Fluid Axilrod-Teller

Figure 3. Comparison of z-component of two-(2B) and three-body (3B) forces on particle 27 in conventional molecular dynamics simulation of Lennard-fones plus Axilrod-Teller fluid. At — time step = 2.15 (10 ) sec, pa = 0.65, kT " = 1.033. Note that the scale for three-body force is an order of magnitude smaller than that for the two-body force.

In Figure 5 the radial distribution functions for the Lennard-Jones and Lennard-Jones plus Axilrod-Teller fluids are compared at the high density state condition. It appears that the three body interactions have no effect except in the first peak region where the triplet interactions lower g(r) by about 3%. However, we estimate the statistical error in g(r) for these simulations is about +3%, so it is unclear to what extent the observed effect is real. We note that Schommers has reported small three body effects on the distribution function for the two dimensional fluid, as well (16). However, the perturbation theory calcula-... 

Figure 5. Effect of Axilrod-Teller potential on radial distribution function at = 0.817. For Lennard-Jones fluid, kT< = 0.746 for Lennard-Jones plus Axilrod-Teller fluid, kTr = 0.740.

Figure 6. Comparison of trajectories of particle 27 in Lennard- ones and Len-nard-Jones plus Axilrod-Teller fluids at pa = 0.65. Both runs were started from the same point in phase space and trajectories shown are from time steps 500-2000 in each simulation. For this calculation the Axilrod-Teller strength constant V was assigned a value of three times that for argon given in Section 2. Note that the circles represent positions of the center of mass of the atom, not the atomic diameter.

Little is known concerning three body contributions to dynamic fluid properties. Fisher and Watts have calculated the self diffusion coefficient using the BFW pair potential without including the Axilrod-Teller interaction and obtained results similar to those for a Lennard-Jones fluid at the same densities (23). Schommers two dimensional Lennard-Jones plus Axllrod Teller simulations show significant three body effects on the velocity autocorrelation function however, the two dimensional self diffusion coefficient is little affected (16). Schommers is careful to point out, however, that results found in two-dimensional fluids do not necessarily extrapolate to three dimensions. 

Little study has been made of nonaddltlve effects in fluids composed of nonspherlcal molecules. Singh and coworkers have developed a thermodynamic perturbation theory for this purpose (24. 25). Stogryn has given the analog of the Axilrod-Teller potential for nonspherlcal molecules (26). 

This section reports the results obtained from two self-consistent schemes that have been extended to deal with the triple-dipole interaction, which reduces to a state-dependent effective pair potential. The pair potential of Aziz and Slaman [106] (AS) is combined with the Axilrod and Teller [108] (AT) triple-dipole potential to describe the interactions in Xe and Kr fluids. Note that other investigations have been performed with ab initio potentials [113, 114]. 

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