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)

A paper involving Michael Engel with coauthors Joshua Anderson and Sharon Glotzer from University of Michigan, Masaharu Isobe from Nagoya Institute of Technology, Etienne Bernard then from Massachusetts Institute of Technology, and Werner Krauth from École Normale Supérieure has been chosen as a Milestone Paper “that made significant contributions to their field” among all articles published in the journal Physical Review E in 2013.

Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods
Michael Engel, Joshua A. Anderson, Sharon C. Glotzer, Masaharu Isobe, Etienne P. Bernard, and Werner Krauth
Phys. Rev. E 87, 042134 (2013)

In a recent ACS Nano publication, Alberto Leonardi proposes an etching synthesis method for controlling the shape of core-shell nanocrystals:

“The application of nanocrystals as heterogeneous catalysts and plasmonic nanoparticles requires fine control of their shape and chemical composition. A promising idea to achieve synergistic effects is to combine two distinct chemical and/or physical functionalities in bimetallic core@shell nanocrystals. Although techniques for the synthesis of single-component nanocrystals with spherical or anisotropic shape are well-established, new methods are sought to tailor multicomponent nanocrystals. Here, we probe etching in a controlled redox environment as a synthesis technique for multicomponent nanocrystals. Our Monte Carlo computer simulations demonstrate the appearance of characteristic non-equilibrium intermediate microstructures that are further thermodynamically tested and analyzed with molecular dynamics. Convex platelet, concave polyhedron, pod, cage, and strutted-cage shapes are obtained at room temperature with fully coherent structure exposing crystallographic facets and chemical elements along distinct particle crystallographic directions. We observe that structural and dynamic properties are markedly modified compared to the untreated compact nanocrystal.”

Read about it here:

Particle Shape Control via Etching of Core-Shell Nanocrystals
A. Leonardi, M. Engel
ACS Nano 12, 9186-9195 (2018)

Artistic visualization of core-shell nanocrystal etching. Image credit: Alberto Leonardi.

A publication with experiments by Christian Scholz, then a postdoc at MSS and now at Universität Düsseldorf, appeared in Nature Communications:

“Biological organisms and artificial active particles self-organize into swarms and patterns. Open questions concern the design of emergent phenomena by choosing appropriate forms of activity and particle interactions. A particularly simple and versatile system are 3D-printed robots on a vibrating table that can perform self-propelled and self-spinning motion. Here we study a mixture of minimalistic clockwise and counter-clockwise rotating robots, called rotors. Our experiments show that rotors move collectively and exhibit super-diffusive interfacial motion and phase separate via spinodal decomposition. On long time scales, confinement favors symmetric demixing patterns. By mapping rotor motion on a Langevin equation with a constant driving torque and by comparison with computer simulations, we demonstrate that our macroscopic system is a form of active soft matter.”

Read about it here:

Rotating Robots Move Collectively and Self-Organize
C. Scholz, M. Engel, T. Pöschel
Nature Communications 9, 931 (2018)

Press coverage pro-physik.de (in German):
Roboter mit Fraktionszwang

A research collaboration with Uni Fribourg (Switzerland) lead to a joint publication in PNAS:

“It has been shown recently that disordered dielectrics can support a photonic band gap in the presence of structural correlations. This finding is surprising, because light transport in disordered media has long been exclusively associated with photon diffusion and Anderson localization. Currently, there exists no picture that may allow the classification of optical transport depending on the structural properties. Here, we make an important step toward solving this fundamental problem. Based on numerical simulations of transport statistics, we identify all relevant regimes in a 2D system composed of silicon rods: transparency, photon diffusion, classical Anderson localization, band gap, and a pseudogap tunneling regime. We summarize our findings in a transport phase diagram that organizes optical transport properties in disordered media.”

Band gap formation and Anderson localization in disordered photonic materials with structural correlations
L.S. Froufe-Perez, M. Engel, J.J. Saenz, F. Scheffold
Proceedings of the National Academy of Sciences 114, 9570-9574 (2017)

A research collaboration involving Michael Engel reported the self-assembly of gold nanoparticles of a particular shape with DNA ligands into clathrate colloidal crystals. The work required a combined effort of state-of-the-art synthesis techniques and DEM computer simulations.

Clathrate Colloidal Crystals
Haixin Lin, Sangmin Lee, Lin Sun, Matthew Spellings, Michael Engel, Sharon C. Glotzer, Chad A. Mirkin
Science 335, 931-935 (2017)

Some publicity:

We are very excited about two new nanoparticle publications in top-level journals, a review article on self-assembly in Chemical Reviews and an upcoming paper about quasicrystals in Nature Materials:

“Chemical methods developed over the past two decades enable preparation of colloidal nanocrystals with uniform size and shape. These Brownian objects readily order into superlattices. Recently, the range of accessible inorganic cores and tunable surface chemistries dramatically increased, expanding the set of nanocrystal arrangements experimentally attainable. In this review, we discuss efforts to create next-generation materials via bottom-up organization of nanocrystals with preprogrammed functionality and self-assembly instructions. […]”

Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials
M.A. Boles, M. Engel, D.V. Talapin
Chemical Reviews 116, 11220-11289 (2016)

“Expanding the library of self-assembled superstructures provides insight into the behaviour of atomic crystals and supports the development of materials with mesoscale order. Here we build on recent findings of soft matter quasicrystals and report a quasicrystalline binary nanocrystal superlattice that exhibits correlations in the form of partial matching rules reducing tiling disorder. We determine a three-dimensional structure model through electron tomography and direct imaging of surface topography. […]”

Quasicrystalline Nanocrystal Superlattice with Partial Matching Rules
X. Ye, J. Chen, M.E. Irrgang, M. Engel, A. Dong, S.C. Glotzer, C.B. Murray
Nature Materials, in press (2016)

“We study photonic band gap formation in two-dimensional high-refractive-index disordered materials where the dielectric structure is derived from packing disks in real and reciprocal space. Numerical calculations of the photonic density of states demonstrate the presence of a band gap for all polarizations in both cases. We find that the band gap width is controlled by the increase in positional correlation inducing short-range order and hyperuniformity concurrently. Our findings suggest that the optimization of short-range order, in particular the tailoring of Bragg scattering at the isotropic Brillouin zone, are of key importance for designing disordered PBG materials.”

Role of Short-Range Order and Hyperuniformity in the Formation of Band Gaps in Disordered Photonic Materials
L.S. Froufe-Perez, M. Engel, P.F. Damasceno, N. Muller, J. Haberko, S.C. Glotzer, F. Scheffold
Physical Review Letters 117, 053902 (2016)