Hard sphere adhesive state

Using the hard sphere adhesive state equation proposed by Baxter (16), it is possible to calculate the demixing line due to interactions. This state equation corresponds to the exact solution of the Percus-Yevick equation in the case of an hard sphere potential with an infinitively thin attractive square well. In our calculation we assum that the range of the potential is short in comparison to the size of the particles (in fact less than 10 %). 

The equation of state and free energy of a system of hard spheres with surface adhesion are calculated from the internal energy of the fluid as given by the Percus-Yevick theory. A first-order phase change occurs. Further, the liquid-vapor coexistence curve, which cannot be found by the more usual routes to the equation of state, is calculated. It is found that the equation of state exhibits van der Waals type sigmoid isotherms in the region in which the Percus-Yevick theory has solutions. 

It has been shown that for a system of hard spheres with surface adhesion that, in the PY approximation, the equation of state can be obtained from the energy equation and that the resulting thermodynamic properties show typical van der Waals behavior. The critical temperature and density are considerably higher than those obtained from the compressibility equation. 

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