Virial coefficients of Onsager crosses

Onsager crosses are particles formed by rigidly connecting three perpendicular, elongated rods of length L and diameter D. We have investigated the behaviour of the virial coefficients of Onsager crosses as a function of the aspect ratio L/D of the rods. The interest in these particles stems from the fact that they should exhibit a cubatic liquid crystalline phase in the limit (L/D)-> ¥. It is shown that in order for the theory predicting this phase to be strictly valid, the rod aspect ratio should be extremely large L/D³1000.).