On the possibility of extending the Noro-Frenkel generalized law of correspondent states to nonisotropic patchy interactions

Colloidal systems (and protein solutions) are often characterized by attractive interactions whose ranges are much smaller than the particle size. When this is the case and the interaction is spherical, systems obey a generalized law of correspondent states (GLCS), first proposed by Noro and Frenkel (Noro, M. G.; Frenkel, D. J. Chem. Phys. 2000, 113, 2941). The thermodynamic properties become insensitive to the details of the potential, depending only on the value of the second virial coefficient B-2 and the density rho. The GLCS does not generically hold for the case of nonspherical potentials. In this Letter, we suggest that when particles interact via short-ranged small-angular amplitude patchy interactions (so that the condition of only one bond per patch is fulfilled), it is still possible to generalize the GLCS close to the liquid-gas critical point.