Self-Assembly of Nanocrystals

Nanocrystals can be prepared via chemical synthesis with highly uniform size and shape. They move by Brownian motion and are building blocks for self-assembly processes to create functional materials. Applications rely on the unique optical, magnetic, electronic, and catalytic properties of individual nanoparticles as well as their assemblies. We have developed geometric models and computational methods to derive and validate fundamental principles governing nanocrystal self-assembly. We investigate important design parameters such as the particle shape, anisotropic interactions, and the role of the assembly environment.

  • 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, 16, 214-219, (2017)
  • 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)
  • A Directional Entropic Force Approach to Anisotropic Nanoparticle Assembly
    K.L. Young, M.L. Personick, M. Engel, P.F. Damasceno, S.N. Barnaby, R. Bleher, T. Li, S.C. Glotzer, B. Lee, C.A. Mirkin
    Angewandte Chemie 52, 13980-13984 (2013)
  • Shape Alloys of Nanorods and Nanospheres from Self-Assembly
    X. Ye, J.A. Millan, M. Engel, J. Chen, B.T. Diroll, S.C. Glotzer, C.B. Murray
    Nano Letters 13, 4980-4988 (2013)
  • Competition of Shape and Interaction Patchiness for Self-Assembling Nanoplates
    X. Ye, J. Chen, M. Engel, J.A. Millan, W. Li, L. Qi, G. Xing, J.E. Collins, C.R. Kagan, J. Li, S.C. Glotzer, C.B. Murray
    Nature Chemistry 5, 466-473 (2013)


Amorphous Photonic Band Gap Materials

Photonic materials create fascinating structural color effects in plants, insects, and mammals. An important characteristic is the appearance of a photonic band gap, a frequency band where the propagation of light is strictly prohibited. In collaboration with the Scheffold Lab we study photonic band gap formation in amorphous dielectric materials. We used numerical calculations of the photonic density of states in materials where the dielectric structure is derived from hard and hyperuniform disk patterns. A central goal is to better understand the role of short-range order for tailoring Bragg scattering at the isotropic Brillouin zone.

  • Transport Phase Diagram and Anderson Localization in Hyperuniform Disordered Photonic Materials
    L.S. Froufe-Perez, M. Engel, J.J. Saenz, F. Scheffold
  • 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)


Rotationally Driven Active Matter

Particles driven to motion self-organize like schools of fish, flocks of birds, or bacteria. Research efforts to create matter from such ‘active’ particles involves biopolymers and self-propelled colloids. In general one distinguishes active matter with an internal energy source from that set into motion by an external field. Our work in this field focuses on particles that interact mechanically like gears and transfer energy input from rotation to translation. We observed phase separation of gears driven in opposite direction and super-diffusive motion along interfaces.


Phase Behavior of Polyhedral Particles

Predicting structure from the attributes of a material’s building blocks is a central goal for materials science. Isolating the role of building block shape provides insight into the ordering of molecules and the crystallization of colloids, nanoparticles, proteins, and viruses. While in the Glotzer lab, we systematically investigated the self-assembly of convex polyhedra. Our results demonstrate a remarkably high propensity for self-assembly and structural diversity. Notable discoveries are the discovery of a quasicrystal from tetrahedra and many more liquid crystals, plastic crystals, and crystals.


Complexity with Pair Potentials

The interaction of atoms and soft colloids is frequently modeled using effective classical pair potentials. This allows studying their thermodynamics, phase behavior, and transport phenomena. Pair potentials with just one length scale are common models for many gases and simple fluids and well established, but complex fluids and crystallization into non-close-packed crystals require angular terms or multiple length scales. Important findings so far are the first computational self-assembly of an icosahedral quasicrystal and clathrates from molecular dynamics simulations.


Large-Scale Parallel Monte Carlo Simulations

Current trends in parallel processors call for the design of efficient massively parallel algorithms for scientific computing. Parallel algorithms for Monte Carlo simulations of thermodynamic ensembles of particles have received little attention because of the inherent serial nature of the statistical sampling. With Joshua Anderson we devised a massively parallel method that obeys detailed balance and implement it for a system of hard disks on the graphics processors (GPUs). We applied the method to elucidate the nature of the two-dimensional melting transition of hard disks and polygons.

  • Fluid-to-Solid Transition of Hard Regular Polygons
    J.A. Anderson, J. Antonaglia, J.A. Millan, M. Engel, S.C. Glotzer
  • Massively Parallel Monte Carlo for Many-Particle Simulations on GPUs
    J.A. Anderson, E. Jankowski, T.L. Grubb, M. Engel, S.C. Glotzer
    Journal of Computational Physics 254, 27-38 (2013)
  • Hard-Disk Equation of State: First-Order Liquid-Hexatic Transition in Two Dimensions with Three Simulation Methods
    M. Engel, J.A. Anderson, S.C. Glotzer, M. Isobe, E.P. Bernard, W. Krauth
    Physical Review E 87, 042134 (2013)


Dynamics and Stabilization of Quasicrystals

A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. Shortly after the discovery of quasicrystals in 1982 it was proposed that the atoms are not fully trapped in a single local equilibrium position but chose between several minima. Elementary excitations are called phason flips and the associated collective motions are phason modes. We established the existence of phason flips in simulation and proved that the entropy contribution of phason modes is sufficient to stabilize random tiling quasicrystals over similar approximant crystals.


Directional Entropic and Enthalpic Forces

Directional binding is the foundation of organic chemistry, molecular biology, and can lead to liquid crystalline order. More recently directionality was studied in the context of colloidal and nanoscale building blocks, which are called patchy particles if they exhibit preferential geometric attachment. We introduced the concept of directional entropic forces and entropically patchy particles, in which the particle shape itself is the cause of the geometric attachment. Entropic patchiness is a means to rationalize the phase behavior of many anisotropic particles.


Maximization of Packing Density

A packing problem is an optimization problem that asks how to pack objects in space. Packing problems are easy to grasp and notoriously hard to solve. Recent work on nanoparticle and colloidal self-assembly, jammed granular matter, and biological cell aggregation and crowding further motivated the study of packings. Packing in containers has applications in operations research, such as optimal storage, packaging, and transportation. We discovered the densest packing of tetrahedra and studied a three-parameter family of symmetric polyhedra using a simulated annealing algorithm.


Dislocations in Complex Metallic Alloys

Complex metallic alloys, characterized by large unit cells, are interesting because they show unusual physical behaviors and properties. One such property is the appearance of metadislocations. These line defects involve a reorganization of the material in an extended region around the dislocation core. We developed a geometric theory and derived an optimized crystal structure with ab initio methods for the description of metadislocations in Al-Pd-Mn alloys.