Structural diversity in three-dimensional self-assembly of nanoplatelets by spherical confinement.

Nanoplatelets offer many possibilities to construct advanced materials due to new properties associated with their (semi)two-dimensional shapes. However, precise control of both positional and orientational order of the nanoplatelets in three dimensions, which is required to achieve emerging and collective properties, is challenging to realize. Here, we combine experiments, advanced electron tomography and computer simulations to explore the structure of supraparticles self-assembled from nanoplatelets in slowly drying emulsion droplets. We demonstrate that the rich phase behaviour of nanoplatelets, and its sensitivity to subtle changes in shape and interaction potential can be used to guide the self-assembly into a wide range of different structures, offering precise control over both orientation and position order of the nanoplatelets. Our research is expected to shed light on the design of hierarchically structured metamaterials with distinct shape- and orientation- dependent properties.

Interplay between spherical confinement and particle shape on the self-assembly of rounded cubes.

Self-assembly of nanoparticles (NPs) inside drying emulsion droplets provides a general strategy for hierarchical structuring of matter at different length scales. The local orientation of neighboring crystalline NPs can be crucial to optimize for instance the optical and electronic properties of the self-assembled superstructures. By integrating experiments and computer simulations, we demonstrate that the orientational correlations of cubic NPs inside drying emulsion droplets are significantly determined by their flat faces. We analyze the rich interplay of positional and orientational order as the particle shape changes from a sharp cube to a rounded cube. Sharp cubes strongly align to form simple-cubic superstructures whereas rounded cubes assemble into icosahedral clusters with additionally strong local orientational correlations. This demonstrates that the interplay between packing, confinement and shape can be utilized to develop new materials with novel properties.

Hard Competition: Stabilizing the Elusive Biaxial Nematic Phase in Suspensions of Colloidal Particles with Extreme Lengths.

We use computer simulations to study the existence and stability of a biaxial nematic N_{b} phase in systems of hard polyhedral cuboids, triangular prisms, and rhombic platelets, characterized by a long (L), medium (M), and short (S) particle axis. For all three shape families, we find stable N_{b} states provided the shape is not only close to the so-called dual shape with M=sqrt[LS] but also sufficiently anisotropic with L/S>9,11,14,23 for rhombi, (two types of) triangular prisms, and cuboids, respectively, corresponding to anisotropies not considered before. Surprisingly, a direct isotropic-N_{b} transition does not occur in these systems due to a destabilization of N_{b} by a smectic (for cuboids and prisms) or a columnar (for platelets) phase at small L/S or by an intervening uniaxial nematic phase at large L/S. Our results are confirmed by a density functional theory provided the third virial coefficient is included and a continuous rather than a discrete (Zwanzig) set of particle orientations is taken into account.

Self-assembly of polyhedral metal-organic framework particles into three-dimensional ordered superstructures.

Self-assembly of particles into long-range, three-dimensional, ordered superstructures is crucial for the design of a variety of materials, including plasmonic sensing materials, energy or gas storage systems, catalysts and photonic crystals. Here, we have combined experimental and simulation data to show that truncated rhombic dodecahedral particles of the metal-organic framework (MOF) ZIF-8 can self-assemble into millimetre-sized superstructures with an underlying three-dimensional rhombohedral lattice that behave as photonic crystals. Those superstructures feature a photonic bandgap that can be tuned by controlling the size of the ZIF-8 particles and is also responsive to the adsorption of guest substances in the micropores of the ZIF-8 particles. In addition, superstructures with different lattices can also be assembled by tuning the truncation of ZIF-8 particles, or by using octahedral UiO-66 MOF particles instead. These well-ordered, sub-micrometre-sized superstructures might ultimately facilitate the design of three-dimensional photonic materials for applications in sensing.

Microphase Separation in Oil-Water Mixtures Containing Hydrophilic and Hydrophobic Ions.

We develop a lattice-based Monte Carlo simulation method for charged mixtures capable of treating dielectric heterogeneities. Using this method, we study oil-water mixtures containing an antagonistic salt, with hydrophilic cations and hydrophobic anions. Our simulations reveal several phases with a spatially modulated solvent composition, in which the ions partition between water-rich and water-poor regions according to their affinity. In addition to the recently observed lamellar phase, we find tubular and droplet phases, reminiscent of those found in block copolymers and surfactant systems. Interestingly, these structures stem from ion-mediated interactions, which allows for tuning of the phase behavior via the concentrations, the ionic properties, and the temperature.

From 2D to 3D: Critical Casimir interactions and phase behavior of colloidal hard spheres in a near-critical solvent.

