Many-body attractions do not stabilize gas-liquid phase separation in aqueous dispersions of charged colloids within the Poisson-Boltzmann framework.

Attractive three-body interactions have been reported for like-charged colloids in low-salt suspensions, based on both finite-element Poisson-Boltzmann calculations and direct experimental measurements, and have been proposed as a mechanism to drive colloidal clustering. However, these Poisson-Boltzmann calculations typically neglect charge regulation and higher-order many-body effects. Here, we construct machine-learned many-body interaction potentials for charge-regulating colloids, trained on finite-element Poisson-Boltzmann calculations, to accurately capture three-body and higher-order contributions. We find that the three-body contribution to the many-body potential as obtained from Poisson-Boltzmann calculations on isolated colloid triplets is strongly attractive, consistent with previous work, whereas the four-body contribution for an equilateral pyramid configuration of four colloids is repulsive. We then construct machine-learned many-body potentials for charged colloids using finite-element Poisson-Boltzmann calculations on clusters of 13 colloids, and find that the incorporation of higher-body interactions weakens the cohesive nature of the interactions. We identify a parameter regime exhibiting gas-liquid or gas-solid phase separation using the machine-learned potentials in molecular dynamics simulations. However, when we include clusters of 48 colloids in the training data, the cohesion diminishes further, and molecular dynamics simulations using these potentials no longer include broad phase separation in aqueous dispersions of charged colloids. Finally, we compute the potential of mean force of pairs, triplets and quartets of colloids using primitive model simulations. We find that the resulting potentials are in good agreement with those obtained from the Poisson-Boltzmann calculations, thereby supporting the validity of the Poisson-Boltzmann approach for determining many-body interactions.