Polymorph Selection in Charged Colloids in the Second Nucleation Step

TL;DR

The paper investigates polymorph selection in a charged-colloid model by simulating a core-softened Yukawa system across long-, intermediate-, and short-range interactions, where BCC is stable for long-range and FCC for shorter ranges. Using MD, Topological Cluster Classification (TCC), and Bond Orientational Order Parameters (BOOP), it identifies hexagonally ordered precursor regions that precede nucleation and shows a second-stage transformation to the stable phase (BCC or FCC). The work reveals that, despite differences in freezing structure, the metastable fluids share similar higher-order motifs before nucleation, and that hexagonal precursors guide the nucleation pathway. These findings illuminate how precursor organization and local order influence polymorph selection in colloidal crystallization and may inform broader understanding of nucleation mechanisms in soft matter. The results also highlight the utility of combining TCC and BOOP analyses to resolve precursor structures and nucleation pathways across interaction ranges.

Abstract

We study polymorph selection in a model of charged colloids, with a focus on the higher-order structure prior to and during nucleation. Specifically, we carry out molecular dynamics simulations of a repulsive Yukawa system with a slightly softened (Weeks-Chandler-Andersen) core. We consider the case where the interaction is long-ranged and the BCC crystal is stable, and also intermediate- and short-ranged cases where the FCC crystal is stable. We use two methods for structure identification, the topological cluster classification (TCC) [A. Malins et al., J. Chem. Phys. 139, 234506 (2013)] and the bond orientational order parameter analysis of W. Lechner and C. Dellago [J. Chem. Phys.129, 114707 (2008)]. Under conditions of high supersaturation, appropriate to experiments with colloids, we find that the system forms a precursor state in which the particles are hexagonally ordered. ~That is to say, the precursors are indistinguishable from an HCP crystal using the bond orientational order parameters. This ordering occurs at state points both when the body-centred cubic crystal is the stable phase, and also when the face-centred cubic crystal is stable. In all cases, the stable polymorph forms from the precursor phase in a second stage. Although at freezing, the fluid is very much more ordered when the interactions are short-ranged (when FCC is stable), at the supersaturations where nucleation occurs in our simulations, the higher-order structure of the metastable fluids is almost identical for the long-, short-, and intermediate-ranged systems when measured with the TCC.

Figures (14)

• Figure 1: Phase diagram of the hard core-Yukawa system for a contact potential $\beta \epsilon_\mathrm{yuk} =39$. Reproduced with permission from A.-P. Hynninen and M. Dijkstra, Phys. Rev. E.68, 021407 (2003). Copyright 2003 American Physical Society. State points shown are the weakest supercooling that crystallised in this work. Arrows indicate the degree of supercooling with respect to the phase boundary. Violet data is the long-ranged case with BCC the stable polymorph. Blue data is the short-ranged case with BCC the stable polymorph. Green data is the intermediate-ranged case where, for the supersaturations studied here, FCC is the stable polymorph. FCC.
• Figure 2: Higher-order structures identified by the topological cluster classification and crystals. Numbers correspond to the number of particles in the cluster. Letters to the range of the Morse potential $\rho_0$ for which these are minimum energy clusters (See Eq. \ref{['eqMorse']} in the Appendix) doye1995. Reproduced from [A. Malins et al., J. Chem. Phys.139, 234506 (2013)], with the permission of AIP Publishing.
• Figure 3: Population of particles in clusters identified by the topological cluster classification at freezing. Shown are data for the long-ranged system (violet), intermediate (green), short-ranged (blue) and WCA (red). The WCA system is mapped to the freezing point of hard spheres.
• Figure 4: Population of particles in clusters identified by the topological cluster classification for supersaturated fluids prior to nucleation. Shown are data for the long-ranged system (violet) and short-ranged (blue). The state points shown are $\phi=0.3597$ and $0.2793$ for the long-ranged system and short-ranged systems respectively.
• Figure 5: Bond orientational order parameters for polymorphs considered. (a) $q_4-q_6$ representation. (b) $w_6-q_6$ representation. In (a) and (b), the data are coloured as fluid, grey, BCC, violet, HCP, teal and FCC, blue. FCC at melting (FCC$_\mathrm{m}$) is shown in red. Lines in (b) indicate regions identified with the structures indicated in black type. Grey type refers to data from simulations for each state point. (c) Probability distribution of $q_6$ for the HCP (teal) and FCC at melting (red) states. Here the teal line is HCP and the red is FCC at melting. Further details of the state points samples are given in Table \ref{['tableBop']} in the Appendix.