Nonlinear screening and gas-liquid separation in suspensions of charged colloids

We calculate phase diagrams of charged colloidal spheres (valency $Z$ and radius $a$) in a 1:1 electrolyte from multi-centered nonlinear Poisson-Boltzmann theory. Our theory takes into account charge-renormalization of the colloidal interactions and volume terms due to many-body effects. For valencies as small as Z=1 and as large as ${10}^4$ we find a gas–liquid spinodal instability in the colloid-salt phase diagram provided $Z\text{lB}\mathrm{/}a\gtrsim 24\pm 1$, where $\text{lB}$ is the Bjerrum length.