Digital Alchemy for Materials Design: Colloids and Beyond

Starting with the early alchemists, a holy grail of science has been to make desired materials by modifying the attributes of basic building blocks. Building blocks that show promise for assembling new complex materials can be synthesized at the nanoscale with attributes that would astonish the ancient alchemists in their versatility. However, this versatility means that making direct connection between building block attributes and bulk behavior is both necessary for rationally engineering materials, and difficult because building block attributes can be altered in many ways. Here we show how to exploit the malleability of the valence of colloidal nanoparticle "elements" to directly and quantitatively link building block attributes to bulk behavior through a statistical thermodynamic framework we term "digital alchemy". We use this framework to optimize building blocks for a given target structure, and to determine which building block attributes are most important to control for self assembly, through a set of novel thermodynamic response functions, moduli and susceptibilities. We thereby establish direct links between the attributes of colloidal building blocks and the bulk structures they form. Moreover, our results give concrete solutions to the more general conceptual challenge of optimizing emergent behaviors in nature, and can be applied to other types of matter. As examples, we apply digital alchemy to systems of truncated tetrahedra, rhombic dodecahedra, and isotropically interacting spheres that self assemble diamond, FCC, and icosahedral quasicrystal structures, respectively.Comment: 17 REVTeX pages, title fixed to match journal versio

Molecular Tilt on Monolayer-Protected Nanoparticles

The structure of the tilted phase of monolayer-protected nanoparticles is investigated by means of a simple Ginzburg-Landau model. The theory contains two dimensionless parameters representing the preferential tilt angle and the ratio (epsilon) between the energy cost due to spatial variations in the tilt of the coating molecules and that of the van der Waals interactions which favors uniform tilt. We analyze the model for both spherical and octahedral particles. On spherical particles, we find a transition from a tilted phase, at small (epsilon), to a phase where the molecules spontaneously align along the surface normal and tilt disappears. Octahedral particles have an additional phase at small characterized by the presence of six topological defects. These defective configurations provide preferred sites for the chemical functionalization of monolayer-protected nanoparticles via place-exchange reactions and their consequent linking to form molecules and\ud bulk materials

Particle dynamics and the development of string-like motion in a simulated monoatomic supercooled liquid

The microscopic details of local particle dynamics is studied in a glass-forming one component supercooled liquid modeled by a Dzugutov potential developed for simple metallic glass formers. Our main goal is to investigate particle motion in the supercooled liquid state, and to ascertain the extent to which this motion is cooperative and occurring in quasi-one-dimesional, string-like paths. To this end we investigate in detail the mechanism by which particles move along these paths. In particular, we show that the degree of coherence—that is, simultaneous motion by consecutive particles along a string—depends on the length of the string. For short strings, the motion is highly coherent. For longer strings, the motion is highly coherent only within shorter segments of the string, which we call “microstrings.” Very large strings may contain several microstrings within which particles move simultaneously, but individual microstrings within a given string are temporally uncorrelated with each other. We discuss possible underlying mechanism for this complex dynamical behavior, and examine our results in the context of recent work by Garrahan and Chandler [Phys. Rev. Lett. 89, 035704 (2002)] in which dynamic facilitation plays a central role in the glass transition. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70607/2/JCPSA6-120-9-4415-1.pd

Growing spatial correlations of particle displacements in a simulated liquid on cooling toward the glass transition

We define a correlation function that quantifies the spatial correlation of single-particle displacements in liquids and amorphous materials. We show for an equilibrium liquid that this function is related to fluctuations in a bulk dynamical variable. We evaluate this function using computer simulations of an equilibrium glass-forming liquid, and show that long range spatial correlations of displacements emerge and grow on cooling toward the mode coupling critical temperature

Icosahedral packing of polymer-tethered nanospheres and stabilization of the gyroid phase

We present results of molecular simulations that predict the phases formed by the self-assembly of model nanospheres functionalized with a single polymer "tether", including double gyroid, perforated lamella and crystalline bilayer phases. We show that microphase separation of the immiscible tethers and nanospheres causes confinement of the nanoparticles, which promotes local icosahedral packing that stabilizes the gyroid and perforated lamella phases. We present a new metric for determining the local arrangement of particles based on spherical harmonic "fingerprints", which we use to quantify the extent of icosahedral ordering.Comment: 8 pages, 4 figure

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, little is known about the thermodynamically stable phases of polyhedrally-shaped building blocks, such as faceted nanoparticles and colloids. Although hard particles are known to organize due to entropy alone, and some unusual phases are reported in the literature, the role of entropic forces in connection with polyhedral shape is not well understood. Here, we study thermodynamic self-assembly of a family of truncated tetrahedra and report several atomic crystal isostructures, including diamond, {\beta}-tin, and high- pressure lithium, as the polyhedron shape varies from tetrahedral to octahedral. We compare our findings with the densest packings of the truncated tetrahedron family obtained by numerical compression and report a new space filling polyhedron, which has been overlooked in previous searches. Interestingly, the self-assembled structures differ from the densest packings. We show that the self-assembled crystal structures can be understood as a tendency for polyhedra to maximize face-to-face alignment, which can be generalized as directional entropic forces.Comment: Article + supplementary information. 23 pages, 10 figures, 2 table