Lennard-Jones intermolecular pressure

Figure 9.5 Molecular dynamics calculations of the nondimcnsional surface pressure (difference between pressure inside a drop and the gas) for a Lennard-Jones intermolecular potential. Classical liquid drop theory begins to break down fordroplei radii smallcrihan about 10 times the Lennard-Jones diameter CTij. Calculations for Ar/su = 0.71 and = 0,58. (After Thompson et al, 1984.)...

Fig. 12 Symmetrization run for n-hexane. Left, the evolution of the overall asymmetry index (upper curve) and of the overall density (lower curve). Right the evolution of pressure (atm) and of intramolecular, intermolecular Lennard-Jones and total energy (kJ moP ). The abscissa shows the number of million MC moves, corresponding to a time of a few picoseconds...

Carbon tetrafluoride. Carbon tetra-fluoride, which undergoes a transition to a plastically crystalline (orientationally disordered) phase, has been investigated by the Parrinello-Rahman molecular dynamics method under constant-pressure conditions (6). A simple intermolecular potential model of the Lennard-Jones form was derived by taking into account the experimen-... 

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. 

For atomic gases the intermolecular potential most used in calculations of B, has been the Lennard-Jones 6-12, with the parameters e and r determined from gas viscosities and pressure virial coefScients. For non-dipolar gases possessing higher moments, most authors have used the 6-12 potential together with the appropriate terms from equations (27) and (28), while for dipolar gases some form of equations (26)—(28) is used with a shape-dependent term added to uq. 

The pure component intermolecular potential parameters used in this study are shown in Table I. They were obtained as follows for carbon dioxide, we fitted the experimental critical temperature and pressure (12) using data from ( ) for the critical constants of the Lennard-Jones (U) system (T - 1.31, - 0.13). For acetone, a... 

The interface between the droplet and the gas is not discontinuous the average molecular density decreases over a narrow region from the liquid side to the vapor. When the size of the droplet becomes sufhctently small compared with the thickness of the transition layer, the use of classical thermodynamics and the bulk surface tension become inaccurate the Kelvin relation and Laplace formula no longer apply. This effect has been studied by molecular dynamics calculations of the behavior of liquid droplets composed of 41 to 2(X)4 molecules that interact through a Lennard-Jones (LI) intermolecular potential (Thomp.son et al., 1984). The results of this analysis are shown in Fig. 9.5, in which the nondimensional pressure difference between the drop interior and the surrounding vapor (Pd — p)rr / ij is... 

The differential cross sections of argon and neon have been measured by using refinements of the modulated molecular-beam technique. From these measurements the intermolecular potentials were found. These potentials differ significantly from the Lennard-Jones potential. The neon and argon potentials have different shapes and are not related by any simple scaling factor. The macroscopic properties have been calculated and are in reasonable agreement with experiment. The face-centered cubic structure was found to be the most stable crystal lattice for neon. The effect of the argon potential on the critical properties and saturation pressures is also discussed. 

The theory describing diffusion in binary gas mixtures at low to moderate pressures has been well developed. Modem versions of the kinetic theory of gases have attempted to account for the forces of attraction and repulsion between molecules. Hirschfelder et al. (1949), using the Lennard-Jones potential to evaluate the influence of intermolecular forces, presented an equation for the diffusion coefficient for gas pairs of nonpolar, nonreacting molecules ... 

The liquid structure factor of CCI4 and its derivatives with respect to temperature at fixed pressure or fixed volume, needed by eq. (2), were evaluated by Molecular Dynamics (MD) simulations. We have used the OPLS model for tetrachloromethane [9] In this model, the CCI4 molecules are described as rigid tetrahedra (dc-ci = 1 -769 A) and the intermolecular potentials are atom centered 6-12 Lennard-Jones potentials plus the coulombic interaction with partial charges on C and Cl. We performed NVT simulations with 512 molecules for about 1 ns each. The different x-ray structure factors were obtained from the accumulated partial radial distribution functions [10], using the atomic form-factors from the DABAX database [11]. In order to estimate the partial derivatives of the structure factor, we have used finite differences we considered two different temperatures, Ti = 300 K and T2 = 328 K, and two molar volumes, Vi = 97.3 cm mol and V2 = 100.65 cm mol which are the molar volumes along the liquid-vapor coexistence line for the two temperatures Tj and Tz respectively [12]. Three simulations were then run for the temperature and molar volume conditions (TiiVi), T2,V )... 

Recently the DFT method combined with SAFT equations of state has been used to predict the interfacial properties of real fluids. LDA methods are accurate enough to treat liquid-liquid and liquid-liquid interfaces where the density profiles are usually smooth functions, and have been used in combination with the SAFT-VR approach to predict the surface-tension of real fluids successfully. The intermolecular model parameters required to treat real substances are determined by fitting to experimental vapour-pressure and saturated liquid density data in the usual way (see section 8.5.1) and the resulting model is found to provide accurate predictions of the surface tension. A local DFT treatment has also been combined with the simpler SAFT-HS approach, but in this case only qualitative agreement with experimental surface tension data is found due to the less accurate description of the bulk properties provided by the SAFT-HS equation. Kahl and Winkelman" have followed a perturbation approach similar to the one proposed with the SAFT-VR equation and have coupled a local DFT treatment with a Lennard-Jones based SAFT equation of state. They predict the surface tension of alkanes from methane to decane and of cyclic and aromatic compounds in excellent agreement with experimental data. 

Figure 3.9 False color image of the disjoining pressure n(x,y) in the vicinity of topographic steps [substrate in black) (a) of height 21 and (b) of height 0.51 calculated along the lines proposed in Ref. [Ill] assuming Lennard-Jones-type intermolecular interactions. Dark colors correspond to negative values of n and white to very large values of n. To a good approximation the upper part of the perimeter of the white area coincides with the contour line n[x, y) = 0.

For the modified Lennard-Jones potential (Eq. 3) Eq. 7 has to be evaluated numerically. It can, however, be simplified by considering only a purely attractive van der Waals potential. This approximation seems reasonable, since only matrix units located in the attractive part of the intermolecular potential can cause the observed red shift in pure pressure tuning experiments [11]. We obtain for the temperature-pressure shift ... 

The most important test of our bimolecular potential is its use in statistical thermodynamic models for the prediction of phase equilibria. Monovariant, three-phase pressure-temperature measurements and invariant point determinations of various gas hydrates are available and are typically used to fit parameters in molecular computations. The key component needed for phase equilibrium calculations is a model of the intermolecular potential between guest and host molecules for use in the configurational integral. Lennard-Jones and Kihara potentials are usually selected to fit the experimental dissociation pressure-temperature data using the LJD approximation (2,4,6), Although this approach is able to reproduce the experimental data well, the fitted parameters do not have any physical connection to the properties of the molecules involved. 

In Approach 1, experimental equilibrium three-phase dissociation pressure data compiled by Sloan (57), consisting of 97 points for the methane-water system from 148.8 to 320.1 K, were used in the parameter optimization. Although the fits were satisfactory, the intermolecular parameters fitted from the experimental data did not have much physical meaning (9). We also found that none of the simple potentials, including Lennard-Jones 12-6, Kihara, and optimized potential from liquid simulation (OPLS), were able to predict both... 

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