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

Abstract

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.