Stabilizing colloidal crystals by leveraging void distributions

Abstract

Colloids often crystallize into polymorphic structures, which are only separated by marginal differences in free energy. Due to this fact, the face-centred cubic and hexagonal close-packed hard-sphere morphologies, for example, usually crystallize simultaneously from a supersaturated solution. The resulting lack of long-range order in these polymorphic structures has been a significant barrier to the widespread application of these crystals in, for instance, photonic bandgap materials. Here, we report a simple method to stabilize one out of two competing polymorphs by exploiting the fact that they have significantly different spatial distributions of voids. We use a variety of polymeric additives whose geometries can be tuned such that their entropy loss, which is related to crystal void symmetries, is different in the two competing polymorphs. This, in turn, controls which polymorph is most thermodynamically stable, providing a generalizable means to stabilize a selected crystal polymorph from a suite of competing structures.

Fluid–fluid coexistence in an athermal colloid–polymer mixture: thermodynamic perturbation theory and continuum molecular-dynamics simulation

“…Although these authors examined the phase transitions in the system, these were of solid-fluid nature (rather than fluid-fluid), except when monomeric LJ particles were used as solvent in place of the polymers. Also of particular relevance to our current study is the series of papers by Panagiotopoulos and co-workers [71,[85][86][87]. Mahynski et al [85] performed continuum simulations to complement their more extensive study [71] in which the polymer chains were constrained to lie on a lattice.…”

“…By contrast, in our current work, we consider a system corresponding to the colloid limit, which is characterised by a size ratio q = R g /R c < 1. Subsequently, Mahynski et al have carried out continuum simulation studies of colloid-polymer mixtures wherein both colloids and polymer-chain segments were first [86] represented using repulsive LJ potentials of Weeks, Chandler and Anderson (WCA) [88] type and, in their most recent study [87], using more-general attractive potentials. Although the size ratios considered in these latter studies correspond to the colloid limit, the authors were concerned with the role played by the polymers in the crystallisation of the colloids.…”

Stabilizing the hexagonal close packed structure of hard spheres with polymers: Phase diagram, structure, and dynamics

“…We choose these specific values of M and q, because previous studies showed that the free-energy penalty to insert such a polymer greatly favours the HCP structure at sufficiently high colloid packing fraction η c [8]. We treat the polymer chains in the grand canonical ensemble, i.e., we fix the polymer fugacity z p .…”

Reentrant equilibrium disordering in nanoparticle–polymer mixtures

“…For large colloids, both face centered cubic (FCC) and hexagonally closed packed (HCP) structures tend to form, since the free energy difference between these two polymorphs is very small. 14 In the nanoparticle limit, when the colloids and chains become comparable in size, we 13 recently showed that colloids preferentially crystallize into the HCP structure in the presence of a dilute concentration of long enough polymers, in preference to the FCC morphology. This preference is driven by the difference in the free energy cost of confining individual polymer chains within the voids of the two different colloidal crystal morphologies.…”

“…Over five decades of experimental, theoretical and simulation work [1][2][3][4][5][6][7][8][9][10][11][12][13] have led to the knowledge that polymer-induced depletion attractions between colloids in solution can cause them to crystallize even at low polymer concentrations. For large colloids, both face centered cubic (FCC) and hexagonally closed packed (HCP) structures tend to form, since the free energy difference between these two polymorphs is very small.…”