2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120763We 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 $Z\lB/a\gtrsim24\pm1$, where $\lB$ is the Bjerrum length.accepted by Phys. Rev. LettSoft Condensed MatterStatistical Mechanicstext