Comments on “Analytic Equation of State for Solid–Liquid–Vapor Phases” (Int. J. Thermophys. 24, 589 (2003))

Abstract

Among the thermodynamic models applicable to solid-liquid-vapor phases, Yokozeki's model is considered as the first repulsion-based analytic equation of state (EOS) in which a discontinuity is introduced in the isotherm. However, it was found that the model violates some physical constraints due to the empirically introduced discontinuity. This work focuses on the evaluation of the empirical basis of the model through scaled-particle theory (SPT) and a modification of the model to satisfy the physical constraint.Keywords Equation of state · Fluid-solid transition · Hard-sphere fluids · Insertion probability Yokozeki [1] presented seven empirically known facts that a unified equation of state (EOS) for solid-vapor-liquid phases should satisfy, and two of them form the basis of the proposed model: (1) the developed EOS should avoid a solid-fluid critical transition and (2) a negative-pressure region is allowed to describe the stability of the solid phase and model the solid-fluid transition via the Maxwell equal-area rule. It is not clear in the author's first paper [1] that the latter requirement holds for the case where the attraction does not exist. However, considering the author's subsequent works [2,3], the latter requirement is expected to hold for the fluids without attractive forces. To satisfy these requirements, Yokozeki considered that "the solid-phase branch in an EOS must be analytically discontinuous at solid-fluid transitions" and modified the repulsive part of the Van der Waals EOS to have two volume limits as follows:

Development of Single Insertion Probability for Equation of State Applicable to Three Phases of Matter

“…This implies that a discontinuity is merely sufficient but not necessary to avoid a critical point. Moreover, the EOS proposed by Yokozeki was found to violate physical constraints in the framework of insertion probability due to empirically introduced discontinuity …”

“…Although this EOS poses a discontinuity, the resulting Helmholtz energy has finite value except φ = a , yielding finite chemical potential …”

Identification of the phase of a substance from the derivatives of pressure, volume and temperature, without prior knowledge of saturation properties: Extension to solid phase

“…Multiple volume roots need to be determined at any given pressure and temperature in this approach. These equations also suffer from other deficiencies that have been highlighted by Lee and Yoo [19]. 3.…”

A Modified Solid–Liquid–Gas Phase Equation of State

“…Yokozeki 12 introduced the discontinuity of the solid–liquid transition in the isothermal p–V phase diagram of pure substances, avoiding the solid–liquid critical point, and proposed an analytic equation of state (SLV-EOS) considering the three solid–liquid–gas phases. Lee 13 pointed out that Yokozeki’s equation modified the repulsive part of the EOS so that it had two singularities, one for the upper limit of the fluid region and the other for that of the solid region. This approach produces a discontinuous isotherm, implying a discontinuous variation of the phase transition and a repulsive term p HC less than zero during the solid–liquid phase transition.…”