Detection of Solid-Liquid Retrograde Melting From Computing Solid-Fluid-Fluid Equilibrium Lines

S. B. RODRIGUEZ-REARTES; M. CISMONDI; M. S. ZABALOY

San Petersburgo

Simposio; 25rd European Symposium on Applied Thermodynamics; 2011

St.Petersburg State Univ., Russian Acad. Sci., the Mendeleev Russian Chem. Soc.

The occurrence of a temperature minimum, in the pressure-temperature (P-T) plane, for a solid-liquid phase boundary corresponding to a constant composition mixture (isopleth), is recognized as the phenomenon of solid-liquid retrograde melting [1]. According to Gregorowicz [1], the negative slope of the solid-liquid line emerging from the solid-fluid-fluid (SFF) equilibrium curve is the necessary condition for the retrograde phenomena to occur. Therefore, if a model for describing fluid-fluid and solid-fluid equilibria is available, and the model parameters are set equal to specific values, the possible occurrence of solid-liquid retrograde melting, within the universe of the model, should be established by computing the (P vs. T) slope of the solid-liquid isopleths emerging from the SFF curves given by the model. In this work, we propose an effective way for doing that, for the case of binary asymmetric systems. First, we compute, through a numerical continuation method (NCM), all the three-phase SFF equilibrium curves given by the model for a specific binary system. Next, for a given (already computed) three-phase SFF point, we use the information on the solid phase and on the liquid phase to obtain the Jacobian matrix corresponding to the system of equations that describes the two-phase solid-liquid isopleth with liquid composition equal to the liquid composition of the selected SFF point. From the Jacobian matrix, we compute a sensitivity vector. One of the components of such vector is the (P vs. T) slope of the two-phase solid-liquid isopleth at the point where the isopleth meets the threephase SFF point. We repeat this procedure for all points of the computed SFF lines. The final result is a set of 2D plots which make possible to establish at a glance whether the model gives retrograde melting, at the specific parameter values previously set. When retrograde melting does exist for model, the 2D plots show the ranges of conditions of occurrence of such phenomena. We present results for SFF curves of varying shapes. Thanks to the use of a NCM, we can generate all the information required to build the 2D plots in a single run, for a given SFF curve. We also present in this work some calculated isopleths which we have obtained using an isopleth-specific NCM different from the SFF-specific NCM. For such calculated isopleths we show both, the stable and unstable parts. This makes possible to gain a deeper understanding of the retrograde melting phenomena. In the present exploratory work, we used the Peng-Robinson equation of state (EOS) for representing the properties of the fluid phases. Because of the highly asymmetric nature of the binary systems that we have considered in this work, the model assumes the solid phase as made of the pure heavy component. We used a standard equation for describing the fugacity of the pure heavy component, as a function of temperature and pressure. The present model has proven to be realistic in our previous work related to the description solid-fluid equilibria over wide ranges of conditions.