Fractional crystallization of colloids by sequential tuning of depletion forces.

Fractional crystallization is a powerful and precise separation method capable of discriminating even between molecular isomers by exploiting subtle solubility differences. While colloidal particles are inherently insoluble, they undergo crystallization and melting transitions governed by interparticle interactions, akin to molecular systems. Inspired by this molecular approach, here we show a simple thermodynamic method to separate colloidal particles by size using depletion forces. By tuning interparticle potentials to emulate Mie-type interactions, we show that particles crystallize independently when the depth of the attractive well exceeds a species-specific threshold. Due to greater excluded volume overlap, larger particles experience stronger depletion attractions, allowing them to crystallize while smaller particles stay in the fluid. Building upon this principle, we establish a sequential fractional crystallization protocol-comprising crystallization, melting, and recrystallization-that achieves fractionation of colloids with <10% size differences. Notably, when all particle species marginally exceed the crystallization threshold, they preferentially crystallize into their respective lattices to maximize coordination numbers and enthalpic gains. Under stronger attractions, particles first form kinetically arrested glassy alloys that later relax into metastable crystalline alloys without macroscopic separation.