Machine-learned many-body potentials for charged colloids reveal gas–liquid spinodal instabilities only in the strong-coupling regime of primitive models

Past experimental observations of gas-liquid and gas-crystal coexistence in low-salinity suspensions of highly charged colloids have suggested the existence of like-charge attraction. Evidence for this phenomenon was also observed in primitive-model simulations of (asymmetric) electrolytes and of low-charge nanoparticle dispersions. These results from low-valency simulations have often been extrapolated to experimental parameter regimes of high colloid valency, where like-charge attraction between colloids has been reported. However, direct simulations of highly charged colloids remain computationally demanding. To circumvent slow equilibration, we employ a machine-learning (ML) framework to construct ML potentials that accurately describe the effective colloid interactions. Our ML potentials enable fast simulations of dispersions and successfully reproduce the gas-liquid and gas-solid phase separation observed in primitive-model simulations at low charge numbers. Extending the ML-based simulations to higher valencies, where primitive-model simulations become prohibitively slow, also reveals like-charge attractions and gas-liquid spinodal instabilities, however, only in the regime of strongly coupled electrostatic interactions and not in the weakly coupled Poisson-Boltzmann regime of the experimental observations of colloidal like-charge attractions.