  Fractionation is necessary for self-assembly in multicomponent mixtures.
Here, reversible fractionation and crystallization are realized and studied in
a two-dimensional binary colloids which is supersaturated by enhancing the
attraction between colloidal particles. As a deep and fast supersaturation
results in gels with a uniform distribution of binary particles, a gradual
quasistatic supersaturating process leads to a two-step crystallization in
which small particles and large particles are fractionated as coexisting
crystal and liquid phases respectively. Fractionation occurs as well in the
quasistatic melting of gel. We show that the synchronized fractionation and
phase separation arises from the competition between the size-dependent
repulsion and the tunable attraction. The results in this study demonstrate a
robust mechanism of fractionation via phase separation, and have important
implication in understanding the reversible formation of membraneless
organelles in living cells.
