Fluid Lennard-Jones

Truncation at the first-order temi is justified when the higher-order tenns can be neglected. Wlien pe higher-order tenns small. One choice exploits the fact that a, which is the mean value of the perturbation over the reference system, provides a strict upper bound for the free energy. This is the basis of a variational approach [78, 79] in which the reference system is approximated as hard spheres, whose diameters are chosen to minimize the upper bound for the free energy. The diameter depends on the temperature as well as the density. The method was applied successfiilly to Lennard-Jones fluids, and a small correction for the softness of the repulsive part of the interaction, which differs from hard spheres, was added to improve the results. 

Straub J E, Borkovec M and Berne B J 1988 Molecular dynamics study of an isomerizing diatomic Lennard-Jones fluid J. Chem. Phys. 89 4833... 

There are various, essentially equivalent, versions of the Verlet algoritlnn, including the origmal method employed by Verlet [13, 44] in his investigations of die properties of the Lennard-Jones fluid, and a leapfrog fonn [45]. Here we concentrate on the velocity Verlet algoritlnn [46], which may be written... 

Lotfi A, Vrabeo J and Fisoher J 1992 Vapour liquid equilibria of the Lennard-Jones fluid from the NpT plus test partiole method Mol. Phys. 76 1319-33... 

Holcomb C D, Clancy P and Zollweg J A 1993 A critical study of the simulation of the liquid-vapour interface of a Lennard-Jones fluid Mol. Phys. 78 437-59... 

Torrie, G.M., Valleau, J.P. Monte Carlo free energy estimates using non-Boltzmann sampling application to the subcritical Lennard-Jones fluid. Chera. Phys. Lett. 28 (1974) 578-581. 

We consider a Lennard-Jones fluid consisting of atoms interacting with a Lennard-Jones potential given by... 

Fig. 11(a) displays plots of the in-plane pair correlation function for s = 2. and 3.0 well outside the regime where K exhibits its first maximum (see Fig. 12). The plots indicate that the transverse structures of one- and two-layer fluids (see Fig. 10) are essentially identical and typical of dense Lennard-Jones fluids. However, the transverse structure of a two-layer fluid is significantly affected as the peak of K is approached, as can be seen in Fig. 11(b) where g (zi,pi2) is plotted for s = 2.55 and 2.75, which points...

R. Kjellander, S. Sarman. A study of anisotropic pair distribution theories for Lennard-Jones fluids in narrow slits. II. Pair correlations and solvation forces. Mol Phys 74 665-688, 1991. 

V. P. Gregory, J. C. Schug. NPT Monte Carlo ealeulation of isotherms for the Lennard-Jones fluid. Mol Phys 82 677-6SS, 1994. 

Obviously, the mean-field treatment of the attraetive van der Waals inter-aetion results in negleet of the influenee of the interpartiele eorrelations on as well as the influenee of attraetive forees on assoeiation effeets (ef. the definition of Eq. (78)). To obtain a more adequate approximation, Johnson and Gubbins (see, e.g., [114]), have developed an aeeurate equation of state for assoeiating Lennard-Jones fluids, or more preeisely for the following nonassoeiative potential... 

Now we turn our attention to the results obtained from the pair theory for the system of assoeiating Lennard-Jones fluid in eontaet with a hard wall. The nonassoeiative part of the interpartiele potential is given by Eq. (87), whereas the assoeiative interaetion is given by Eq. (60), with d = 0.45 and <3 = 0.1. The diameter of fluid partieles a is taken as the unit of length. 

A dimerizing Lennard-Jones fluid has been studied for the bulk density p = 0.75, and at temperature T — 1.35, for different values of the assoeia-tion energy, namely = 2, 6, 10, and 11.5 [118]. The results for... 

The density profiles are shown in Fig. 7(a). Fig. 7(b), however, illustrates the dependenee of the degree of dimerization, x( ) = P i )lon the distance from the wall. It ean be seen that, at a suffieiently low degree of dimerization (s /ksT = 6), the profile exhibits oseillations quite similar to those for a Lennard-Jones fluid and for a hard sphere fluid near a hard wall. For a high degree of dimerization, i.e., for e /ksT = 10 and 11.5, we observe a substantial deerease of the eontaet value of the profile in a wide layer adjacent to a hard wall. In the ease of the highest assoeiation energy,... 

The main conclusion which can be drawn from the results presented above is that dimerization of particles in a Lennard-Jones fluid leads to a stronger depletion of the proflles close to the wall, compared to a nonassociating fluid. On the basis of the calculations performed so far, it is difficult to conclude whether the second-order theory provides a correct description of the drying transition. An unequivocal solution of this problem would require massive calculations, including computer simulations. Also, it would be necessary to obtain an accurate equation of state for the bulk fluid. These problems are the subject of our studies at present. 

Note that, for = 0, the potential given above does not reduce to the Lennard-Jones (12-6) function, because the soft Lennard-Jones repulsive branch is replaced by a hard-sphere potential, located at r = cr. The results for the nonassociating Lennard-Jones fluid can be found in Ref. 159. 

In the case of a Lennard-Jones fluid, the knowledge of the bulk density in the nonreactive part is all that is needed to calculate the chemical potential. Actually, one can use the equation of state of Nicolas et al. [115] (or the... 

