, elastic constants Cij, and the yield stress σy of the CM, X′ their pressure derivative (at ambient conditions). All the elastic constants B, G, Cij and the yield stress σy are linear functions of P at low pressure (P < P*) and extrapolate to zero at the same negative pressure − PX = −P*. (e) PBγ = B∕γ* ratio of the bulk modulus B and Gruneisen parameter γ* at zero pressure. (f) PΔVm is the pressure deduced from the linear relation between the volume jump ΔVm(P) at the transition (melting or crystalline transition) and the pressure. The universal relation P* = Pcoh = PLm = PD = PB = PG = PCij = Pσy = PΔVm is observed and discussed. In molecular compounds such as H2O, H2, and polymers with different intra- and intermolecular interactions, the compression involves two different processes, at low and high pressures, verifying the mVW-EOS with characteristic pressures P1* and P2*. The ratio of these pressures is about the ratio of the weak intermolecular and strong intramolecular bond energies. The generalized modified equation of state (gmVW-EOS) describes the two-step process of compression in materials having two (or several) types of bonds.