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The equation of state of a hard sphere fluid at high density should exhibit asimple pole at the random close packing limit. Here we show that trying toobtain a compact semi-empirical equation of state simultaneously compatiblewith that asymptotic behaviour and with the known virial coefficients raises ananalytical difficulty which can be solved if a glassy transition occurs in thedisordered metastable phase at a density intermediate between the freezingpoint and the random close packing limit, numerically close to the meltingpoint. The estimated value for the transition point, which is identified withrandom loose packing, is in good agreement with earlier estimations.

Looking for a compact semi empirical equation of state for hard spheres: possibility of a glassy transition and random loose packing