The extended law of corresponding states when attractions meet repulsions

Short-range attractive colloids show well-defined phase behaviour in the absence of repulsions, and highly intriguing equilibrium gelation in the presence of long-range repulsions. We present the state diagram of short-range attractive colloids with repulsions that range from fully screened to intermediately ranged, i.e. longer-ranged than the attractions, but shorter ranged than the colloid size. We demonstrate that although the macroscopic phase behaviour does not change perceptibly, there is a dramatic increase of inhomogeneities once the repulsions become longer-ranged than the attractions. The interaction potentials are characterized with small angle neutron scattering, and used to renormalize the state diagram with the minimum in the interaction potential, min[U(r)], and with the reduced second virial coefficient, B2*. We find that the extended law of corresponding states captures the onset of phase separation for shorter ranged repulsions, but fails for longer ranged repulsions. Instead, for a given model of U(r), the transition from visually homogeneous fluid to phase separation and/or gelation can be rescaled with min[U(r)] over the full range of repulsions. Finally, we suggest a generic state diagram to describe the effect of repulsions on short-range attractive systems.