Hard sphere fluids machine

Fig. 12. Comparison of the theoretical equation of state with machine computations for a two-dimensional hard sphere fluid.

We have already in this and the previous sections made a number of comparisons between the various theories of fluids and the machine computations for the hard sphere system. Unfortunately, many recent developments in theory have been evaluated numerically only to the extent that the fourth and fifth virial coefficients can be compared. The table below lists the values of the fourth and fifth virial coefficients for the three-dimensional hard sphere fluid in units of the second virial coefficient b [cf. Eq. (33)]. The bases of calculation have been identified already in Section III except for the older "netted-chain approximation of Rushbrooke and Scoins. ... 

The CS pressures are close to the machine calculations in the fluid phase, and are bracketed by the pressures from the virial and compressibility equations using the PY approximation. Computer simulations show a fluid-solid phase transition tiiat is not reproduced by any of these equations of state. The theory has been extended to mixtures of hard spheres with additive diameters by Lebowitz [35], Lebowitz and Rowlinson [35], and Baxter [36]. 

Hard sphere theories can be compared in a special sense with "experiment . This is not because any real substance possesses a fluid phase which over its whole existence region could be adequately described by this simple model. The "experimental data, rather, are the result of extensive machine calculations of the equation of state of large collections of hard spheres undertaken by Alder and Wainwright and Wood, Parker, and Jacobson, among others. 

These machine calculations provide what is essentially exact information on the consequences of a given intermolecular force law. Application has been made to hard spheres and hard disks, to particles interacting through a Lenard-Jones 12-6 potential function and other continuous potentials of interest in the study of simple fluids, and to systems of charged particles [123]. 

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