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1. Entropic colloidal crystallization pathways via fluid–fluid transitions and multidimensional prenucleation motifs

   https://doi.org/10.1073/pnas.1905929116  

   Lee, Sangmin; Teich, Erin G.; Engel, Michael; Glotzer, Sharon C. (July 2019, Proceedings of the National Academy of Sciences)

   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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2. Tunable Orientation and Assembly of Polymer-Grafted Nanocubes at Fluid–Fluid Interfaces

   https://doi.org/10.1021/acsnano.1c10416  

   Zhou, Yilong; Tang, Tsung-Yeh; Lee, Brian Hyun-jong; Arya, Gaurav (April 2022, ACS Nano)

   Self-assembly of faceted nanoparticles is a promising route for fabricating nanomaterials; however, achieving low-dimensional assemblies of particles with tunable orientations is challenging. Here, we demonstrate that trapping surface-functionalized faceted nanoparticles at fluid–fluid interfaces is a viable approach for controlling particle orientation and facilitating their assembly into unique one- and two-dimensional superstructures. Using molecular dynamics simulations of polymer-grafted nanocubes in a polymer bilayer along with a particle-orientation classification method we developed, we show that the nanocubes can be induced into face-up, edge-up, or vertex-up orientations by tuning the graft density and differences in their miscibility with the two polymer layers. The orientational preference of the nanocubes is found to be governed by an interplay between the interfacial area occluded by the particle, the difference in interactions of the grafts with the two layers, and the stretching and intercalation of grafts at the interface. The resulting orientationally constrained nanocubes are then shown to assemble into a variety of unusual architectures, such as rectilinear strings, close-packed sheets, bilayer ribbons, and perforated sheets, which are difficult to obtain using other assembly methods. Our work thus demonstrates a versatile strategy for assembling freestanding arrays of faceted nanoparticles with possible applications in plasmonics, optics, catalysis, and membranes, where precise control over particle orientation and position is required. 

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3. 2D Colloids: Size- and Shape-Controlled 2D Materials at Fluid–Fluid Interfaces

   https://doi.org/10.1021/acs.langmuir.1c02418  

   Goggin, David M.; Samaniuk, Joseph R. (December 2021, Langmuir)
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5. Fluid Cohomology

   https://doi.org/10.1145/3592402  

   Yin, Hang; Nabizadeh, Mohammad Sina; Wu, Baichuan; Wang, Stephanie; Chern, Albert (August 2023, ACM Transactions on Graphics)

   The vorticity-streamfunction formulation for incompressible inviscid fluids is the basis for many fluid simulation methods in computer graphics, including vortex methods, streamfunction solvers, spectral methods, and Monte Carlo methods. We point out that current setups in the vorticity-streamfunction formulation are insufficient at simulating fluids on general non-simply-connected domains. This issue is critical in practice, as obstacles, periodic boundaries, and nonzero genus can all make the fluid domain multiply connected. These scenarios introduce nontrivial cohomology components to the flow in the form of harmonic fields. The dynamics of these harmonic fields have been previously overlooked. In this paper, we derive the missing equations of motion for the fluid cohomology components. We elucidate the physical laws associated with the new equations, and show their importance in reproducing physically correct behaviors of fluid flows on domains with general topology. 

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