Effect of the Solid Phase on the Global Phase Diagram of Lennard-Jones Mixtures

1. Effect of the Solid Phase on the Global Phase Diagram of Lennard-Jones Mixtures Brian C. Attwood and Carol K. Hall Department of Chemical Engineering North Carolina State University Raleigh, NC http://turbo.che.ncsu.edu

2. Objectives • Calculate the “complete” phase behavior of Lennard-Jones systems at a number of points in the global phase diagram • Evaluate how including the solid phase affects the expected phase behavior

3. What is a global phase diagram? • Idea originally introduced by van Konynenburg and Scott for the van der Waals EOS for binary mixtures • Divides parameter space into regions of like phase behavior • Has been calculated for many different EOS, e.g. van der Waals, Redlich-Kwong, Lennard-Jones, etc. • Considers only fluid phases

4. Calculated by Mazur, et al: binary mixtures of equal diameter atoms using polynomial fit of Ree as EOS Interaction Parameters Global Phase Diagram for L-J Mixtures

5. Gibbs-Duhem Integration Kofke, 1993 • Integrate an appropriate form of the Clapeyron equation, which for binary mixtures is: where, • Use semigrand canonical simulation to evaluate the enthalpy and composition of the coexisting phases

6. Gibbs-Duhem Integration Procedure • Require a coexistence point to start the integration • For binary systems, the integrand at x2=0 or 1 can be related to the Henry’s constant • To find liquid-liquid immiscibility requires another approach

7. P2>P1 T x Finding L-L Immiscibility P1 Two approaches: • Calculate a T-x diagram at pressure for which VLL equilibria will occur integrate at constant T to the desired pressure • Find the intersection of the L-L immiscibility with the S-L coexistence envelope T x

8. P2 Finding L-L Immiscibility Two approaches: • Calculate a T-x diagram at pressure for which VLL equilibria will occur integrate at constant T to the desired pressure • Find the intersection of the L-L immiscibility with the S-L coexistence envelope T x

9. Results - Type I ( = 0.2,  = -0.1) For Type I phase behavior, inclusion of solid phase makes V-S equilibria possible above the triple point of either component

10. Type II-A (  = 0.0,  = 0.2) At low pressure, L-L immiscibility is masked and a vapor-solid eutectic is formed

11. Type III ( = 0.4,  = 0.3) L-L immiscibility at low T is replaced by V-S, L-S, and S-S phase equilibria

12. Type V ( = 0.6,  = -0.1) The LCST for L-L immiscibility appears to be obscured for all values of pressure up to P=0.50

13. Summary • Developed a method for using Gibbs-Duhem integration for locating low T liquid-liquid equilibrium • For mixtures in which the two components have similar critical temperatures the solid phase does not greatly alter the phase behavior • For mixtures in which the two components have greatly dissimilar critical temperatures the solid phase can significantly alter the phase behavior

14. Acknowledgments • Dr. Monica Lamm, University of Michigan • Department of Energy • American Chemical Society, Petroleum Research Fund