Predictive Self-Assembly of Polyhedra into Complex Structures

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 starting shapes, the packing behavior could be quantitatively described using just two criteria; one for the particle shape as a function of its volume and surface area, and one for the number of nearest neighbors. Two parameters relating to particle shape and nearest neighbors reveal the preferred packing of complex structures. Predicting structure from the attributes of a material’s building blocks remains a challenge and central goal for materials science. Isolating the role of building block shape for self-assembly provides insight into the ordering of molecules and the crystallization of colloids, nanoparticles, proteins, and viruses. We investigated 145 convex polyhedra whose assembly arises solely from their anisotropic shape. Our results demonstrate a remarkably high propensity for thermodynamic self-assembly and structural diversity. We show that from simple measures of particle shape and local order in the fluid, the assembly of a given shape into a liquid crystal, plastic crystal, or crystal can be predicted.

[1]  L. Pauling.  THE PRINCIPLES DETERMINING THE STRUCTURE OF COMPLEX IONIC CRYSTALS , 1929 .

[2]  L. Onsager.  THE EFFECTS OF SHAPE ON THE INTERACTION OF COLLOIDAL PARTICLES , 1949 .

[3]  George Polya,et al.  Induction and Analogy in Mathematics , 1954 .

[4]  B. Alder,et al.  Phase Transition for a Hard Sphere System , 1957 .

[5]  N. Johnson.  Convex Polyhedra with Regular Faces , 1966, Canadian Journal of Mathematics.

[6]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[7]  I. Nezbeda.  Virial expansion and an improved equation of state for the hard convex molecule system , 1976 .

[8]  Daan Frenkel,et al.  The hard ellipsoid-of-revolution fluid I. Monte Carlo simulations , 1985 .

[9]  J. Israelachvili.  Intermolecular and surface forces , 1985 .

[10]  D. Frenkel,et al.  Thermodynamic stability of a smectic phase in a system of hard rods , 1988, Nature.

[11]  S. Sathiya Keerthi,et al.  A fast procedure for computing the distance between complex objects in three-dimensional space , 1988, IEEE J. Robotics Autom..

[12]  D. Frenkel,et al.  Entropy-driven formation of a superlattice in a hard-sphere binary mixture , 1993, Nature.

[13]  J. Ashby.  References and Notes , 1999 .

[14]  D. Frenkel.  ENTROPY-DRIVEN PHASE TRANSITIONS , 1999 .

[15]  G. Rohrer.  Structure and Bonding in Crystalline Materials , 2001 .

[16]  Maximizing Entropy by Minimizing Area: Towards a New Principle of Self-Organization , 2001, cond-mat/0103171.

[17]  Goran Ungar,et al.  Giant Supramolecular Liquid Crystal Lattice , 2003, Science.

[18]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[19]  Daan Frenkel,et al.  The hard ellipsoid-of-revolution fluid , 1985 .

[20]  S. Glotzer,et al.  Anisotropy of building blocks and their assembly into complex structures. , 2007, Nature materials.

[21]  Restricted dislocation motion in crystals of colloidal dimer particles. , 2008, Physical review letters.

[22]  J. P. Garrahan,et al.  Random Tiling and Topological Defects in a Two-Dimensional Molecular Network , 2008, Science.

[23]  S. Woodley,et al.  Crystal structure prediction from first principles. , 2008, Nature materials.

[24]  S. Torquato,et al.  Dense packings of the Platonic and Archimedean solids , 2009, Nature.

[25]  M. Dzugutov,et al.  Structural model for octagonal quasicrystals derived from octagonal symmetry elements arising in β-Mn crystallization of a simple monatomic liquid , 2009, 0905.3311.

[26]  Sharon C. Glotzer,et al.  Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra , 2009, Nature.

[27]  Christopher B. Murray,et al.  Quasicrystalline order in self-assembled binary nanoparticle superlattices , 2009, Nature.

[28]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[29]  W. L. Miller,et al.  On the phase behavior of hard aspherical particles. , 2010, The Journal of chemical physics.

[30]  Jiye Fang,et al.  Superlattices with non-spherical building blocks , 2010 .

[31]  F. Bates,et al.  Discovery of a Frank-Kasper σ Phase in Sphere-Forming Block Copolymer Melts , 2010, Science.

[32]  M. Dijkstra,et al.  Phase behavior and structure of a new colloidal model system of bowl-shaped particles. , 2010, Nano letters.

[33]  R. Bruinsma,et al.  Entropic crystal–crystal transitions of Brownian squares , 2011, Proceedings of the National Academy of Sciences.

[34]  Andreas Stein,et al.  Colloidal Assembly: The Road from Particles to Colloidal Molecules and Crystals , 2011 .

[35]  Oleg Gang,et al.  Continuous phase transformation in nanocube assemblies. , 2011, Physical review letters.

[36]  P. Geissler,et al.  Self-assembly of uniform polyhedral silver nanocrystals into densest packings and exotic superlattices. , 2012, Nature materials.

[37]  David J. Pine,et al.  Cubic crystals from cubic colloids , 2011 .

[38]  Degenerate quasicrystal of hard triangular bipyramids. , 2011, Physical review letters.

[39]  Fernando A Escobedo,et al.  Mesophase behaviour of polyhedral particles. , 2011, Nature materials.

[40]  Marjolein Dijkstra,et al.  Phase diagram of colloidal hard superballs: from cubes via spheres to octahedra , 2011, 1111.4357.

[41]  M. Dijkstra,et al.  Dense regular packings of irregular nonconvex particles. , 2011, Physical review letters.

[42]  M. Engel,et al.  Phase diagram of hard tetrahedra. , 2011, The Journal of chemical physics.

[43]  M. Dijkstra,et al.  Vacancy-stabilized crystalline order in hard cubes , 2011, Proceedings of the National Academy of Sciences.

[44]  P. Damasceno,et al.  Crystalline assemblies and densest packings of a family of truncated tetrahedra and the role of directional entropic forces. , 2011, ACS nano.

[45]  Michael H. Huang,et al.  Shape‐Controlled Synthesis of Polyhedral Nanocrystals and Their Facet‐Dependent Properties , 2012 .

[46]  Kaylie L. Young,et al.  Assembly of reconfigurable one-dimensional colloidal superlattices due to a synergy of fundamental nanoscale forces , 2012, Proceedings of the National Academy of Sciences.