(335k) V.L.E. Of Ethanol And Ethanediol From Molecular Dynamics Simulations And Voronoi Tessellations

Two-phase Molecular Dynamics (MD) simulations were performed to determine the vapor-liquid equilibrium of ethanol and ethanediol. Simulations were performed in the canonical (NVT) ensemble using the OPLS-AA potential¹, the electrostatics contributions to the force and energy were calculated by reaction field², and the simulations were performed using two time scale rRESPA.

In order to simulate a two-phase system by MD, we chose to put a slab of vapor in contact with a slab of liquid and then allow it to equilibrate. The box geometry was controlled to insure that the liquid droplet was larger than twice the cut-off for the interaction potentials and there were enough vapor molecules to obtain good statistics. To insure the equilibration of the two phases, the difference in the normal and tangential components of the pressure profile was used as a test³.  

 The densities for the system were determined by using our VorMd method⁴ that utilizes Voronoi Tessellations to determine the volume of every molecule (or atom) in the simulation cell. The molecular (or atomic) volumes are then used along with statistical parameters such as the mean and variance to determine the average liquid and average vapor densities in conjunction with single phase simulations. When the normalized variances of the molecular volume from the two-phase simulation matches the normalized variances from the single-phase liquid and vapor simulations then the average density on the two-phase envelope is known. 

The determination of the phase densities by VorMd eliminates all arbitrary parameters to determine the phases from a MD simulation. Furthermore, the VorMd method allows one to determine at any instant in time what molecules are in the vapor and liquid phases which can be seen in Figure 1. In Figure 1, ethanol is shown at a temperature of 425 K. The green molecules are the one designated as liquid, the vapor molecules are red, and finally the molecules that are neither vapor nor liquid (ie. interface) are blue.

Figure 1: Final configuration for ethanol at 425 K. Red molecules are vapor, green molecules are liquid, and blue molecules are interface.

The resulting two-phase envelope for ethanol can be seen in Figure 2. The triangles are results for the OPLS-AA potential generated by Gibbs Ensemble Monte Carlo (GEMC) by Marcus G. Martin at Sandia National Laboratories⁵. The solid line is the fit of experimental data by Dillion and Penoncello⁶, and finally the squares represent this work. As can be seen from the figure, there is excellent agreement with the data from GEMC. One advantage of the VorMD method over GEMC is that it is able to generate points on the phase diagram arbitrarily close to the critical point, allowing one to study near sub-critical phenomena.  The discrepancy between either of the two simulation methods and the experimental phase diagram is attributed to limitations in the interaction potential.  Other results shown are surface tension, molecule orientation at the interface, and the vapor pressure. In addition to these properties, the effect of potential cut-off is briefly investigated.   

Figure 2: Two-phase envelope for ethanol using the VorMd method (orange squares) as compared to published GEMC values⁵ (yellow triangles), and a fit of experimental data ⁶ (line).

In conclusion, the VorMd method has been extended to poly-atomic systems. Results have been shown for the two-phase envelope, surface tension, molecule orientation at the interface, and the vapor pressure for both ethanol and ethanediol. There is good agreement between the ethanol results from this work and the published GEMC results.  Implementation of the VorMd method is also discussed.

Acknowledgements

The authors gratefully acknowledge the financial support of the Office of Fossil Energy of the U.S. Department of Energy (DOE). Through the UT Computational Science Initiative, this research project used resources of the Center for Computational Sciences at Oak Ridge National Laboratory, which is supported by the Office of Science of the DOE under Contract DE-AC05-00OR22725.

References

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