Lennard-Jones fluid steps

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. 

The corresponding result for the surface tension [9] provides quite reasonable accuracy for a Lennard Jones fluid or an inert gas fluid, except helium which displays large quantum effects. Thus we can conclude that the leading mechanisms of surface tension in a simple fluid is the loss of binding energy of the liquid phase at the gas-liquid interface and the second most important mechanism is likely to be the adsorption-depletion at the interface which creates a molecularly smooth density profile instead of an abrupt step in the density. 

In eonelusion, the preceding results permit one to establish the validity of the two-dimensional Steele approximation, despite the simplifications involved in it, as a first step in the development of a more complex theory of adsorption. It has been shown how different experimental results for rare gases on graphite ean be reproduced by starting from molecular considerations. In particular, the use of the Cuadros-Mulero expression for the equation of state of two-dimensional Lennard-Jones fluids seems to be the most straightforward way to apply the aforementioned two-dimensional approach. The use of more complex expressions, such as the one proposed by Reddy and O Shea, requires more ealeulation effort and does not lead to signifieantly better results. 

At = 2.15 (10 sec. This value of the time step is about one-fifth that used by Verlet (31) and Rahman (34) in simulations of the pairwise additive Lennard-Jones fluid. 

The LJ atomic fluid We conducted an MD simulation for 100 time steps of 32,000 atoms interacting with each other via the well-known 6-12 LJ potential (Lennard-Jones 1924) ... 

The solvation of an HS solvaton in a real fluid is important in the study of the solvation thermodynamic of any real solvaton. The solvation process of a real particle may be performed in two steps first, the creation of a suitable cavity, then turning on the other parts of the interactions between the solvaton and the (real) solvent. In order to define the size of the cavity we need to assign an effective hard-core diameter to the solvent molecules. For simple spherical molecules, such as the noble gases, a natural choice of the effective diameter might be the van der Waals or Lennard-Jones diameter of the molecules. For more complex molecules there is no universal way of defining an effective HS diameter to be assigned to the solvent molecules. 

For Lennard-Jones (LJ) and similar fluids, the first step toward the development of appropriate expressions is the decomposition of the fluid-fluid potential into repulsive and attractive terms. The Weeks-Chandler-Anderson (WCA) division is usually used [259], according to which the attractive part of the Lennard-Jones potential is given by... 

Figure 6. Comparison of trajectories of particle 27 in Lennard- ones and Len-nard-Jones plus Axilrod-Teller fluids at pa = 0.65. Both runs were started from the same point in phase space and trajectories shown are from time steps 500-2000 in each simulation. For this calculation the Axilrod-Teller strength constant V was assigned a value of three times that for argon given in Section 2. Note that the circles represent positions of the center of mass of the atom, not the atomic diameter.

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