Design of Patchy Particles Using Quaternary Self-Assembled Monolayers

Binary and ternary self-assembled monolayers (SAMs) adsorbed on gold nanoparticles (NPs) have been previously studied for their propensity to form novel and unexpected patterns. The patterns found were shown to arise from a competition between immiscibilty of unlike surfactants and entropic gains due to length or other architectural differences between them. We investigate patterns self-assembled from quaternary monolayers on spherical nanoparticles. We perform simulations to study the effect of NP radius, degree of immiscibility between surfactants, length differences, and stoichiometry of the SAM on the formation of patterns. We report patterns analogous to binary and ternary cases, as well as some novel patterns specific to quaternary SAMs

Self-Assembly of Archimedean Tilings with Enthalpically and Entropically Patchy Polygons

Considerable progress in the synthesis of anisotropic patchy nanoplates (nanoplatelets) promises a rich variety of highly ordered two-dimensional superlattices. Recent experiments of superlattices assembled from nanoplates confirm the accessibility of exotic phases and motivate the need for a better understanding of the underlying self-assembly mechanisms. Here, we present experimentally accessible, rational design rules for the self-assembly of the Archimedean tilings from polygonal nanoplates. The Archimedean tilings represent a model set of target patterns that (i) contain both simple and complex patterns, (ii) are comprised of simple regular shapes, and (iii) contain patterns with potentially interesting materials properties. <i>Via</i> Monte Carlo simulations, we propose a set of design rules with general applicability to one- and two-component systems of polygons. These design rules, specified by increasing levels of patchiness, correspond to a reduced set of anisotropy dimensions for robust self-assembly of the Archimedean tilings. We show for which tilings entropic patches alone are sufficient for assembly and when short-range enthalpic interactions are required. For the latter, we show how patchy these interactions should be for optimal yield. This study provides a minimal set of guidelines for the design of anisostropic patchy particles that can self-assemble all 11 Archimedean tilings

Symmetry Considerations for the Targeted Assembly of Entropically Stabilized Colloidal Crystals <i>via</i> Voronoi Particles

The relationship between colloidal building blocks and their assemblies is an active field of research. As a strategy for targeting novel crystal structures, we examine the use of Voronoi particles, which are hard, space-filling particles in the shape of Voronoi cells of a target structure. Although Voronoi particles stabilize their target structure in the limit of high pressure by construction, the thermodynamic assembly of the same structure at moderate pressure, close to the onset of crystallization, is not guaranteed. Indeed, we find that a more symmetric crystal is often preferred due to additional entropic contributions arising from configurational or occupational degeneracy. We characterize the assembly behavior of the Voronoi particles in terms of the symmetries of the building blocks as well as the symmetries of crystal structures and demonstrate how controlling the degeneracies through a modification of particle shape and field-directed assembly can significantly improve the assembly propensity

Entropically Patchy Particles: Engineering Valence through Shape Entropy

Patchy particles are a popular paradigm for the design and synthesis of nanoparticles and colloids for self-assembly. In “traditional” patchy particles, anisotropic interactions arising from patterned coatings, functionalized molecules, DNA, and other enthalpic means create the possibility for directional binding of particles into higher-ordered structures. Although the anisotropic geometry of nonspherical particles contributes to the interaction patchiness through van der Waals, electrostatic, and other interactions, how particle shape contributes entropically to self-assembly is only now beginning to be understood. The directional nature of entropic forces has recently been elucidated. A recently proposed theoretical framework that defines and quantifies directional entropic forces demonstrates the anisotropicthat is, patchynature of these emergent, attractive forces. Here we introduce the notion of entropically patchy particles as the entropic counterpart to enthalpically patchy particles. Using three example “families” of shapes, we show how to modify entropic patchiness by introducing geometric features to the particles <i>via</i> shape operations so as to target specific crystal structures assembled here with Monte Carlo simulations. We quantify the emergent entropic valence <i>via</i> a potential of mean force and torque. We show that these forces are on the order of a few <i>k</i>_B<i>T</i> at intermediate densities below the onset of crystallization. We generalize these shape operations to shape anisotropy dimensions, in analogy with the anisotropy dimensions introduced for enthalpically patchy particles. Our findings demonstrate that entropic patchiness and emergent valence provide a way of engineering directional bonding into nanoparticle systems, whether in the presence or absence of additional, non-entropic forces

Virial Coefficients and Equations of State for Hard Polyhedron Fluids

Hard polyhedra are a natural extension of the hard sphere model for simple fluids, but there is no general scheme for predicting the effect of shape on thermodynamic properties, even in moderate-density fluids. Only the second virial coefficient is known analytically for general convex shapes, so higher-order equations of state have been elusive. Here we investigate high-precision state functions in the fluid phase of 14 representative polyhedra with different assembly behaviors. We discuss historic efforts in analytically approximating virial coefficients up to <i>B</i>₄ and numerically evaluating them to <i>B</i>₈. Using virial coefficients as inputs, we show the convergence properties for four equations of state for hard convex bodies. In particular, the exponential approximant of Barlow et al. (<i>J. Chem. Phys</i>. <b>2012</b>, <i>137</i>, 204102) is found to be useful up to the first ordering transition for most polyhedra. The convergence behavior we explore can guide choices in expending additional resources for improved estimates. Fluids of arbitrary hard convex bodies are too complicated to be described in a general way at high densities, so the high-precision state data we provide can serve as a reference for future work in calculating state data or as a basis for thermodynamic integration

Shape Alloys of Nanorods and Nanospheres from Self-Assembly

Mixtures of anisotropic nanocrystals promise a great diversity of superlattices and phase behaviors beyond those of single-component systems. However, obtaining a colloidal shape alloy in which two different shapes are thermodynamically coassembled into a crystalline superlattice has remained a challenge. Here we present a joint experimental–computational investigation of two geometrically ubiquitous nanocrystalline building blocksnanorods and nanospheresthat overcome their natural entropic tendency toward macroscopic phase separation and coassemble into three intriguing phases over centimeter scales, including an AB₂-type binary superlattice. Monte Carlo simulations reveal that, although this shape alloy is entropically stable at high packing fraction, demixing is favored at experimental densities. Simulations with short-ranged attractive interactions demonstrate that the alloy is stabilized by interactions induced by ligand stabilizers and/or depletion effects. An asymmetry in the relative interaction strength between rods and spheres improves the robustness of the self-assembly process

Biomimetic Hierarchical Assembly of Helical Supraparticles from Chiral Nanoparticles

Chiroptical materials found in butterflies, beetles, stomatopod crustaceans, and other creatures are attributed to biocomposites with helical motifs and multiscale hierarchical organization. These structurally sophisticated materials self-assemble from primitive nanoscale building blocks, a process that is simpler and more energy efficient than many top-down methods currently used to produce similarly sized three-dimensional materials. Here, we report that molecular-scale chirality of a CdTe nanoparticle surface can be translated to nanoscale helical assemblies, leading to chiroptical activity in the visible electromagnetic range. Chiral CdTe nanoparticles coated with cysteine self-organize around Te cores to produce helical supraparticles. d<i>-/</i>l<i>-</i>Form of the amino acid determines the dominant left/right helicity of the supraparticles. Coarse-grained molecular dynamics simulations with a helical pair-potential confirm the assembly mechanism and the origin of its enantioselectivity, providing a framework for engineering three-dimensional chiral materials by self-assembly. The helical supraparticles further self-organize into lamellar crystals with liquid crystalline order, demonstrating the possibility of hierarchical organization and with multiple structural motifs and length scales determined by molecular-scale asymmetry of nanoparticle interactions