Molecular Simulation of the Phase Transitions

               

Principal Investigator

Richard Sadus

School of Information Technology,

Swinburne University of Technology

The aim of this work is to use molecular simulation techniques to investigate the affect of intermolecular
interactions on the phase transitions of pure fluids and fluid mixtures.
The phase behaviour of fluids is influenced profoundly by molecular interactions. This is evident qualitatively by the different types of phase transitions exhibited by molecules of different physical and chemical properties. A good example of the link between phase equilibria and different molecular interactions is the variation of critical equilibria exhibited by binary mixtures. Binary mixtures of non-polar molecules of similar size exhibit continuous critical vapour-liquid equilibria between the critical points of the pure components. In contrast upper critical critical solution equilibria are observed between polar/non-polar combinations of molecules or molecules of contrasting size. Molecular simulation techniques provide powerful tools for relating this link exactly to intermolecular interactions. In contrast to conventional theoretical method such as equation of state calculations, the phase transitions predicted by molecular simulation are solely the outcome of the choice of intermolecular potential and the nature of multi-body interactions of the fluid. The Gibbs ensemble method and recent improvements to histogram reweighing methods allow us to investigate efficiently phase transitions via molecular simulation. Many applications of the Gibbs ensemble have been reported assuming pairwise additivity, however the affect of three- or more-body interactions has not been investigated widely.
   

Co-Investigators

     

Ya Song Wei

Dorde Plackov

School of Information Technology,

Swinburne University of Technology

     
         

Projects

g36 ­ VPP

     
         
               

     
               

What are the results to date and the future of the work?

Phase behaviour of pure fluids

The Gibbs ensemble algorithm has been implemented to determine the vapour-liquid equilibria of both pure fluids and binary mixtures. A feature of this work is the use of the Axilrod-Teller intermolecular potential to investigate the affect of three-body interaction. Three-body interactions contribute typically only five percent of the total energy of the fluid. Despite this,

               
- Appendix B

 
               

       

three-body interactions have a considerable affect on the coexisting properties of the fluid. In a pure fluid the affect of three-body interactions is to decrease substantially the density of the coexisting liquid phase. The density of the vapour phase is not affected, however, including three-body interactions improves substantially the predicted critical point (Figure 1). In contrast, two-body only calculations consistently overestimate the critical temperature and pressure.

 

Figure. 1. Comparison of the experimental (l) vapour-liquid coexistence of argon with simulations using the Lennard-Jones (®) and Lennard-Jones + Axilrod-Teller (°) intermolecular potentials. [Sadus, 1997]

Phase behaviour of binary mixtures

The affect of three-body interactions on the vapour-liquid equilibria exhibited by binary mixtures has been investigated. In contrast to pure fluids in which there is only one type of three-body interaction, four distinct types of three-body interactions are possible in binary mixtures corresponding to different triplet combinations of the two molecules. It was found that three-body interactions can have a significant influence on phase equilibria. In the case of liquid-liquid equilibria, the two-phase equilibria predicted using three-body interactions occurs over a more narrow range of both density and composition (Figure 2) compared with two-body only interactions. Three-body interactions also affect directly the transition between vapour-liquid and liquid-liquid equilibria. This is the first time that three-body interactions have been linked to the transition between vapour-liquid and liquid-liquid equilibria.

       
Appendix B -

       

     

 

Fig. 2. The temperature-composition projection at P* = 1 for binary mixtures exhibiting liquid-liquid equilibria. Results are shown for calculations using the Lennard-Jones potential (D, [16]) and the Lennard-Jones + Axilrod-Teller potential with a = 1 (°) and a = 0.5 (l). The solid lines were obtained from fitting the simulation data to the critical exponent relationships. The estimated critical point is identified (x). [Sadus, 1997]

Future work will centre on examining three-body interactions in ternary mixtures and using improved potentials for intermolecular interactions. It can be expected that three-body interactions will affect the phase behaviour of ternary mixtures significantly because there are nine distinct types of triplets when three molecules are involved. The use of improved intermolecular potentials is important for the accurate quantitative prediction of phase equilibria via molecular simulation.

What computational techniques are used?

The NPT-Gibbs ensemble was used to simulate the coexistence of two liquid phases. A total of 200 molecules were partitioned between two boxes to simulate the two coexisting liquid phases. The temperature of the entire system was held constant and surface effects were avoided by placing each box at the centre of a periodic array of identical boxes. Equilibrium was achieved

     
- Appendix B

 
     

       

by attempting molecular displacements (for internal equilibrium), volume fluctuations (for mechanical equilibrium) and particle interchanges between the boxes (for material equilibrium).

The simulations were performed in cycles with each cycle consisting of 200 attempted displacements, a single volume fluctuation, and 500 interchange attempts. The maximum molecular displacement and volume changes were adjusted to obtain, where possible, a 50% acceptance rate for the attempted move. Ensemble averages were accumulated only after the system had reached equilibrium. The equilibration period was typically 2500 cycles and a further 2500 cycles was used to accumulate the averages. The calculations were truncated at intermolecular separations greater than half the box length, and appropriate long-range corrections were used to obtain the full contribution of pair interactions to energy and pressure.

Publications

D. Plackov, and R. J. Sadus, Molecular simulation of intermolecular attraction and repulsion in coexisting liquid and vapour phases. Fluid Phase Equilibria, 1997, in press.

R. J. Sadus, Exact calculation of the effect of three-body Axilrod-Teller interactions on vapour-liquid phase coexistence. Fluid Phase Equilibria, 1997, in press.

R. J. Sadus, The effect of three-body interactions on the liquid-liquid phase coexistence of binary fluid mixtures. Fluid Phase Equilibria, 1998, in press.

R.J. Sadus, The effect of three-body interactions between dissimilar molecules on the phase behaviour of binary mixtures: the transition from vapour-liquid equilibria to type III behaviour. Industrial & Engineering Chemistry Research, 1998, in press.

       
Appendix B -