Second virial coefficient at the critical point in a fluid of colloidal spheres plus depletants

Vliegenthart-Lekkerkerker (VL) criterion B₂ = 6v_c for second virial coefficient B₂ at the critical (colloidal) gas-liquid point is considered for a mixture of spheres with volume v_c plus depletants. For the onset of fluid-phase instability, the VL criterion holds for a wide range of shapes of direct attractive forces between hard-core spheres (Vliegenthart, G. A.; Lekkerkerker, H. N. W. J. Chem. Phys. 2000, 112, 5364). In the case of long-ranged attractions imposed indirectly via depletants, it is found that the VL relation fails. Instead, B₂/v_c at the critical point depends strongly on the sphere/depletant size ratio. By making the hard spheres sticky, we find that B₂ moves gradually toward the VL criterion upon increasing the stickiness.