Lennard-Jones potential, liquid-solid

The Morse function which is given above was obtained from a study of bonding in gaseous systems, and dris part of Swalin s derivation should probably be replaced with a Lennard-Jones potential as a better approximation. The general idea of a variable diffusion step in liquids which is more nearly akin to diffusion in gases than the earlier treatment, which was based on the notion of vacant sites as in solids, remains as a valuable suggestion. 

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... 

A useful potential in modeling the condensed states of solids or liquids is the Lennard-Jones potential... 

Statistical mechanical theory and computer simulations provide a link between the equation of state and the interatomic potential energy functions. A fluid-solid transition at high density has been inferred from computer simulations of hard spheres. A vapour-liquid phase transition also appears when an attractive component is present in the interatomic potential (e g. atoms interacting through a Lennard-Jones potential) provided the temperature lies below T, the critical temperature for this transition. This is illustrated in figure A2.3.2 where the critical point is a point of inflexion of the critical isotherm in the / - F plane. 

Lattice Energy, Lattice Vibrational Frequencies, and Intensity Ratios for Solid COj [Frequencies are in units of cm- with half-intensity widths in parentheses. Experimental frequencies and intensity ratios are those for liquid helium temperature. Calculated values are listed for two potential models (I) Lennard-Jones potential plus quadrupole-quadrupole term (Walmsley and Pople, 1964). Nearest neighbor interactions only (11) Diatomic potential with 6-12 terms (Suzuki and Schnepp, 1971). Interactions to 10 neighbor shells included.]... 

The majority of the liquid-solid simulation studies have involved simple, single-component systems in which the particles interact either with a Lennard-Jones potential (discussed in Section 4.2) or via a pairwise additive, purely repulsive inverse power potential ... 

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... 

Since Lennard-Jones (6-12) potential has been widely used for calcn of properties of matter in the gaseous, liquid, and solid states, Hirschfelder et al (Ref 8e, pp 162ff) discuss it in detail. They show that the parameters o and ( of the potential function may be determined by analysis of the second virial coefficient of the LJD equation of state... 

Benzene-benzene interactions were modeled with a Buckingham potential that was shown to yield reasonable predictions of the properties of liquid and solid benzene. Benzene-zeolite interactions were modeled by a short-range Lennard-Jones term and a long-range electrostatic term. In total, 16 benzene molecules were simulated in a unit cell of zeolite Y, corresponding to a concentration of 2 molecules per supercage. Calculations ran for 24 ps (after an initial 24-ps equilibration time) for diffusion at 300 K. 

The original Gay-Beme potential forms a nematic phase and a Smectic B phase, which is more solid like than liquid like. Ellipsoidal bodies do usually not form smectic A phases because they can easily diffuse from one layer to another layer. However, if one increases the side by side attraction it becomes possible to form smectic A phases [6]. When one calculates transport coefficients very long simulation runs are required. Therefore one sometimes re-places the Lennard-Jones core by a purely repulsive 1/r core in order to decrease the range of the potential. Thereby one decreases the number of interactions, so that the simulations become faster. The Gay-Beme potential can be generalised to biaxial bodies by forming a string of oblate ellipsoids the axes of which are parallel to each other and perpendicular to the line joining their centres of mass [35]. One can also introduce an ellipsoidal core where the three axis are different [38]. 

The first computer simulation of liquid-solid coexistence, carried out by Hiwatari et al. was the molecular dynamics study of the fee (100) surface of a system of atoms interacting through truncated Lennard-Jones repulsive potentials. Subsequent molecular dynamics studies have looked at the same interface for Lennard-Jones and repulsive potentials, at the fee (111)... 

Tanemura et al. examined crystallization in a liquid of soft spheres and found both fee and bcc structures. They used the method of Voronoi polyhedra to characterize the evolving solid clusters. Hsu and Rahman extended the use of Voronoi polyhedra in a systematic study of the effect of potential on the structure observed. They found that a model rubidium potential always crystallized to a bcc structure, while a truncated rubidium, Lennard-Jones,... 

A unique feature of H20 is the formation and sharing of hydrogen bonds with other molecules. Such bonds play a major role in determining the structure of both liquid and solid phases of H20. It is believed that for intermolecular spacings of less than 2 A, the two water molecules exert strong repulsive forces on each other. As such, there exists a hard sphere radius of little interpenetration of the molecules. Usually, the repulsive part of Lennard-Jones 6—12 potential can be considered appropriate to describe these repulsive characteristics. At distances of separation greater than 5 A, dipole-dipole interaction plays a dominant role. This is reasonable, because each H20 molecule has a large dipole moment, p = 1.84 D. 

These values were obtained by fitting experimental Henry s law constants to the theoretical expression for potentials obtained by assuming that the gas-solid interaction energy is given by a pairwise sum over the carbon atoms of Lennard-Jones (LJ) inverse 12-6 functions of separation distance [45]. From fits of experimental liquid state data to simulations of the LJ liquid [46]. 

The application of this approach to the hard-sphere system was presented by Ree and Hoover in a footnote to their paper on the hard-sphere phase diagram. They made a calculation where they used Eq. (2.27) for the solid phase and an accurate equation of state for the fluid phase to obtain results that are in very close agreement with their results from MC simulations. The LJD theory in combination with perturbation theory for the liquid state free energy has been applied to the calculation of solid-fluid equilibrium for the Lennard-Jones 12-6 potential by Henderson and Barker [138] and by Mansoori and Canfield [139]. Ross has applied a similar approch to the exp-6 potential. A similar approach was used for square well potentials by Young [140]. More recent applications have been made to nonspherical molecules [100,141] and mixtures [101,108,109,142]. 

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