To conclude, the introduction of species-selective membranes into the simulation box results in the osmotic equilibrium between a part of the system containing the products of association and a part in which only a one-component Lennard-Jones fluid is present. The density of the fluid in the nonreactive part of the system is lower than in the reactive part, at osmotic equilibrium. This makes the calculations of the chemical potential efficient. The quahty of the results is similar to those from the grand canonical Monte Carlo simulation. The method is neither restricted to dimerization nor to spherically symmetric associative interactions. Even in the presence of higher-order complexes in large amounts, the proposed approach remains successful. 

J. Broughton, G. Gilmer, K. Jackson. Crystallization rates of a Lennard Jones fluid. Phys Rev Lett 49 1496, 1982. 

Equilibrium Systems. Magda et al (12.) have carried out an equilibrium molecular dynamics (MD) simulation on a 6-12 Lennard-Jones fluid In a silt pore described by Equation 41 with 6 = 1 with fluid particle Interactions given by Equation 42. They used the Monte Carlo results of Snook and van Me gen to set the mean pore density so that the chemical potential was the same In all the simulations. The parameters and conditions set In this work were = 27T , = a, r = 3.5a, kT/e = 1.2, and... 

Travis, K. P., Gubbins, K. E., Poiseuille flow of Lennard-Jones fluids in narrow slit pores, J. Chem. Phys. 112, 4 (2000) 1984-1994. 

The second generalization is the reinterpretation of the excluded volume per particle V(). Realizing that only binary collisions are likely in a low-density gas, van der Waals suggested the value Ina /I for hard spheres of diameter a and for particles which were modeled as hard spheres with attractive tails. Thus, for the Lennard-Jones fluid where the pair potential actually is... 

We shall illustrate the applicability of the GvdW(S) functional above by considering the case of gas-liquid surface tension for the Lennard-Jones fluid. This will also introduce the variational principle by which equilibrium properties are most efficiently found in a density functional theory. Suppose we assume the profile to be of step function shape, i.e., changing abruptly from liquid to gas density at a plane. In this case the binding energy integrals in Ey can be done analytically and we get for the surface tension [9]... 

FIG. 1 The calculated surface tension of an argon fluid represented as a Lennard-Jones fluid is shown as a function of temperature. The GvdW(HS-B2)-functional is used in all cases. The filled squares correspond to step function profile and local entropy, the filled circles to tanh profile with local entropy, and the open circles to tanh profile with nonlocal entropy. The latter data are in good agreement with experiment. 

This functional gives a good account of both the equation of state and the surface tension of a Lennard-Jones fluid. The surface tension is shown in Fig. 1. The critical parameters obtained from the equation of state are shown in Table 1. 

A Lennard-Jones fluid was simulated. All quantities were made dimensionless using the well depth eLJ, the diameter CTlj, and the time constant... 

Figure 5. Molecular dynamics simulation of the decay forward and backward in time of the fluctuation of the first energy moment of a Lennard-Jones fluid (the central curve is the average moment, the enveloping curves are estimated standard error, and the lines are best fits). The starting positions of the adiabatic trajectories are obtained from Monte Carlo sampling of the static probability distribution, Eq. (246). The density is 0.80, the temperature is Tq — 2, and the initial imposed thermal gradient is pj — 0.02. (From Ref. 2.)...

Figure 8 shows the r-dependent thermal conductivity for a Lennard-Jones fluid (p = 0.8, 7o = 2) [6]. The nonequilibrium Monte Carlo algorithm was used with a sufficiently small imposed temperature gradient to ensure that the simulations were in the linear regime, so that the steady-state averages were equivalent to fluctuation averages of an isolated system. 

Figure 9. Simulated thermal conductivity X/(t) for a Lennard-Jones fluid. The density in the center of the system is p = 0.8 and the zeroth temperature is To = 2. (a) A fluid confined between walls, with the numbers referring to the width of the fluid phase. (From Ref. 6.) (b) The case I, — 11.2 compared to the Markov (dashed) and the Onsager-Machlup (dotted) prediction.

Adams, D.J., Grand canonical ensemble Monte Carlo for a Lennard-Jones fluid, Mol. Phys. 1975, 29, 307-311... 

Wilding, N. B., Critical-point and coexistence-curve properties of the Lennard-Jones fluid a finite-size scaling study, Phys. Rev. E1995, 52, 602-611... 

Fig. 3.3. Typical results from a density-of-states simulation in which one generates the entropy for aliquid at fixed N and V (i.e., fixed density) (adapted from [29]). The dimensionless entropy. r/ In ( is shown as a function of potential energy U for the 110-particle Lennard-Jones fluid at p = 0.88. Given an input temperature, the entropy function can be reweighted to obtain canonical probabilities. The most probable potential energy U for a given temperature is related to the slope of this curve, d// /dU(U ) = l/k T, and this temperature-energy relationship is shown by the dotted line. Energy and temperature are expressed in Lennard-Jones units...

Fig. 3.6. Evolution of a WL simulation for the Lennard-Jones fluid at p = 0.88 and N = 110. The calculated quantity of interest is the dimensionless entropy, as a function of potential energy. The average statistical error is determined from the standard deviation offrom 10 independent runs. The modification factor curve (the dotted line) has also been averaged over these runs, and consequently appears smoother than would normally be the case...

Fig. 3.8. Transition matrix of move proposal probabilities for the Lennard-Jones fluid at p = 0.88 and N = 110. The energy range of —700 to —500 in Lennard-Jones units has been discretized into 100 bins. Due to the adjustment of the random displacement moves to achieve 50% acceptance, the transition probabilities are highly banded. The tuned moves change the potential energy by only a small amount, and as a result, each energy level is effectively only connected to a few neighbors...

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