Lennard-Jones interfaces

This lack of sensitivity of the diffusion width to the orientation of the interface has also been seen in the Lennard-Jones interfaces (discussed in the next section). 

Two simulation methods—Monte Carlo and molecular dynamics—allow calculation of the density profile and pressure difference of Eq. III-44 across the vapor-liquid interface [64, 65]. In the former method, the initial system consists of N molecules in assumed positions. An intermolecule potential function is chosen, such as the Lennard-Jones potential, and the positions are randomly varied until the energy of the system is at a minimum. The resulting configuration is taken to be the equilibrium one. In the molecular dynamics approach, the N molecules are given initial positions and velocities and the equations of motion are solved to follow the ensuing collisions until the set shows constant time-average thermodynamic properties. Both methods are computer intensive yet widely used. 

Molecular dynamics calculations have been made on atomic crystals using a Lennard-Jones potential. These have to be done near the melting point in order for the iterations not to be too lengthy and have yielded density functioi). as one passes through the solid-vapor interface (see Ref. 45). The calculations showed considerable mobility in the surface region, amounting to the presence of a... 

Molecular dynamics and density functional theory studies (see Section IX-2) of the Lennard-Jones 6-12 system determine the interfacial tension for the solid-liquid and solid-vapor interfaces [47-49]. The dimensionless interfacial tension ya /kT, where a is the Lennard-Jones molecular size, increases from about 0.83 for the solid-liquid interface to 2.38 for the solid-vapor at the triple point [49], reflecting the large energy associated with a solid-vapor interface. 

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]. 

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... 

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]. 

The elasticity can be related to very different contributions to the energy of the interface. It includes classical and nonclassical (exchange, correlation) electrostatic interactions in ion-electron systems, entropic effects, Lennard-Jones and van der Waals-type interactions between solvent molecules and electrode, etc. Therefore, use of the macroscopic term should not hide its relation to microscopic reality. On the other hand, microscopic behavior could be much richer than the predictions of such simplified electroelastic models. Some of these differences will be discussed below. 

One of the first studies of multiple ions at the water/solid interface was by Spohr and Heinzinger, who carried out a simulation of a system of 8 Li" and 81" ions dissolved in 200 water molecules between uncharged flat Lennard-Jones walls.However, the issues discussed in their paper involved water structure and dynamics and the single-ion properties mentioned earlier. No attempt was made to consider the ions distributions and ion-ion correlations. This work has recently been repeated using more realistic water-metal potentials. ... 

Molecular dynamics has been used extensively to explore the solid-liquid interface. In one such study, a modified Lennard-Jones potential has been used to model this interaction in the spreading of a droplet [4], of the form... 

Ve see in Figure 7 that Tolman s representation of the radially dependent surface tension also leads to a vanishing thermodynamic barrier, at high but metastable supersaturations, when a value of 6 computed from solutions of the YBG equation on the planar interface is used. This value of the Tolman parameter is consistent with values obtained from simulation studies of the planar Lennard-Jones surface (28,29). It is apparent that the physical picture of nucleation is highly dependent upon the assumed radial dependence of the surface tension. 

The important advances in adsorption technology made possible by the BET theory (S, 4) clearly justify Model 1 in many applications. But one of the Models 2, 3, or 4 is apparently required for first-layer adsorption in a Type II isotherm. That an important condensation potential at the solid-gas interface is the Lennard-Jones 3-9 potential now seems well established (3, 7, 9, 10, 15). Equally clear is the fact that this potential is not solely responsible for physical adsorption the type of surface polarization predicted by the theory of structural adsorption (10) has been demonstrated by observed changes due to adsorption in linear... 

To illustrate the SS-LMBW methodology, we calculated the stractuie of the planar liquid/vapour as well as liquid/liquid interfaces of non-polar and polar molecular fluids hexane and methanol at ambient conditions. The site-site interaction potentials to appear in the closure (7) were specified in the form comprising the Coulomb and 12-6 Lennard-Jones terms,... 

Consider fluid of particles interacting through the Lennard-Jones potential y>(r) = 4e[(energy parameters cylindrical coordinates and position the interface in the plane z = 0. The lOZ equation has the form [15]... 

FIGURE 5.9. Reduced density profiles of the planar liquid/vapour interface of the Lennard-Jones fluid, obtained from the lOZ-KH/LMBW theory at reduced temperature T = ksT/s = 0.725, 0.825, 0.925, 1.000, 1.050, 1.075. Bolder lines correspond to lower temperatures. 

FIGURE 5.10. Sections of the inhomogeneous two-particle distribution function g(s, zi, Z2> of the Lennard-Jones fluid along the liquid/vapour interface for reduced temperature T = 1.15 at the distance z = Z = Z2 = -lOcr 0 -HOct from the interface, respectively in the vapour phase (thin solid line) at the interface (bold solid line) and in the liquid phase (dashed line). Predictions of the lOZ-KHM/LMBW theory. 

FIGURE 5.11. Sections of the inhomogeneous two-paiticle direct conelation function c(s, z, zi) of the Lennard-Jones fluid along the liquid/vapour interface (part a), and its Hankel transform c(p, zt,zz) (ptut b). Line nomenclature is the same as in Figure 5.10. Results of die lOZ-KHM/LMBW theory. The inset in part a zooms in the long-range tail of c(s, Zi,Z2) with the asynqitodcs (47). 

As a modep) we assume an ideal infinite pore with radius a (fig. 1.32a). The liquid in the pore is not identical to that of the bulk because it is influenced by the interaction with the wall. The molar energy depends in some way on the distance to the wall, say = U r). e.g. according to a Lennard-Jones relationship. The pressure difference across the interface is given by the Laplace equation... 

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