Weeks-Chandler-Andersen fluid

At this stage, undiscutable data, external of the IETs, were necessarily required to shed some light on these peculiar behaviors, which provides exact reference data for more realistic potentials. First, Nicolas et al. [33] derived an EOS for the Lennard-Jones fluid and Johnson et al. [34] provided MD results for the classical thermodynamic quantities. Notice that Heyes and Okumura [35] recently derived an EOS of the Weeks-Chandler-Andersen fluid. 

Figure 19 Shear-induced microstructure in a Weeks-Chandler-Andersen fluid of 500 particles under low shear (T = 0.722, p = 0.844, and y = 0.6). The unit of length is the WCA potential a. The direction of flow (x) is out of the page, and the particles are projected on the yz plane.

Figure 20 The Weeks-Chandler-Andersen fluid under high shear (T = 0.722, p 0.844, y = 3.0) outlines of hexagonal structure are used to guide the eye.

As we have already pointed out, the theoretical basis of free energy calculations were laid a long time ago [1,4,5], but, quite understandably, had to wait for sufficient computational capabilities to be applied to molecular systems of interest to the chemist, the physicist, and the biologist. In the meantime, these calculations were the domain of analytical theories. The most useful in practice were perturbation theories of dense liquids. In the Barker-Henderson theory [13], the reference state was chosen to be a hard-sphere fluid. The subsequent Weeks-Chandler-Andersen theory [14] differed from the Barker-Henderson approach by dividing the intermolecular potential such that its unperturbed and perturbed parts were associated with repulsive and attractive forces, respectively. This division yields slower variation of the perturbation term with intermolecular separation and, consequently, faster convergence of the perturbation series than the division employed by Barker and Henderson. 

To address this, Liem, Brown, and Clarke ° simulated in excess of 40,000 particles interacting via a Weeks-Chandler-Andersen (WCA) potential. While the x and z directions were treated normally, the y direction was divided into three regions two atomistic walls separated by a fluid region. The walls consisted of three hexagonally close-packed layers of particles. The wall atoms interacted with the fluid particles and with each other through the same WCA potential used for the fluid-fluid interactions. Additionally, each wall particle felt a harmonic potential centered at its triangular lattice site. This setup allowed heat transfer from the fluid to the wall while allowing the wall to remain crystalline. The momenta of the wall particles were rescaled to keep the total... 

H. C. Andersen, D. Chandler, and J. D. Weeks, Optimized cluster expansions for clasacal fluids. III Application to ionic solutions and sim(de liquids, J. Chem. Phys. 57, 2626-2631 (1972), and references cited therein. 

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