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Thermodynamic properties of charge-stabilised colloidal suspensions arecommonly modeled by implementing the mean-field Poisson-Boltzmann (PB) theorywithin a cell model. This approach models a bulk system by a single macroion,together with counterions and salt ions, confined to a symmetrically shaped,electroneutral cell. While easing solution of the nonlinear PB equation, thecell model neglects microion-induced correlations between macroions, precludingmodeling of macroion ordering phenomena. An alternative approach, avoidingartificial constraints of cell geometry, maps a macroion-microion mixture ontoa one-component model of pseudo-macroions governed by effective interactions.In practice, effective-interaction models are usually based on linear screeningapproximations, which can accurately describe nonlinear screening only byincorporating an effective (renormalized) macroion charge. Combining chargerenormalization and linearized PB theories, in both the cell model and aneffective-interaction (cell-free) model, we compute osmotic pressures of highlycharged colloids and monovalent microions over a range of concentrations. Bycomparing predictions with primitive model simulation data for salt-freesuspensions, and with predictions of nonlinear PB theory for salty suspensions,we chart the limits of both the cell model and linear-screening approximationsin modeling bulk thermodynamic properties. Up to moderately strongelectrostatic couplings, the cell model proves accurate in predicting osmoticpressures of deionized suspensions. With increasing salt concentration,however, the relative contribution of macroion interactions grows, leadingpredictions of the cell and effective-interaction models to deviate. Noevidence is found for a liquid-vapour phase instability driven by monovalentmicroions. These results may guide applications of PB theory to soft materials.

Poisson-Boltzmann Theory of Charged Colloids: Limits of the Cell Model for Salty Suspensions