Relative stability of the FCC and HCP polymorphs with interacting polymers

Recent work [Mahynski et al., Nat. Commun., 2014, 5, 4472] has demonstrated that the addition of long linear homopolymers thermodynamically biases crystallizing hard-sphere colloids to produce the hexagonal close-packed (HCP) polymorph over the closely related face-centered cubic (FCC) structure when the polymers and colloids are purely repulsive. In this report, we investigate the effects of thermal interactions on each crystal polymorph to explore the possibility of stabilizing the FCC crystal structure over the HCP. We find that the HCP polymorph remains at least as stable as its FCC counterpart across the entire range of interactions we explored, where interactions were quantified by the reduced second virial coefficient, -1.50 < B∗2 < 1.01. This metric conveniently characterizes the crossover from entropically to energetically dominated systems at B∗2 ≈ 0. While the HCP relies on its octahedral void arrangement for enhanced stability when B∗2 > 0, its tetrahedral voids produce a similar effect when B∗2 < 0 (i.e. when energetics dominate). Starting from this, we derive a mean-field expression for the free energy of an infinitely-dilute polymer adsorbed in the crystal phase for nonzero B∗2. Our results reveal that co-solute biasing of a single polymorph can still be observed in experimentally realizable scenarios when the colloids and polymers have attractive interactions, and provide a possible explanation for the experimental finding that pure FCC crystals are elusive in these binary mixtures.