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.”

Read this work here:

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’.

Read about this work here:

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)

There is an observation that has been puzzling the colloid community for years: Experiments with binary mixtures of quasi-hard colloids and free energy calculations predicted binary crystals. But simulations of binary hard sphere systems never confirmed this phenomenon. Is there a discrepancy between experiment and simulation? Our manuscript, now published in Physical Review Letters, directly answers this question.

In brief: No, there is no discrepancy. With the right simulation method and good order parameters it is in fact possible to detect crystalline order in binary hard spheres. As we show in detail and also quantitatively for Laves phases, diffusion in the fluid is the reason why crystallization is much slower than in systems of identical spheres.

The results also lead to new scientific insights by demonstrating the existence of a transition from a nucleation and growth regime to a spinodal decomposition regime. The findings add to an active discussion in the glass physics community. Finally, state diagrams are reported as reference for future research.

Read about the research here:

Praveen K. Bommineni, Marco Klement, Michael Engel
Spontaneous Crystallization in Systems of Binary Hard Sphere Colloids
Physical Review Letters 124, 218003 (2020)

New work with the Vogel lab, this time on structural color:

“Micrometer‐scale crystalline colloidal clusters are produced by confined self‐assembly in emulsion droplets. Structural color is used to characterize icosahedral, decahedral, and face‐centered cubic clusters. Their color motifs arise from internal grain arrangement, which gives rise to circle, strips, bowtie patterns, and so on. Monitoring color evolution provides information on the dynamics of rotation and the colloid crystallization in confinement in real time.”

Read about the research here:

Structural Color of Colloidal Clusters as a Tool to Investigate Structure and Dynamics
J. Wang, U. Sultan, E.S.A. Görlitzer, C.F. Mbah, M. Engel, N. Vogel
Advanced Functional Materials TBA, 1907730 (2019)

Our joint work with Nicolas Vogel and Erdmann Spiecker advanced the understanding of the structure, defect accumulation and thermodynamics of colloidal clusters on and off magic numbers and was awarded this month’s cover for ACS Nano. Congratulations Junwei and Chrameh!

Read about it here:

Free Energy Landscape of Colloidal Clusters in Spherical Confinement
J. Wang, C.F. Mbah, T. Przybilla, S. Englisch, E. Spiecker, M. Engel, N. Vogel
ACS Nano 13, 9005-9015 (2019)

Fractional crystallization is crystal formation out of chemical mixtures or solutions. In this process, the growing crystal typically has a different composition than the fluid. This makes fractional crystallization an important method for separating or purifying substances based on differences in solubility. In geology, fractional crystallization is operating within the Earth’s crust and mantle during the formation of igneous rocks.

The simplest case of fractional crystallization in simulation is the crystallization of hard spheres. Praveen Bommineni, MAP student Nydia Varela-Rosales and Marco Klement in the group of Michael Engel now calculated the crystallization behavior of mixtures of hard spheres as a function of size-dispersity (composition) and packing fraction (density). The work was achieved using advanced statistical sampling to speed up simulation and access long times required for observing the crystallization phenomenon. The crystals discovered have relevance for the behavior of nanoparticles, micelles, and the structure of alloys and the elements.

Crystallization from size-disperse mixture of spheres.

Complex Crystals from Size-Disperse Spheres
P.K. Bommineni, N.R. Varela-Rosales, M. Klement, M. Engel
Physical Review Letters 122, 128005 (2019)

In a joint collaboration combining experiment (synthesis and self-assembly), analysis (electron microscopy including tomography), and simulation (molecular dynamics and free energy calculations), a team from FAU involving Junwei Wang and Chrameh Mbah reported magic number colloidal clusters:

“Clusters in systems as diverse as metal atoms, virus proteins, noble gases, and nucleons have properties that depend sensitively on the number of constituent particles. Certain numbers are termed ‘magic’ because they grant the system with closed shells and exceptional stability. To this point, magic number clusters have been exclusively found with attractive interactions as present between atoms. Here we show that magic number clusters exist in a confined soft matter system with negligible interactions. Colloidal particles in an emulsion droplet spontaneously organize into a series of clusters with precisely defined shell structures. Crucially, free energy calculations demonstrate that colloidal clusters with magic numbers possess higher thermodynamic stability than those off magic numbers. A complex kinetic pathway is responsible for the efficiency of this system in finding its minimum free energy configuration. Targeting similar magic number states is a strategy towards unique configurations in finite self-organizing systems across the scales.”

Read about it here:

Magic Number Colloidal Clusters as Minimum Free Energy Structures
J. Wang, C.F. Mbah, T. Przybilla, B.A. Zubiri, E. Spiecker, M. Engel, N. Vogel
Nature Communications 9, 5259 (2018)