Fluids of dimerizing hard spheres, and fluid mixtures of hard spheres and dispheres

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Abstract
We continue the study of a fluid of hard spheres which contain an off‐center attraction site, with the range of attraction restricted so that dimers, but no higher s‐mers can be formed. Two approximations, an integral equation and a version of thermodynamic perturbation theory, were previously found to perform well when tested against Monte Carlo simulations. Here, the limit in which the attraction becomes an infinitely strong glue spot of infinitesimal extent is evaluated analytically for the two theories. The resulting equation of state may be identified with the equation of state of a mixture of hard spheres and hard dispheres. In the limit of complete dimerization the system is equivalent to a one‐component fluid of hard dispheres. The equation of state of hard dispheres, known from Monte Carlo simulations, is accurately represented by the Tildesley–Streett (TS) fitting function. In the pure disphere limit, our version of thermodynamic perturbation theory predicts an equation of state which is numerically almost indistinguishable from the TS fitting function. For the integral equation, the disphere limit of the compressibility equation of state is also very good, showing a maximum deviation from the TS fitting function of 2% over the density range of the simulations. The virial equation of state is much less satisfactory, with the deviation rising to 15% at the highest density.