A Case Study of Sedimentation of Charged Colloids: The Primitive Model and the Effective One-Component Approach

TL;DR

This study compares theoretical and simulation approaches to sedimentation profiles of charge-stabilized colloids, revealing that effective one-component models can accurately replicate multi-component models, but Poisson-Boltzmann theory has limitations due to correlation effects.

Contribution

It demonstrates that effective one-component models can match multi-component models in sedimentation studies, highlighting the limitations of Poisson-Boltzmann theory in certain regimes.

Findings

Effective one-component models agree with multi-component simulations.

Poisson-Boltzmann theory matches effective models with adjusted charge.

Correlations are poorly treated in Poisson-Boltzmann approximation.

Abstract

Sedimentation-diffusion equilibrium density profiles of suspensions of charge-stabilized colloids are calculated theoretically and by Monte Carlo simulation, both for a one-component model of colloidal particles interacting through pairwise screened-Coulomb repulsions and for a three-component model of colloids, cations, and anions with unscreened-Coulomb interactions. We focus on a state point for which experimental measurements are available [C.P. Royall et al., J. Phys.: Cond. Matt. {\bf 17}, 2315 (2005)]. Despite the apparently different picture that emerges from the one- and three-component model (repelling colloids pushing each other to high altitude in the former, versus a self-generated electric field that pushes the colloids up in the latter), we find similar colloidal density profiles for both models from theory as well as simulation, thereby suggesting that these pictures represent different view points of the same phenomenon. The sedimentation profiles obtained from an effective one-component model by MC simulations and theory, together with MC simulations of the multi-component primitive model are consistent among themselves, but differ quantitatively from the results of a theoretical multi-component description at the Poisson-Boltzmann level. We find that for small and moderate colloid charge the Poisson-Boltzmann theory gives profiles in excellent agreement with the effective one-component theory if a smaller effective charge is used. We attribute this discrepancy to the poor treatment of correlations in the Poisson-Boltzmann theory.