How do a small number of larger colloidal particles behave when mixed with many smaller ones inside spherical droplets? We found that entropy alone drives the larger particles to the droplet surface, where they consistently settle at the twelve vertices of an icosahedral structure formed by the smaller particles. Using a combination of experiment and simulation, we showed that this trapping effect is robust and results from the system’s tendency to maximize free volume during self-assembly. These findings offer new insight into how complex structures can form without external guidance and support the design of programmable materials through simple physical principles.

The large colloids (red) get trapped at the icosahedral vertices.

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Praveen K. Bommineni, Junwei Wang, Nicolas Vogel, Michael Engel
Entropic Trapping of Hard Spheres in Spherical Confinement
Physical Review Letters 134, 198201 (2025)

Scientists have long known that the shape of tiny crystals (nanocrystals) can affect their properties, such as how they interact with light or how well they function as catalysts. However, precisely understanding how these shapes form has been challenging, since many factors are involved: temperature, chemicals in the solution, and even the arrangement of atoms at the crystal’s edges. In this study, the researchers introduced a theoretical and computational approach that focuses on the critical spots where atoms attach as the crystal grows. By examining the energy required to add atoms at these sites, they explain why certain shapes, including cubes, octahedra, or other symmetrical forms, often appear.

Beyond explaining why various shapes emerge, this method can guide experimental design. It enables scientists to predict which conditions favor different morphologies and to control crystal growth toward specific outcomes. The study shows that the first atom to grow on the surface, referred to as the adatom, dominates the process by creating temporary pathways that lead to particular shapes. This new understanding not only clarifies how nanocrystals form but also suggests ways to refine their shapes for targeted uses in technology and medicine.

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Carlos L. Bassani, Michael Engel
Kinetically Trapped Nanocrystals with Symmetry-Preserving Shapes
Journal of the American Chemical Society 147, 9487-9495 (2025)

The shape diagram summarizes the change of nanocrystal shape across growth parameters. Here: the growth rates of adatoms on the three major crystallographic facets.

Surface strain can help increase the performance of nanocatalysts, and we have designed a new strategy to stabilize the surface strain in materials. The groups of Yimo Han and Matthew R. Jones at Rice University synthesized nanoparticles and used four-dimensional scanning transmission electron microscopy (4D-STEM) to capture an electron diffraction pattern at each scan position, which produces detailed structural information. Molecular dynamics simulations of Alberto Leonardi investigated the inhibition of dislocation nucleation due to reduced shear stress at corners.

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Chuqiao Shi, Zhihua Cheng, Alberto Leonardi, Yao Yang, Michael Engel, Matthew R. Jones, Yimo Han
Preserving Surface Strain in Nanocatalysts via Morphology Control
Science Advances 10, eadp378 (2024)

The lab published two in-depth overview articles in the field of mesostructure formation:

Nanocrystal Assemblies: Current Advances and Open Problems
This review appeared in ACS Nano and is coauthored by 42 authors. The paper grew from discussions on these topics among the participants of the workshop “Nanoparticle Assemblies: A New Form of Matter with Classical Structure and Quantum Function”, held at the Kavli Institute for Theoretical Physics (KITP), Santa Barbara/CA, USA, from March 27 to May 19, 2023. This study is a broader-view study linking different scales, fundamentals, and methods, emphasizing open problems to inspire and push forward research in the field.

Mesomorphology of Clathrate Hydrates from Molecular Ordering
This perspective appeared in the Journal of Chemical Physics. The paper discusses the coupling of molecular ordering with the mesoscales, including (i) the emergence of porous patterns as a combined factor from the walk over the free energy landscape and 3D competitive nucleation and growth and (ii) the role of molecular attachment rates in crystallization–diffusion models that allow predicting the timescale of pore sealing. It discusses the use of discrete models (molecular dynamics) to build continuum models (phase field models, crystallization laws, and transport phenomena) to predict multiscale manifestations at a feasible computational cost.

The tetrahedral geometry is ubiquitous in natural and synthetic systems. Regular tetrahedra do not tile space, which makes understanding their self-assembly behavior a formidable challenge. In 2009, simulations of hard tetrahedra —that is particles with the shape of a regular tetrahedron, interacting only by excluded volume interactions— discovered a dodecagonal quasicrystal stabilized by entropy alone. But while this quasicrystal forms robustly and reproducibly in simulation, it competes with periodic approximants and cannot be the thermodynamic ground state in the limit of infinite pressure. In this limit, the densest packing will eventually prevail, which is a simple (in comparison) dimer crystal.

