Lennard-Jones potentials tension

The gradient model for interfacial tension described in Eqs. III-42 and III-43 is limited to interaction potentials that decay more rapidly than r. Thus it can be applied to the Lennard-Jones potential but not to a longer range interaction such as dipole-dipole interaction. Where does this limitation come from, and what does it imply for interfacial tensions of various liquids ... 

One fascinating feature of the physical chemistry of surfaces is the direct influence of intermolecular forces on interfacial phenomena. The calculation of surface tension in section III-2B, for example, is based on the Lennard-Jones potential function illustrated in Fig. III-6. The wide use of this model potential is based in physical analysis of intermolecular forces that we summarize in this chapter. In this chapter, we briefly discuss the fundamental electromagnetic forces. The electrostatic forces between charged species are covered in Chapter V. 

We proceed with the discussion of the calculation of the interfacial tensions. The interfacial tensions of the pure components can be computed by minimising Equation 2 under the constraint that the number of moles is fixed. Details on the numerical methods used to obtain the concentration profiles and inter cial tensions are given elsewhere [11]. First of all, a value for the influence parameter, c, is required. The simplest way to obtain this parameter is to use a constant value (ci c(p,T)) for all temperatures and densities. Originally van der Waals [12,1] prescribed the value that was obtained from Equation 3. But, if in this equation the attractive perturbation of the Lennard-Jones potential is substituted, the value of the interfaci tensions at low temperatures becomes almost two times higher than the experimental values [13,14]. 

That is, the surface of tension (so defined) lies about one-third oi a molecular diameter on the liquid side of the equimolar dividing surfece, and their limiting separation is, in this approximation, independent oi the index of the Lennard-Jones potential. Harasima s pressure tensor gives a value of 8 smaller by about a factor of... 

Fic. 6.S. The surface tension of argon (1), and its representation by a Lennard-Jones potential (2), by the pair potential of Barker, Fisher, and Watts (3al, and by this potential with a three-body correction (3b). 

Lennard-Jones mixture 53, 81 Lennard-Jones parameters 67, 74, 78 Lennard-Jones particle 95 Lennard-Jones potential 22-24, 34, 67, 69 Line tension 196 LiouvUle equation 142 Liquid crystal 243... 

There are many potential models that have been proposed in the Hterature. Among the popular ones that are currently enjoying widespread applications are the Lennard-Jones (LJ 12-6) equation and the Buckingham Exp-6 equation. The parameters of these equations are usually obtained by matching the theory (i.e., DFT) or simulation results (e.g., MC simulations) against various experimental properties, e.g., second virial coefficient, viscosity, vapor pressure, saturated liquid density, or surface tension, at the temperature at which the adsorption is carried out. 

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... 

In a recent study, a new model of fluids was described by using the generalized van der Waals theory. Actually, van der Waals over 100 years ago suggested that the structure and thermodynamic properties of simple fluids could be interpreted in terms of neatly separate contributions from intermolecular repulsions and attractions. A simple cubic equation of state was described for the estimation of the surface tension. The fluid was characterized by the Lennard-Jones (12-6) potential. In a recent study the dependence of surface tension of liquids on the curvature of the liquid-vapor interface has been described. ... 

This work was repeated and extended by Lee, Barkn, and Pound who used his method not only to calculate the surface profile and tension of a Lennard-Jones liquid, also to estimate the dffierence in surface ten n between diat liquid and one of a liquid with a pair potential that accuratdy represents the interaction of argon molecules, and the further difference on adding die three-body attractive forces. In this way they were able to show that the experimental surface tension of argon could be matdied to the best estimate firom an accurate pair potentiid, if proper allowanoe is made for the three-body forces ( 6.4 and Fig. 6.5). 

The main objective of this work is to show that it is possible to model a LLI, using Lennard-Jones (LJ) potential and MD simulation technique. The idea is to simulate not a realistic system but a "simple model suitable for the study of the generic properties of an interface between non miscible liquids. To do that, we have chosen the MD simulation technique and periodic boundary conditions, for a system of particles interacting via a LJ potential already used for unstable mixtures. The results show that the LLI thus obtained is stable over the simulation time scale, as indicated by the density profiles. It is also interesting to note that the interfacial tension yielded by this model is in the range of the experimental values. The model and some computational details are described in section II. The results are reported in the following part and discussed in terms of stability and spatial extension of the LLI. The paper ends with some concluding remarks. 

An advantage of a soft, coarse-grained, off-lattice model is the ability to simultaneously and accurately calculate the pressure, p, and the chemical potential, p. Abandoning the lattice-description allows a precise calculation of the pressure, p, and simulations at constant pressure or tension. This is also possible in off-lattice models with harsh excluded volume interactions (e.g., a Lennard-Jones bead-spring model). The accurate calculation of the chemical potential by particle insertion methods. 

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