Simulations 6-12 Lennard-Jones fluid

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... 

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. 

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. 

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... 

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.

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. 10.10. Calculated ,x( U) from a Wang-Landau simulation for the Lennard-Jones fluid at V = 125. The potential energy has been discretized into 1,000 bins and is expressed in Lennard-Jones units. Reprinted figure with permission from [75], 2002 by the American Physical Society...

If we accept the first three postulates, we can lift each of these approximations using statistical mechanics and the companion techniques of computer simulation. But to do so we must consider a material for which complete thermodynamic and the necessary structural information is available. Ve, therefore, consider the Lennard-Jones fluid in most of the following discussion. 

In order to understand the above questions/paradoxes, a mode coupling theoretical (MCT) analysis of time-dependent diffusion for two-dimensional systems has been performed. The study is motivated by the success of the MCT in describing the diffusion in 3-D systems. The main concern in this study is to extend the MCT for 2-D systems and study the diffusion in a Lennard-Jones fluid. An attempt has also been made to answer the anomaly in the computer simulation studies. 

Figure 5. Results from a multicanonical simulation of the 3D Lennard-Jones fluid at a point on the coexistence curve. The figure shows both the multicanonical sampling distribution PAP) (symbol o) and the corresponding estimate of the equilibrium distribution Ro(p) with p = N/V the number density (symbol ). The inset shows the value of the equilibrium distribution in the...

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).

Roccatano D, Amadei A, Apol MEF, Nola AD, Berendsen HJC (1998) Application of the quasi-Gaussian entropy theory to molecular dynamic simulation of Lennard-jones fluids, J Chem Phys, 109 6358-6363... 

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,... 

An example drawn from Deitrick s work (Fig. 2) shows the chemical potential and the pressure of a Lennard-Jones fluid computed from molecular dynamics. The variance about the computed mean values is indicated in the figure by the small dots in the circles, which serve only to locate the dots. A test of the thermodynamic goodness of the molecular dynamics result is to compute the chemical potential from the simulated pressure by integrating the Gibbs-Duhem equation. The results of the test are also shown in Fig. 2. The point of the example is that accurate and affordable molecular simulations of thermodynamic, dynamic, and transport behavior of dense fluids can now be done. Currently, one can simulate realistic water, electrolytic solutions, and small polyatomic molecular fluids. Even some of the properties of micellar solutions and liquid crystals can be captured by idealized models [4, 5]. 

FIGURE 5.8. Liquid/vapour coexistence curve of the Lennard-Jones fluid predicted by the lOZ/LMBW theory in the KHM, KH and VM approximation (solid, short-dash and long-dash lines, respectively). Monte Carlo (MC) simulations are shown by the open circles. 

A commonly used model system in liquid crystal simulation is the Gay-Beme fluid. It can be regarded as a Lennard-Jones fluid generalised to ellipsoidal molecular cores. 

H. A. Posch, F. Vesely, and W. Steele. Atomic pair dynamics in a Lennard-Jones fluid Comparison of theory with computer simulation. Molec. Phys., 44 241-264 (1981). 

To close this Section we comment on two papers that do not fit under any neat heading. The first of these is by Xiao et al,261 who study the final stages of the collapse of an unstable bubble or cavity using MD simulations of an equilibrated Lennard-Jones fluid from which a sphere of molecules has been removed. They find that the temperature inside this bubble can reach up to an equivalent of 6000 K for water. It is at these temperatures that sonolumines-cence is observed experimentally. The mechanism of bubble collapse is found to be oscillatory in time, in agreement with classical hydrodynamics predictions and experimental observation. The second paper, by Lue,262 studies the collision statistics of hard hypersphere fluids by MD in 3, 4 and 5 dimensions. Equations of state, self-diffusion coefficients, shear viscosities and thermal conductivities are determined as functions of density. Exact expressions for the mean-free path in terms of the average collision time and the compressibility factor in terms of collision rate are also derived. Work such as this, abstract as it may appear, may be valuable in the development of microscopic theories of fluid transport as well as provide insight into transport processes in general. 

Salamacha and coworkers304 306 have carried out a series of studies on Lennard-Jones fluids confined to nanoscopic slit pores made from parallel planes of face centred cubic crystals. Grand canonical and canonical ensemble MC simulations have been used to determine the structure and phase behaviour as the width of the pore and the strength of the fluid-wall interactions were varied. The pore widths were small accommodating 2 to 5 layers of fluid molecules.304,305 The strength of the fluid-wall interaction is linked to the degree of corrugation of the surface, and it is found that the structure of the... 

Wongkoblap et al.307 study Lennard-Jones fluids in finite pores, and compare their results with Grand canonical ensemble simulations of infinite pores. Slit pores of 3 finite layers of hexagonally arranged carbon atoms were constructed. They compare the efficiency of Gibbs ensemble simulations (where only the pore is modelled) with Canonical ensemble simulations where the pore is situated in a cubic cell with the bulk fluid, and find that while the results are mostly the same, the Gibbs ensemble method is more efficient. However, the meniscus is only able to be modelled in the canonical ensemble. 

Neimark and Vishnyakov316,317 have carried out an interesting study into the formation of a bubble in a Lennard-Jones fluid confined to a spherical pore at a metastable state. Various simulation techniques are used and compared. The Lennard-Jones parameters are selected to resemble nitrogen and the results are compared with experimental results, with qualitative agreement obtained. 

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