Finally, after 14 years, our simulation predictions are confirmed. Yi Wang from the group of Xingchen Ye at Indiana University (USA) experimentally realized multiple phases of tetrahedron colloids where vertex sharpness, surface ligands, and the self-assembly environment play key roles in the formation of the quasicrystal and the dimer crystal. Our colleagues at the Institute of Micro- and Nanostructure Research at FAU resolved the complex three-dimensional structure of the quasicrystal by a combination of electron microscopy, tomography, and synchrotron X-ray scattering. The joint findings demonstrate the predictive power of computer simulations as well as the importance of accurate control over nanocrystal attributes and the assembly method to realize increasingly complex nanopolyhedron supracrystals.

Read about the research here:

Yi Wang, Jun Chen, Ruipeng Li, Alexander Götz, Dominik Drobek, Thomas Przybilla, Sabine Hübner, Philipp Pelz, Lin Yang, Benjamin Apeleo Zubiri, Erdmann Spiecker, Michael Engel, Xingchen Ye
Controlled Self-Assembly of Gold Nanotetrahedra into Quasicrystals and Complex Periodic Supracrystals
Journal of the American Chemical Society 145, 17902 (2023)

This look at the geometry of crystals beyond the constraints of chemistry accomplished by computer simulation has been 8+ years in the making:

“Which crystal structures are possible if the restrictions of the quantum realm are lifted? Our knowledge of ordered particle geometries was previously restricted to the kinds of structures observable in hard condensed matter—on the atomic scale. Here, we use freely tunable computational models to represent particles with variable properties, and we determine the crystal structures into which they self-assemble. The resulting arrangements often correspond to structures known from atomic-scale materials; however, we discover a comparable number of previously unknown crystal structures with different local coordination motifs, incompatible with the limitations of the chemical bond. Our results can be used to engineer soft condensed matter with unprecedented, ordered geometries, paving the way toward materials with potentially novel properties.”

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Julia Dshemuchadse, Pablo F. Damasceno, Carolyn L. Phillips, Michael Engel, Sharon C. Glotzer
Moving Beyond the Constraints of Chemistry via Crystal Structure Discovery with Isotropic Multiwell Pair Potentials
Proceedings of the National Academy of Sciences 118, e2024034118 (2021)

You need soap to remove dirt from your skin. The surfactant molecules it contains squeeze their way into the surface area between the dirt and the skin and help to dissolve the dirt in water. Researchers at FAU and Heinrich-Heine-Universität Düsseldorf (HHU) have observed the same phenomenon with rotating microrobots. Microrobots rotating in a clockwise direction separate from those rotating in an anticlockwise direction to form two cohesive groups clearly separated from each other, just like water and oil. By linking the microrobots to make chains, researchers were able to observe various effects: the chains are capable of mixing the groups and acting like surfactants to create new structures, the same as what happens with soap and soap bubbles.

3D-printed microrobots are driven to rotate on a vibrating table. The angle of the legs determines the rotation direction. Below, two oppositely-rotating robots are chained together.
If the chain consists of oppositely rotating robots, then the chain spontaneously closes; the start and end interlock irreversibly. We call this structure a `rotelle’.

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Christian Scholz, Anton Ldov, Thorsten Pöschel, Michael Engel, Hartmut Löwen
Surfactants and Rotelles in Active Chiral Fluids
Science Advances 7, abf8998 (2021)
Highlighted in: FAU Research

What happens when you etch nanoparticles? This process has now been recorded in real time and in situ by our collaborator Xingchen Ye using a small droplet sandwiched between two graphene sheets. Alberto Leonardi resolved details of the anisotropic kinetics of their gradual dissolution using molecular dynamics and lattice Monte Carlo simulations. Together, experiment and simulation help understanding the mechanism of etching at atomistic resolution, which is important to design more stable catalysts.

Schematic illustration of a graphene liquid cell encapsulating a solution of Pd@Au nanocubes and oxidative etchants. Carbon atoms of graphene sheets are enlarged for clarity purpose.

Read about this work here:

Lei Chen, Alberto Leonardi, Jun Chen, Muhan Cao, Na Li, Dong Su, Qiao Zhang, Michael Engel, Xingchen Ye
Imaging the Kinetics of Anisotropic Dissolution of Bimetallic Core-Shell Nanocubes using Graphene Liquid Cells
Nature Communications 11, 3041 (2020)