Impurity partitioning during colloidal crystallization

We have found that an impurity partitioning takes place during growth of colloidal crystals, which was recognized by the fact that the impurity concentration in the solid (C_S) was different from that in the initial solution (C₀). The effective partition coefficient k _eff (=C_S/C₀) was investigated for pure polystyrene and polystyrene dyed with fluorescent particles by changing the ratio of particle diameters d_imp/d_cryst and growth rate V. At each size ratio for the polystyrene impurity, k_eff was less than unity and increased to unity with increasing V, whereas at a given growth rate, k_eff increased to unity as d_imp/d_cryst approached unity. These results were consistent with the solute behavior analyzed using the Burton, Prim, and Slichter (BPS) model. The obtained k ₀, equilibrium partition coefficient, from a BPS plot increased as d_imp/d_cryst approached unity. In contrast, while the fluorescent particles also followed the BPS model, they showed higher k ₀ values than those of the same size of polystyrene particles. A k₀ value greater than unity was obtained for impurities that were similar in size to the host particle. This behavior is attributed to the positive free energy of fusion associated with the incorporation of the fluorescent particles into the host matrix. Such positive free energy of fusion implies the presence of the enthalpy associated with interaction between particles.