Interdisciplinary Applied Mathematics

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Pairwise Intermolecular Potentials

In many atomistic simulations, it is sufficient to use the simplest models to represent the essential physics, and many pairwise (two-body) potentials have been proposed (Maitland et al., 1981). Typically, these potentials are parameterized such that the simulations based on them can reproduce certain experimental measurements, e.g., the second virial coefficient, diffusion coefficient, and viscosity of a certain material (Sadus, 1999). Here we outline some of the most commonly used pairwise intermolecular potentials. Unless mentioned otherwise, r denotes the distance between the two particles interacting via the pairwise intermolecular potentials.

1. Square-Well Potential. The square-well potentials is one of the simplest intermolecular potentials that is capable of representing the properties of liquids (Sadus, 1999). It is given by

where A is some multiple of the hard-sphere diameter (a) and e is a measure of the attractive interaction. This potential belongs to the genre of “hard-sphere + attractive term” potentials. In the “hard-sphere” potential (Allen and Tildesley, 1994) the atoms are approximated as impenetrable hard spheres. The properties of the square-well fluid have been investigated widely (Haile, 1992), and it remains a useful    starting    point    for    the    development    of    liquid    state    theories

(Yuste and Santos, 1994).

2. Yukawa Potential. Considerable interest has been demonstrated in simulating the properties of atoms interacting via the hard-sphere Yukawa potential (Frenkel and Smit, 2002; Rudisill and Cummings, 1989; Rosenfeld, 1993; Kalyuzhnyi and Cummings, 1996), which is described by

ioo,    r < a,

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