Partial molar properties from molecular simulation using multiple linear regression

Abstract

Partial molar volumes, energies, and enthalpies can be computed from NpT-Gibbs ensemble simulations through a post-processing procedure that leverages fluctuations in composition, total volume, and total energy of a simulation box. By recording the instantaneous box volumes V and instantaneous number of molecules $N_i$ of each of n species for M frames, a large $M\times n$ matrix $\mathbf{N}$ is constructed, as well as the $M\times 1$ vector $\mathbf{V}$. The $1\times n$ vector of partial molar volumes $\overline{\mathbf{V}}$ may then be solved using $\mathbf{N}\cdot \overline{\mathbf{V}}=\mathbf{V}$. A similar construction permits calculation of partial molar energies using M instantaneous measurements of the total energy of the simulation box, and $\mathbf{N}\cdot \overline{\mathbf{U}}=\mathbf{U}$. Partial molar enthalpies may be derived from $\overline{\mathbf{U}}$, $\overline{\mathbf{V}}$, and pressure p. These properties may be used to calculate enthalpy and entropy of transfer (absorption, extraction, and adsorption) for species in complex mixtures. The method is demonstrated on three systems in the NpT-Gibbs ensemble: a highly compressible natural gas condensate of methane, n-butane, and n-decane, the liquid-phase adsorption of 1,5-pentanediol and ethanol onto the MFI zeolite, and a relatively incompressible mixture of ethanol, n-dodecane, and water at liquid-liquid equilibrium. Property predictions are compared to those from numerical differentiation of simulation data sequentially changing the composition and from equations of state. The method can also be extended to reaction equilibria in a closed system and is applied to a reactive first-principles Monte Carlo simulation of compressed nitrogen/oxygen.

GRAPHICAL ABSTRACT

Keywords:

• Monte Carlo simulation
• thermodynamics
• phase equilibria
• reaction equilibria

Acknowledgements

A portion of the computer resources were provided by the Minnesota Supercomputing Institute at the University of Minnesota. The University of Minnesota Disability Resource Center also supported this work through providing access assistants to MSM. We thank Yangzesheng Sun for helpful conversations about correlations.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Tyler R. Josephson http://orcid.org/0000-0002-0100-0227

Ramanish Singh http://orcid.org/0000-0002-7908-060X

Mona S. Minkara http://orcid.org/0000-0003-1821-2725

Evgenii Fetisov  http://orcid.org/0000-0002-2889-9850

J. Ilja Siepmann http://orcid.org/0000-0003-2534-4507

Additional information

Funding

This research was primarily supported by the U.S. Department of Energy (DOE), Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences under Award DE-FG02-17ER16362 (development and testing of the MLR approach and simulations of adsorption equilibria). This research was also supported by the Abu Dhabi Petroleum Institute Research Center, Project Code LTR14009 (simulations of ethanol/n-dodecane/water and natural gas mixtures). Simulations of reactive equilibria of compressed NO were supported by the National Science Foundation (CHE-1265849) and used resources of the Argonne Leadership Computing Facility (Argonne National Laboratory), which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357.