We study suspensions of colloidal spheres with a constant zeta-potential within Poisson-Boltzmann theory, quantifying the discharging of the spheres with increasing colloid density and decreasing salt concentration. We use the calculated renormalized charge of the colloids to determine their pairwise effective screened-Coulomb repulsions. Bulk phase diagrams in the colloid concentration-salt concentration representation follow, for various zeta-potentials, by a mapping onto published fits of phase boundaries of point-Yukawa systems. Although the resulting phase diagrams do feature face-centered cubic and body-centered cubic phases, they are dominated by the (re-entrant) fluid phase due to the colloidal discharging with increasing colloid concentration and decreasing salt concentration.
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