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Complex crystallization pathways are common in protein crystallization, tetrahedrally coordinated systems, and biomineralization, where single or multiple precursors temporarily appear before the formation of the crystal. The emergence of precursors is often explained by a unique property of the system, such as short-range attraction, directional bonding, or ion association. But, structural characteristics of the prenucleation phases found in multistep crystallization remain unclear, and models are needed for testing and expanding the understanding of fluid-to-solid ordering pathways. Here, we report 3 instances of 2-step crystallization of hard-particle fluids. Crystallization in these systems proceeds via a high-density precursor fluid phase with prenucleation motifs in the form of clusters, fibers and layers, and networks, respectively. The density and diffusivity change across the fluid–fluid phase transition increases with motif dimension. We observe crystal nucleation to be catalyzed by the interface between the 2 fluid phases. The crystals that form are complex, including, notably, a crystal with 432 particles in the cubic unit cell. Our results establish the existence of complex crystallization pathways in entropic systems and reveal prenucleation motifs of various dimensions.
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Graph Theoretical Description of Phase Transitions in Complex Multiscale Phases with Supramolecular Assemblies
Abstract Phase transitions are typically quantified using order parameters, such as crystal lattice distances and radial distribution functions, which can identify subtle changes in crystalline materials or high‐contrast phases with large structural differences. However, the identification of phases with high complexity, multiscale organization and of complex patterns during the structural fluctuations preceding phase transitions, which are essential for understanding the system pathways between phases, is challenging for those traditional analyses. Here, it is shown that for two model systems— thermotropic liquid crystals and a lyotropic water/surfactant mixtures—graph theoretical (GT) descriptors can successfully identify complex phases combining molecular and nanoscale levels of organization that are hard to characterize with traditional methodologies. Furthermore, the GT descriptors also reveal the pathways between the different phases. Specifically, centrality parameters and node‐based fractal dimension quantify the system behavior preceding the transitions, capturing fluctuation‐induced breakup of aggregates and their long‐range cooperative interactions. GT parameterization can be generalized for a wide range of chemical systems and be instrumental for the growth mechanisms of complex nanostructures.
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- PAR ID:
- 10576678
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Advanced Science
- Volume:
- 11
- Issue:
- 33
- ISSN:
- 2198-3844
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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