Exploring the zone of anisotropy and broken symmetries in DNA-mediated nanoparticle crystallization

Abstract

In this work, we present a joint experimental and molecular dynamics simulations effort to understand and map the crystallization behavior of polyhedral nanoparticles assembled via the interaction of DNA surface ligands. In these systems, we systematically investigated the interplay between the effects of particle core (via the particle symmetry and particle size) and ligands (via the ligand length) on crystallization behavior. This investigation revealed rich phase diagrams, previously unobserved phase transitions in polyhedral crystallization behavior, and an unexpected symmetry breaking in the ligand distribution on a particle surface. To understand these results, we introduce the concept of a zone of anisotropy, or the portion of the phase space where the anisotropy of the particle is preserved in the crystallization behavior. Through comparison of the zone of anisotropy for each particle we develop a foundational roadmap to guide future investigations.ver the past decade, major advances in the control of nanoparticle interactions have led to powerful methods to assemble colloidal crystals (1-9). A high degree of structural control can be achieved in these methods if surface-bound ligands are used as nanoscale bonding elements to control the specificity, spacing, and strength of interactions. DNA has emerged as a particularly versatile ligand whose chemically and structurally defined nature can be used to program the symmetry, lattice parameters, and habit of colloidal crystals (1,2,7,(10)(11)(12)(13)(14)(15)(16)(17)(18)(19). The shape of the underlying nanoparticle influences the directionality of DNA interactions, which can result in correlated nanoparticle orientations and predictable crystal symmetries based on geometric considerations (7,13,16,19,20). However, predictive control can be lost if the DNA shell does not preserve the anisotropy of the particle core (13), and thus key questions pertain to (i) the phase space over which predictable directional interactions persist and (ii) the nature of the phase transitions that occur as the anisotropy of the particle disappears. Identifying this "zone of anisotropy" and the broken symmetries that form are critical to establish design rules for work with nonspherical particles and to develop nanostructured materials with controlled properties.Herein, we systematically investigate the phase space encoded by particle symmetry, particle size (L), and DNA length (D) to understand and map where directional interactions persist (Fig. 1). We show that particle symmetry dictates the crystalline states that can be accessed and how easily changes in L and D affect phase transitions between these states, which include transitions in Bravais lattice (i.e., the symmetry of how the particles are arranged within the unit cell) and particle orientation. The concepts introduced herein provide a roadmap to understand and predict particle crystallization behavior toward the construction of functional nanoparticle-based materials.To map the zone of anisotropy in DNA-mediated nan...

Orbitals for classical arbitrary anisotropic colloidal potentials

“…In such systems, when colloids come close to each other, the polymer coating may deform. In systems of DNA coated polyhedra, this has been shown to strongly affect broken symmetry regimes, driving transitions between different crystal lattices [9]. These deformations have been the starting point of the orbital topological model, which for polymer coated spheres predicts different equilibrium structures than a regular non-deformable potential [39].…”

“…Efforts to synthesize and assemble anisotropic particles such as Janus particles [1][2][3][4][5], patchy colloids [6,7], polyhedral particles [8] and functionalized polyhedral nanoparticles [9] have led to materials with diverse structures and functionalities. Systems described by and modeled on anisotropic interactions also include proteins [10][11][12][13] and polyhedral colloids [14][15][16][17].…”

“…Systems described by and modeled on anisotropic interactions also include proteins [10][11][12][13] and polyhedral colloids [14][15][16][17]. The anisotropy of the interaction field is akin to that of the electron orbitals of individual atoms or molecules, and could enhance control of structural properties such as that of the crystal lattices formed [9,13].…”

Programmable Atom Equivalents: Atomic Crystallization as a Framework for Synthesizing Nanoparticle Superlattices

“…Finally, the PAEs with programmed valency and directional binding as a result of anisotropic core shape or surface functionalization (Section .) have exhibited several unique lattice arrangements not currently realized in PAEs with isotropic binding, namely 1D and 2D crystals, body‐centered tetragonal (bct) unit cells, layered structures, the Laves phase isostructural to dicopper magnesium (MgCu 2 ), and even diamond symmetry . As these more complex phases indicate, further experimental and theoretical investigations are required to garner a full understanding of the multiple different forces that are important in dictating PAE assembly.…”

Inverse design of simple pair potentials for the self-assembly of complex structures

“…Simple interactions with features whose length scales are on the order of the interparticle distances are experimentally realizable through, for example, DNA-mediated surface functionalization of nanoparticles. [12][13][14][15][16][17][18][19] In this work we optimize isotropic pair potentials (IPPs) as a model for the interaction between point particles that self-assemble into a specific target crystal structure from a fluid (disordered) state. That is, we seek pair potentials that not only have shapes containing minimal features, but also which drive assembly of the target structure rapidly, without need for a seed and without long waiting times for nucleation.…”