Lennard-Jones potential, interfacial

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. 

The behavior of insoluble monolayers at the hydrocarbon-water interface has been studied to some extent. In general, a values for straight-chain acids and alcohols are greater at a given film pressure than if spread at the water-air interface. This is perhaps to be expected since the nonpolar phase should tend to reduce the cohesion between the hydrocarbon tails. See Ref. 91 for early reviews. Takenaka [92] has reported polarized resonance Raman spectra for an azo dye monolayer at the CCl4-water interface some conclusions as to orientation were possible. A mean-held theory based on Lennard-Jones potentials has been used to model an amphiphile at an oil-water interface one conclusion was that the depth of the interfacial region can be relatively large [93]. 

Surface Potentials. Consider the form of the surface-water Interaction potential for an interfacial system with a hydrophobic surface. The oxygen atom of any water molecule is acted upon by an explicitly uncharged surface directly below it via the Lennard-Jones potential (U j) ... 

Extension of more advanced methods, in particular, density functional theory, to non-equilibrium phenomena is the principal aim of this survey. We shall consider a simple one-component fluid with van der Waals interactions as a suitable medium for exploration of basic theoretical problems of interfacial dynamics. In the case when intermolecular interactions are long-range, in particular, in the most important case of Lennard-Jones potential, the transformation from the nonlocal (density functional) to local (van der Waals-Landau-Cahn) equations fails due to divergences appearing in the commonly used expansion of the interaction term in the expression for free energy. Setting bound-... 

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]. 

What is now required are closed expressions for the first and second order contributions of a pure fluid. To this end, we employ a theory that we have recently applied successfully to study both bulk [238] and interfacial properties [99], This theory is based on a perturbation expansion proposed recently for the Lennard-Jones potential [299]. Although the expressions are obtained in a closed analytical form, they are rather lengthy and we refer the reader to the original paper for further details [238]. 

Because, in reality, intermolecular interactions determine both the meehani-cal properties and the interfacial energies at various interfaees, reeent advanees have been made to construct adhesion models by assuming that partiele and substrates interact through particular potentials (e.g., a Lennard-Jones potential 84). These models take into account observations that ean be made by using atomie force techniques. For example, when a particle comes elose to a surface the attrae-... 

The first MC (16) and MD (17) studies were used to simulate the properties of single particle fluids. Although the basic MC (11,12) and MD (12,13) methods have changed little since the earliest simulations, the systems simulated have continually increased in complexity. The ability to simulate complex interfacial systems has resulted partly from improvements in simulation algorithms (15,18) or in the interaction potentials used to model solid surfaces (19). The major reason, however, for this ability has resulted from the increasing sophistication of the interaction potentials used to model liquid-liquid interactions. These advances have involved the use of the following potentials Lennard-Jones 12-6 (20), Rowlinson (21), BNS... 

The above forms for the Lennard-Jones surface-water interaction potential have been used as models of hydrophobic surfaces such as pyrophyl1ite, graphite, or paraffin. If the intention of the study, however, is to understand interfacial processes at mineral surfaces representative of smectites or mica, explicit electrostatic interactions betweeen water molecules and localized charges at the surface become important. 

Lennard-Jones and inverse-power repulsive potentials (Davidchack and Laird, 2005). Using these simulations, they were further able to show how both the magnitude and anisotropy in the surface or interfacial energy scale with potential. 

Recently, detailed molecular pictures of the interfacial structure on the time and distance scales of the ion-crossing event, as well as of ion transfer dynamics, have been provided by Benjamin s molecular dynamics computer simulations [71, 75, 128, 136]. The system studied [71, 75, 136] included 343 water molecules and 108 1,2-dichloroethane molecules, which were separately equilibrated in two liquid slabs, and then brought into contact to form a box about 4 nm long and of cross-section 2.17 nmx2.17 nm. In a previous study [128], the dynamics of ion transfer were studied in a system including 256 polar and 256 nonpolar diatomic molecules. Solvent-solvent and ion-solvent interactions were described with standard potential functions, comprising coulombic and Lennard-Jones 6-12 pairwise potentials for electrostatic and nonbonded interactions, respectively. While in the first study [128] the intramolecular bond vibration of both polar and nonpolar solvent molecules was modeled as a harmonic oscillator, the next studies [71,75,136] used a more advanced model [137] for water and a four-atom model, with a united atom for each of two... 

The interface between two nonpolar atomic solvents interacting through Lennard-Jones-type potentials has been studied [41] diffusion in the interfacial region was found to be anisotropic. 

In covalent bonds between like atoms, the electrons are shared between the two atoms and there is accumulation of electrons in the space between the two atoms. The potential energy function for covalent bonds is often quite well represented by a Lennard-Jones function. Covalent bonds can bridge an interface, and in this case one may consider the interfacial region as a distinct phase. When two atoms have different degrees of electronegativity, the bond between them will have partial ionic character. If the atomic orbitals of the two atoms overlap, the bond will also have partial covalent character. 

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. 

Fig. 5.8. Phase diagram for three growth modes layer-by-layer, Volmer-Weber and Stranski-Krastanov, as a function of the interfacial coupling W and the lattice misfit parameter r] between the deposit and the substrate. The phase limits denoted FCC (face centred cubic) and DC (diamond cubic) correspond to the use of Lennard-Jones and Stillinger-Weber potentials, respectively. The layer-by-layer growth mode is restricted to the axis r] = 0 in the region W > I (after Grabow and Gilmer, 1988).

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