No Access Submitted: 17 June 2015 Accepted: 31 August 2015 Published Online: 21 September 2015
J. Chem. Phys. 143, 114113 (2015); https://doi.org/10.1063/1.4930848
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  • 1Department of Chemistry and Chemical Theory Center, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, USA
  • 2Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
  • a)Present address: School of Molecular Sciences, Arizona State University, PO Box 871504, Tempe, Arizona 85287, USA.

    b)M. Dinpajooh and P. Bai contributed equally to this work.

    c)Author to whom correspondence should be addressed. Electronic mail:

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  • Mohammadhasan Dinpajooh
  • Peng Bai
  • Douglas A. Allan
  • J. Ilja Siepmann
Since the seminal paper by Panagiotopoulos [Mol. Phys. 61, 813 (1997)], the Gibbs ensemble Monte Carlo (GEMC) method has been the most popular particle-based simulation approach for the computation of vapor–liquid phase equilibria. However, the validity of GEMC simulations in the near-critical region has been questioned because rigorous finite-size scaling approaches cannot be applied to simulations with fluctuating volume. Valleau [Mol. Simul. 29, 627 (2003)] has argued that GEMC simulations would lead to a spurious overestimation of the critical temperature. More recently, Patel et al. [J. Chem. Phys. 134, 024101 (2011)] opined that the use of analytical tail corrections would be problematic in the near-critical region. To address these issues, we perform extensive GEMC simulations for Lennard-Jones particles in the near-critical region varying the system size, the overall system density, and the cutoff distance. For a system with N = 5500 particles, potential truncation at 8σ and analytical tail corrections, an extrapolation of GEMC simulation data at temperatures in the range from 1.27 to 1.305 yields Tc = 1.3128 ± 0.0016, ρc = 0.316 ± 0.004, and pc = 0.1274 ± 0.0013 in excellent agreement with the thermodynamic limit determined by Potoff and Panagiotopoulos [J. Chem. Phys. 109, 10914 (1998)] using grand canonical Monte Carlo simulations and finite-size scaling. Critical properties estimated using GEMC simulations with different overall system densities (0.296 ≤ ρt ≤ 0.336) agree to within the statistical uncertainties. For simulations with tail corrections, data obtained using rcut = 3.5σ yield Tc and pc that are higher by 0.2% and 1.4% than simulations with rcut = 5 and 8σ but still with overlapping 95% confidence intervals. In contrast, GEMC simulations with a truncated and shifted potential show that rcut = 8σ is insufficient to obtain accurate results. Additional GEMC simulations for hard-core square-well particles with various ranges of the attractive well and for n-decane molecules represented by the TraPPE force field yield data that support the trends observed for Lennard-Jones particles. The finite-size dependence of the critical properties obtained from GEMC simulations is significantly smaller than those from grand-canonical ensemble simulations. Thus, when resources are not available for a rigorous finite-size scaling study, GEMC simulations provide a straightforward route to determine fairly accurate critical properties using relatively small system sizes.
Financial support from the National Science Foundation (No. CBET-1159837) is gratefully acknowledged. Part of the computer resources were provided by the Minnesota Supercomputing Institute.
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