  The performance of graphene oxide(GO)-based materials strongly depends on the
lateral size and size distribution of GO nanosheets. Various methods are
employed to prepare GO nanosheets with a narrow size distribution. One of the
promising method was proposed recently by directionally freezing of a GO
aqueous dispersion at a controlled growth rate of the freezing front. We
develop a theoretic model of binary colloids suspension, incorporating both the
moving freezing boundary and the preferential adsorption of colloidal particles
to the ice phase. We numerically solve the coupled diffusion equations and
present state diagrams of size fractionation. Selective trapping of colloids
according to their size can be achieved by a suitable choice of the
experimental parameters, such as the adsorption rates and the freezing speed.
