Lennard-Jones fluid pressure

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]. 

The model isotherm for each pore size class was calculated by methods described previously [9], modified to account for cylindrical pore geometry. These calculations model the fluid behavior in the presence of a uniform wall potential. Since the silica surface of real materials is energetically heterogeneous, one must choose an effective wall potential for each pore size that will duplicate the critical pore condensation pressure, p, observed for that size. This relationship is shown in Figure 2. The Lennard-Jones fluid-fluid interaction parameters and Cn/kg were equal to 0.35746 nm and 93.7465 K, respectively. 

Figure 1. The pressure dependence of the glass temperature in model and experimental fluids. The dashed-dotted curve (red) is for the Lennard-Jones with a purely repulsive interaction (UR) fluid, thin solid curve (red) is for the Lennard-Jones fluid (U) and the black dotted curve is for the hard spheres fluid with a. square-well (SW) potential. These curve recall results of...

Table 2. A comparison between Monte Carlo results and the predictions of integral-equation theories of the thermodynamic properties of a Lennard-Jones fluid. MC = Monte Carlo results of Hansen and Verlet (1969) PY and HNC results are from Levesque (1966) and Verlet and Levesque (1967). c = from compressibility equation p = from pressure equation. (Hansen and McDonald, 1986)... 

This section is devoted to studying the 2D Lennard-Jones model in order to serve as the basis in applying Steele s theory. In Section IVA the main studies about that model are summarized and commented on. In Section IVB, the most useful expressions for the equation of state of the model are given. In Section IVC we present results about the application of these equations, which are compared with other theoretical approaches to studying adsorption of 2D Lennard-Jones fluids onto perfectly flat surfaces. In Section FVD, the comparison with experimental results is made, including results for the adsorption isotherms, the spreading pressure, and the isosteric heat. Finally, in Section IVE we indicate briefly some details about the use of computer simulations to model the properties both of an isolated 2D Lennard-Jones system and of adsorbate-adsorbent systems. 

Nagayama et al. [57] carried out nonequilibrium molecular dynamic simulations to study the effect of interface wettability on the pressure driven flow of a Lennard-Jones fluid in a nanochannel. The velocity profile changed significantly depending on the wettability of the wall. The no-slip boundary condition breaks down for a hydrophobic wall. Siegel et al. [58] developed a two-dimensional computational model for fuel cells. 

Equation 10.42 implies that for fluids for which the pairwise potential has the same functional form (for example, all Lennard-Jones fluids), the pressure is a universal function of the reduced temperature T and number density p. In other words, there is a single, universal p v diagram that describes the behavior of fluids with the same pair potential function. This is the law of corresponding states, which holds for classes of structurally similar chemical substances. 

Rare-gas clusters can be produced easily using supersonic expansion. They are attractive to study theoretically because the interaction potentials are relatively simple and dominated by the van der Waals interactions. The Lennard-Jones pair potential describes the stmctures of the rare-gas clusters well and predicts magic clusters with icosahedral stmctures [139, 140]. The first five icosahedral clusters occur at 13, 55, 147, 309 and 561 atoms and are observed in experiments of Ar, Kr and Xe clusters [1411. Small helium clusters are difficult to produce because of the extremely weak interactions between helium atoms. Due to the large zero-point energy, bulk helium is a quantum fluid and does not solidify under standard pressure. Large helium clusters, which are liquid-like, have been produced and studied by Toennies and coworkers [142]. Recent experiments have provided evidence of... 

An intrinsic surface is built up between both phases in coexistence at a first-order phase transition. For the hard sphere crystal-melt interface [51] density, pressure and stress profiles were calculated, showing that the transition from crystal to fluid occurs over a narrow range of only two to three crystal layers. Crystal growth rate constants of a Lennard-Jones (100) surface [52] were calculated from the fluctuations of interfaces. There is evidence for bcc ordering at the surface of a critical fee nucleus [53]. 

Bulk phase fluid structure was obtained by solution of the Percus-Yevick equation (W) which is highly accurate for the Lennard-Jones model and is not expected to introduce significant error. This allows the pressure tensors to return bulk phase pressures, computed from the virial route to the equation of state, at the center of a drop of sufficiently large size. Further numerical details are provided in reference 4. 

In the present work, we performed MC simulations at different operation conditions, constant fluid density and constant pressure, for calculating K2 to investigate the distribution behavior in the supercritical region. We selected C02, benzene, and graphitic slitpore as a model system by adopting the Lennard - Jones (LJ) potential function for intermolecular interactions. 

Fig. 8. Density variation of the inherent structure pressure for a fluid with a smoothly truncated Lennard-Jones potential (Sastry etal., 1997b). Regions A, B, and C identify distinguishing density intervals for the inherent structures discussed in the text.

The small spheres are fluid molecules, and the large spheres are immobile silica particles. The top visualizations are for a disordered material and the bottom visualizations are for an ordered material of the same porosity. The visualizations on the left are for the saturated vapor state, and those on the right are for the corresponding saturated liquid state, (b) Simulated adsorption and desorption isotherms for Lennard-Jones methane in a silica xerogel at reduced temperature kT/Sfi = 0.7. The reduced adsorbate density p = pa is plotted vs the relative pressure X/Xo for methane silica/methane methane well depth ratios ejf/Sff = 1- (open circles) and 1.8 (filled circles) [44]. (Reproduced with permission from S. Ramalingam,... 

Clarke has examined the thermodynamic equation of state and the specific heat for a Lennard-Jones liquid cooled through 7 at zero pressure. He found that drops with decreasing temperature near where the selfdiffusion becomes very small. Wendt and Abraham have found that the ratio of the values of the radial distribution function at the first peak and first valley shows behavior on cooling much like that observed for the volume of real glasses (Fig. 6), with a clearly defined 7. Stillinger and Weber have studied a Gaussian core model and find a self-diffusion constant that drops essentially to zero at a finite temperature. They also find that the ratio of the first peak to the first valley in the radial distribution function showed behavior similar to that found by Wendt and Abraham" for Lennard-Jones liquids. However, the first such evidence for a nonequilibrium (i.e. kinetic) nature of the transition in a numerical simulation was obtained by Gordon et al., who observed breakaways in the equation of state and the entropy of a hard-sphere fluid similar to those in real materials. 

In the pressure wave simulations, the boundaries represent idealized membranes located, respectively, at Zi(t) and z2(t). These membranes have Lennard-Jones interactions with the fluid atoms with identical constants as the fluid-fluid interactions, but in the z direction only. The location of one membrane is varied sinusoidally... 

Comment by H. W. Woolley, NBS In a fluid with hexagonal close packing, the nearest neighbor interactions alone, as in an incomplete Lennard-Jones and Devonshire approach, give a static interaction pressure... 

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