Sixth, seventh and eighth virial coefficients of the Lennard-Jones model

Abstract

We report values of the virial coefficients B _n of the Lennard-Jones (LJ) model, as computed by the Mayer Sampling Monte Carlo method. For n = 4 and 5, values are reported for 103 temperatures T = 0.62 to 40.0 (in LJ units); for n = 6, 31 values are reported for T = 0.625 to 20.0; for n = 7, 15 values are reported from T = 0.625 to 10; and for n = 8, four values are reported from T = 0.75 to 10. Data are used to estimate the location of the LJ critical point, and the critical temperature estimated this way is given to within 0.8% of the established value, while the critical density is too low by 10%. Data derived from the virial equation of state (VEOS) are compared to pressures and internal energies calculated by Monte Carlo simulation. Simulations of systems ranging from 125 to 30,000 particles are extrapolated to infinite system size, and it is shown that the VEOS–when applied at densities where the series has reached convergence–provides results closer to the infinite-system values than obtained by any of the finite-system simulations. For n = 6, convergence of VEOS (within a 1% tolerance) is obtained for densities up to the spinodal for subcritical temperatures and up to ρ = 0.4 (in LJ units) in the vicinity of the critical temperature; the range of applicability of VEOS increases with temperature, reaching for example densities of 0.65 for T = 5.0 and 0.8 for T = 8.0 when truncated at n = 6.

Keywords:

• virial equation of state
• Lennard-Jones
• Mayer sampling Monte Carlo
• critical point

Acknowledgements

Funding for this research was provided by grants CHE-0626305 from the U.S. National Science Foundation, and by the University at Buffalo School of Engineering and Applied Sciences. Computational support was provided by the University at Buffalo Center for Computational Research. Additional resources were provided by the Open Science Grid, which is supported by the National Science Foundation and the U.S. Department of Energy's Office of Science.