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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Two-step crystallization and solid–solid transitions in binary colloidal mixtures
Crystallization is fundamental to materials science and is central to a variety of applications, ranging from the fabrication of silicon wafers for microelectronics to the determination of protein structures. The basic picture is that a crystal nucleates from a homogeneous fluid by a spontaneous fluctuation that kicks the system over a single free-energy barrier. However, it is becoming apparent that nucleation is often more complicated than this simple picture and, instead, can proceed via multiple transformations of metastable structures along the pathway to the thermodynamic minimum. In this article, we observe, characterize, and model crystallization pathways using DNA-coated colloids. We use optical microscopy to investigate the crystallization of a binary colloidal mixture with single-particle resolution. We observe classical one-step pathways and nonclassical two-step pathways that proceed via a solid–solid transformation of a crystal intermediate. We also use enhanced sampling to compute the free-energy landscapes corresponding to our experiments and show that both one- and two-step pathways are driven by thermodynamics alone. Specifically, the two-step solid–solid transition is governed by a competition between two different crystal phases with free energies that depend on the crystal size. These results extend our understanding of available pathways to crystallization, by showing that size-dependent thermodynamic forces can produce pathways with multiple crystal phases that interconvert without free-energy barriers and could provide approaches to controlling the self-assembly of materials made from colloids.
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- Award ID(s):
- 1710112
- NSF-PAR ID:
- 10293403
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 117
- Issue:
- 45
- ISSN:
- 0027-8424
- Page Range / eLocation ID:
- 27927 to 27933
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Summary We combined optical and atomic force microscopy to observe morphology and kinetics of microstructures (typically referred to as bees) that formed at free surfaces of unmodified Performance Graded (PG) 64‐22 asphalt binders upon cooling from 150°C to room temperature (RT) at 5°C min–1, and changes in these microstructures when the surface was terminated with a transparent solid (glass) or liquid (glycerol) overlayer. The main findings are: (1) at free binder surfaces, wrinkled microstructures started to form near the crystallization temperature (∼45°C) of saturates such as wax observed by differential scanning calorimetry, then grew to ∼5 µm diameter, ∼25 nm wrinkle amplitude and 10–30% surface area coverage upon cooling to RT, where they persisted indefinitely without observable change in shape or density. (2) Glycerol coverage of the binder surface during cooling reduced wrinkled area and wrinkle amplitude three‐fold compared to free binder surfaces upon initial cooling to RT; continued glycerol coverage at RT eliminated most surface microstructures within ∼4 h. (3) No surface microstructures were observed to form at binder surfaces covered with glass. (4) Submicron bulk microstructures were observed by near‐infrared microscopy beneath the surfaces of all binder samples, with size, shape and density independent of surface coverage. No tendency of such structures to float to the top or sink to the bottom of mm‐thick samples was observed. (5) We attribute the dependence of surface wrinkling on surface coverage to variation in interface tension, based on a thin‐film continuum mechanics model.
Lay Description Asphalt binder, or bitumen, is the glue that holds aggregate particles together to form a road surface. It is derived from the heavy residue that remains after distilling gasoline, diesel and other lighter products out of crude oil. Nevertheless, bitumen varies widely in composition and mechanical properties. To avoid expensive road failures, bitumen must be processed after distillation so that its mechanical properties satisfy diverse climate and load requirements. International standards now guide these mechanical properties, but yield varying long‐term performance as local source composition and preparation methods vary.
In situ diagnostic methods that can predict bitumen performance independently of processing history are therefore needed. The present work focuses on one promising diagnostic candidate: microscopic observation of internal bitumen structure. Past bitumen microscopy has revealed microstructures of widely varying composition, size, shape and density. A challenge is distinguishing bulk microstructures, which directly influence a binder's mechanical properties, from surface microstructures, which often dominate optical microscopy because of bitumen's opacity and scanning‐probe microscopy because of its inherent surface specificity. In previously published work, we used infrared microscopy to enhance visibility of bulk microstructure. Here, as a foil to this work, we use visible‐wavelength microscopy together with atomic‐force microscopy (AFM) specifically to isolatesurface microstructure, to understand its distinct origin and morphology, and to demonstrate its unique sensitivity to surface alterations. To this end, optical microscopy complements AFM by enabling us to observe surface microstructures form at temperatures (50°C–70°C) at which bitumen's fluidity prevents AFM, and to observe surface microstructure beneath transparent, but chemically inert, liquid (glycerol) and solid (glass) overlayers, which alter surface tension compared to free surfaces. From this study, we learned, first, that, as bitumen cools, distinctly wrinkled surface microstructures form at the same temperature at which independent calorimetric studies showed crystallization in bitumen, causing it to release latent heat of crystallization. This shows that surface microstructures are likely precipitates of the crystallizable component(s). Second, a glycerol overlayer on the cooling bitumen results in smaller, less wrinkled, sparser microstructures, whereas a glass overlayer suppresses them altogether. In contrast, underlying smaller bulk microstructures are unaffected. This shows that surface tension is the driving force behind formation and wrinkling of surface precipitates. Taken together, the work advances our ability to diagnose bitumen samples noninvasively by clearly distinguishing surface from bulk microstructure. -
DNA-coated colloids can self-assemble into an incredible diversity of crystal structures, but their applications have been limited by poor understanding and control over the crystallization dynamics. To address this challenge, we use microfluidics to quantify the kinetics of DNA-programmed self-assembly along the entire crystallization pathway, from thermally activated nucleation through reaction-limited and diffusion-limited phases of crystal growth. Our detailed measurements of the temperature and concentration dependence of the kinetics at all stages of crystallization provide a stringent test of classical theories of nucleation and growth. After accounting for the finite rolling and sliding rates of micrometer-sized DNA-coated colloids, we show that modified versions of these classical theories predict the absolute nucleation and growth rates with quantitative accuracy. We conclude by applying our model to design and demonstrate protocols for assembling large single crystals with pronounced structural coloration, an essential step in creating next-generation optical metamaterials from colloids.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2008561117
