Predictive Self-Assembly of Polyhedra into Complex Structures

  title={Predictive Self-Assembly of Polyhedra into Complex Structures},
  author={Pablo F. Damasceno and Michael Engel and Sharon C. Glotzer},
  pages={453 - 457}
Getting Packed If one neglects the role of specific interactions, the packing of similar-shaped objects will depend only on the particular shape of the object. Damasceno et al. (p. 453; see the Perspective by de Graaf and Manna) present computer simulations of the behavior of different types of polyhedra with simple and complex shapes that are packed under thermal equilibrium into various structures, from crystals to amorphous materials through liquid crystals. Despite the wide variety of… 

A Roadmap for the Assembly of Polyhedral Particles

The most extensive and systematic study thus far on the assembly behavior of polyhedral “hard” particles of many different shapes is reported, which exploits a large set of shapes to determine simple predictive criteria for assembly.

Intermediate crystalline structures of colloids in shape space.

The resulting landscapes show, as a function of shape, regions where ordered structures assemble, what is assembled and at what density, locations of transitions between regions of ordered structures, and regions of disorder.

Supramolecular lattices from tetrahedral nanobuilding blocks

  • Shu Yang
  • Materials Science, Chemistry
  • 2015
The precise synthesis of rigid giant tetrahedra consisting of hydrophobic and hydrophilic polyhedral oligomeric silsesquioxane cages is reported, which assemble a diverse range of highly ordered supramolecular lattices by exploiting the location of thehydrophilic POSS cage substituent and the number of substitutions.

Optimizing the formation of solid solutions with components of different shapes.

  • F. Escobedo
  • Materials Science
    The Journal of chemical physics
  • 2017
It is proposed that component size ratios should maximize their "substitutional symmetry" and hence minimize the combined free-energy cost associated with mutating a host-particle into a guest-particles in each of the solid phases, which stabilizes substitutionally disordered solid solutions but not stoichiometric compounds.

Entropic self-assembly of freely rotating polyhedral particles confined to a flat interface.

A first-order analysis of the particle-surface energies associated with a fluid-fluid interface indicates that such enthalpic interactions will be particularly important in determining particle orientation behavior at low to intermediate concentrations.

Role of Shape in the Self-Assembly of Anisotropic Colloids.

Self-assembly is the process of spontaneous organization of a set of interacting components colloidal particles in suspension interacting with one another can organize into crystals, gels, glasses

Selective assemblies of giant tetrahedra via precisely controlled positional interactions

Creating unusual nanostructures Self-assembly often occurs when dissimilar molecular fragments are forced together by covalent bonding. Surfactants or block copolymers are two common examples. Huang

Relevance of packing to colloidal self-assembly

It is found that the best particle shapes for hard particle colloidal crystals at any finite pressure are imperfect versions of the ideal packing shape, and, contrary to expectations, the ordering mechanism cannot be packing.

Inverse Material Design in Colloidal Self-Assembly

A holy grail in materials science research remains the solution of the inverse design of desired crystal structures, which seeks to identify a set of building block characteristics (shape,

Frustrated self-assembly of non-Euclidean crystals of nanoparticles

It is shown that the unavoidable geometrical frustration of these particle shapes, combined with competing attractive and repulsive interparticle interactions, lead to controllable self-assembly of structures of complex order.



Crystalline assemblies and densest packings of a family of truncated tetrahedra and the role of directional entropic forces.

Polyhedra and their arrangements have intrigued humankind since the ancient Greeks and are today important motifs in condensed matter, with application to many classes of liquids and solids. Yet,

Phase diagram of hard tetrahedra.

It is shown that the quasicrystal approximant is more stable than the dimer crystal for packing densities below 84% using Monte Carlo computer simulations and free energy calculations.

Self-assembly of uniform polyhedral silver nanocrystals into densest packings and exotic superlattices.

It is shown with experiment and computer simulation that a range of nanoscale Ag polyhedra can self-assemble into their conjectured densest packings, and that octahedra form an exotic superstructure with complex helical motifs rather than the densest Minkowski lattice.

Discovery of a Frank-Kasper σ Phase in Sphere-Forming Block Copolymer Melts

Block Copolymer Assembly Despite their structural simplicity, block copolymers can assemble into complex and often surprising structures. Lee et al. (p. 349; see the Perspective by Peterca and

Phase diagram of colloidal hard superballs: from cubes via spheres to octahedra

For hard anisotropic particles the formation of a wide variety of fascinating crystal and liquid-crystal phases is accomplished by entropy alone. A better understanding of these entropy-driven phase

Maximizing Entropy by Minimizing Area: Towards a New Principle of Self-Organization

It is found that the A15 lattice, known to be area minimizing, is favored for a reasonable range of model parameters and so it is among the possible equilibrium states for a variety of colloidal systems.

Mesophase behaviour of polyhedral particles.

It is found that dynamical disorder is crucial in defining mesophase behaviour, and that the apparent kinetic barrier for the liquid-mesophase transition is much lower for liquid crystals (orientational order) than for plastic solids (translational order).

Entropy-driven formation of a superlattice in a hard-sphere binary mixture

A MIXTURE of two dissimilar species (A and B) may freeze to form a substitutionally ordered crystal, the structure of which can vary from a lattice with only a few atoms per unit cell to a complex


Introdzution. The shapes of colloidal particles are often reasonably compact, so that no diameter greatly exceeds the cube root of the volume of the particle. On the other hand, we know many coiloids

On the phase behavior of hard aspherical particles.

This work determines the fluid-solid coexistence pressures of both shape-polydisperse and monodisperse systems of aspherical hard particles and finds that when particles are sufficiently isotropic, the coexistence pressure can be predicted from a linear relation involving the product of two simple geometric parameters characterizing the asphericity of the particles.