Looking for a compact semi empirical equation of state for hard spheres and the possibility of a glassy transition

The equation of state of a hard sphere fluid at high density should exhibit a simple pole at the random close packing limit. Here we show that trying to obtain a compact semi-empirical equation of state simultaneously compatible with that asymptotic behaviour and with the known virial coefficients raises an analytical difficulty which can be solved if a glassy transition occurs in the disordered metastable phase at a density intermediate between the freezing point and the random close packing limit. The comparison of the estimated value for the transition point with earlier estimations suggests a more subtle situation. •Elaboration of a semi-empirical equation of state for disordered hard sphere systems.•Analytical difficulty attributed to a glassy transition between freezing and rcp.•Comparison with earlier estimations of the transition point suggests a more subtle situation.•Possibility of two successive phase transitions.•Suggested identification of the glassy phase with random loose packing.