Phase diagrams Lennard-Jones fluid

Figure 16. Phase diagram of the Lennard-Jones fluid with different approximations MSA (crosses) and DHH (dot line) (taken from Ref. [65]), DHH+DHHDS (solid line) (see Ref. [81]), BB approximation (black circles) (courtesy of the author), the chemical potential had been calculated by using Lee formula). Simulation data are from Lotfi et al. [102] (open circles) and from Panagiotopoulos [103] (solid triangles).

The principal tools have been density functional theory and computer simulation, especially grand canonical Monte Carlo and molecular dynamics [17-19]. Typical phase diagrams for a simple Lennard-Jones fluid and for a binary mixture of Lennard-Jones fluids confined within cylindrical pores of various diameters are shown in Figs. 9 and 10, respectively. Also shown in Fig. 10 is the vapor-liquid phase diagram for the bulk fluid (i.e., a pore of infinite radius). In these examples, the walls are inert and exert only weak forces on the molecules, which themselves interact weakly. Nevertheless,... 

S. T. Lin, M. Blanco, and W. A. Goddard, The two-phase model for calculating thermodynamic properties of liquids from molecular dynamics validation for the phase diagram of Lennard-Jones fluids. J. Chem. Phys., 119 (2003), 11792-805. 

Kaneko, T., Mima, T., Yasuoka, K. Phase diagram of Lennard-Jones fluid confined in slit pores. Chem. Phys. Lett. 490, 165-171 (2010)... 

Smit, B. Phase Diagrams of Lennard-Jones Fluids. J. Chem. Phys. 1992, 96, 8639-8640. 

This technique is most often used in lattice quantum chromodynamics ((JCD) simulations. Mehlig et al. [55] demonstrated its use by simulating Lennard-Jonesium as an example of a condensed matter system. Similarly, Clamp et al. [56] simulated a 2D Lennard-Jones fluid using both MD and hybrid MC and found that hybrid MC is more ergodic and samples phase space more efficiently than MD. A more realistic system was studied by Brotz et al. [57], employed hybrid MC to calculate the phase diagram of silicon. 

The most successful such technique is the Gibbs ensemble of Panagiotopouloset al, which was used by Harismiadis et al (1991) to generate phase diagrams for binary Lennard-Jones fluids of varying values for the size and energy parameters. 

The integrals are over the full two-dimensional volume F. For the classical contribution to the free energy /3/d([p]) the Ramakrishnan-Yussouff functional has been used in the form recently introduced by Ebner et al. [314] which is known to reproduce accurately the phase diagram of the Lennard-Jones system in three dimensions. In the classical part of the free energy functional, as an input the Ornstein-Zernike direct correlation function for the hard disc fluid is required. For the DFT calculations reported, the accurate and convenient analytic form due to Rosenfeld [315] has been used for this quantity. 

The density functional approach has also been used to study capillary condensation in slit-like pores [148,149]. As in the previous section, a simple model of the Lennard-Jones associating fluid with a single associative site is considered. All the parameters of the interparticle potentials are chosen the same as in the previous section. Our attention has been focused on the influence of association on capillary condensation and the evaluation of the phase diagram [42]. 

This approach has been used ° to map out the phase diagram (coexistence and spinodal curves) for the polar hard dumbbell fluid at L = 0.5. The major conclusion from this work is that the critical point, due to electrostatic interactions alone, is at a much lower temperature than the critical point of a corresponding real fluid. Thus, electrostatic interactions are a small perturbation to the thermodynamics of the Lennard-Jones interaction. 

The application of this approach to the hard-sphere system was presented by Ree and Hoover in a footnote to their paper on the hard-sphere phase diagram. They made a calculation where they used Eq. (2.27) for the solid phase and an accurate equation of state for the fluid phase to obtain results that are in very close agreement with their results from MC simulations. The LJD theory in combination with perturbation theory for the liquid state free energy has been applied to the calculation of solid-fluid equilibrium for the Lennard-Jones 12-6 potential by Henderson and Barker [138] and by Mansoori and Canfield [139]. Ross has applied a similar approch to the exp-6 potential. A similar approach was used for square well potentials by Young [140]. More recent applications have been made to nonspherical molecules [100,141] and mixtures [101,108,109,142]. 

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