Lin, Shiang-Tai and Blanco, Mario and Goddard, William A.,III (2003) The two-phase model for calculating thermodynamic properties of liquids from molecular dynamics: Validation for the phase diagram of Lennard-Jones fluids. Journal of Chemical Physics, 119 (22). pp. 11792-11805. ISSN 0021-9606 http://resolver.caltech.edu/CaltechAUTHORS:
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We propose a general approach for determining the entropy and free energy of complex systems as a function of temperature and pressure. In this method the Fourier transform of the velocity autocorrelation function, obtained from a short (20 ps) molecular dynamics trajectory is used to obtain the vibrational density of states (DoS) which is then used to calculate the thermodynamic properties by applying quantum statistics assuming each mode is a harmonic oscillator. This approach is quite accurate for solids, but leads to significant errors for liquids where the DoS at zero frequency, S(0), remains finite. We show that this problem can be resolved for liquids by using a two phase model consisting of a solid phase for which the DoS goes to zero smoothly at zero frequency, as in a Debye solid; and a gas phase (highly fluidic), described as a gas of hard spheres. The gas phase component has a DoS that decreases monotonically from S(0) and can be characterized with two parameters: S(0) and 3Ng, the total number of gas phase modes [3Ng0 for a solid and 3Ng3(N–1) for temperatures and pressures for which the system is a gas]. To validate this two phase model for the thermodynamics of liquids, we applied it to pure Lennard-Jones systems for a range of reduced temperatures from 0.9 to 1.8 and reduced densities from 0.05 to 1.10. These conditions cover the gas, liquid, crystal, metastable, and unstable states in the phase diagram. Our results compare quite well with accurate Monte Carlo calculations of the phase diagram for classical Lennard-Jones particles throughout the entire phase diagram. Thus the two-phase thermodynamics approach provides an efficient means for extracting thermodynamic properties of liquids (and gases and solids).
|Additional Information:||©2003 American Institute of Physics. Received 6 February 2003; accepted 12 September 2003. The authors would like to thank Dr. Tahir Cagin, Dr.Seung Soon Jang, Dr. Prabal Maiti, Dr. Valeria Molinero, and Peng Xu for many useful discussions. This research was partially supported by the NSF (CHE 99-85774, CTS-0132002) and NIH (1R01-GM62523-01). The facilities of the MSC used in this research are also supported by grants from DOE (ASCI and FETL), ARO (MURI and DURIP), ONR (MURI and DURIP), IBM-SUR, General Motors, ChevronTexaco, Seiko-Epson, Asahi Kasai, Beckman Institute, and Toray.|
|Subject Keywords:||density; Lennard-Jones potential; thermodynamic properties; molecular dynamics method; harmonic oscillators; phase diagrams|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Lindsay Cleary|
|Deposited On:||25 Jul 2006|
|Last Modified:||26 Dec 2012 08:57|
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