Colloids dispersed in a binary solvent mixture experience long-ranged solvent-mediated interactions (critical Casimir forces) upon approaching the critical demixing point of the solvent mixture. The range of the interaction is set by the bulk correlation length of the solvent mixture, which diverges upon approaching the critical point. This presents a great opportunity to realize the reversible self-assembly of colloids by tuning the proximity to the critical point of the solvent. Here, we develop a rejection-free geometric cluster algorithm to study the full ternary mixture of colloidal hard spheres suspended in an explicit three-dimensional lattice model for the solvent mixture using extensive Monte Carlo simulations. The phase diagram displays stable colloidal gas, liquid, and crystal phases, as well as broad gas-liquid and gas-crystal phase coexistence, and pronounced fractionation of the solvent in the coexisting colloid phases. The topology of the phase diagram in our three-dimensional study shows striking resemblance to that of our previous studies carried out in two dimensions.

Critical Casimir interactions and colloidal self-assembly in near-critical solvents.

A binary solvent mixture close to critical demixing experiences fluctuations whose correlation length, ξ, diverges as the critical point is approached. The solvent-mediated (SM) interaction that arises between a pair of colloids immersed in such a near-critical solvent can be long-ranged and this so-called critical Casimir interaction is well-studied. How a (dense) suspension of colloids will self-assemble under these conditions is poorly understood. Using a two-dimensional lattice model for the solvent and hard disks to represent the colloids, we perform extensive Monte Carlo simulations to investigate the phase behaviour of this model colloidal suspension as a function of colloid size and wettability under conditions where the solvent reservoir is supercritical. Unlike most other approaches, where the solvent is modelled as an implicit background, our model employs an explicit solvent and treats the suspension as a ternary mixture. This enables us to capture important features, including the pronounced fractionation of the solvent in the coexisting colloidal phases, of this complex system. We also present results for the partial structure factors; these shed light on the critical behaviour in the ternary mixture. The degree to which an effective two-body pair potential description can describe the phase behaviour and structure of the colloidal suspension is discussed briefly.

Critical casimir forces and colloidal phase transitions in a near-critical solvent: a simple model reveals a rich phase diagram.

From experimental studies, it is well known that colloidal particles suspended in a near-critical binary solvent exhibit interesting aggregation phenomena, often associated with colloidal phase transitions and assumed to be driven by long-ranged solvent-mediated (SM) interactions (critical Casimir forces), set by the (diverging) correlation length of the solvent. We present the first simulation and theoretical study of an explicit model of a ternary mixture that mimics this situation. Both the effective SM pair interactions and the full ternary phase diagram are determined for Brownian disks suspended in an explicit two-dimensional supercritical binary liquid mixture. Gas-liquid and fluid-solid transitions are observed in a region that extends well away from criticality of the solvent reservoir. We discuss to what extent an effective pair-potential description can account for the phase behavior we observe. Our study provides a fresh perspective on how proximity to the critical point of the solvent reservoir might influence colloidal self-assembly.

Glassy dynamics of convex polyhedra.

Self-assembly of polyhedral-shaped particles has attracted huge interest with the advent of new synthesis methods that realize these faceted particles in the lab. Recent studies have shown that polyhedral-shaped particles exhibit a rich phase behavior by excluded volume interactions alone; some of these particles are even alleged to show a transition to a glass phase by quenching the liquid sufficiently fast beyond the glass transition (supercooling), such that the formation of structures with long-range order is suppressed. Despite the recent progress, no study has been made on the glass formation of polyhedral-shaped particles. Here, we study the glass behavior of polyhedral particles using advanced Monte Carlo methods. We investigate the formation of a glass of monodisperse hard polyhedral-shaped particles, namely, octahedra, tetrahedra, and triangular cupola, using simulations. Finally, the fragility of these particles is determined and compared to that of a polydisperse hard-sphere system.

Self-assembly, dynamics, and phase transformation kinetics of donor-acceptor substituted perylene derivatives.

The role of alkyl chain substitution on the phase formation and core dynamics is studied in a series of diphenylamine functionalized perylenemonoimides (PMIs), by X-ray scattering, calorimetry and site-specific solid-state NMR techniques. In addition, the strong dipole associated with the donor-acceptor character of the molecules allow an investigation of the dynamics with dielectric spectroscopy. The self-assembly revealed an ordered phase only in PMIs with branched alkyl chains. This phase comprises a helical stacking of molecules with a molecular twist angle of 60 degrees. Results from solid-state NMR further pointed out the importance of intramolecular hydrogen bonding in stabilizing the intracolumnar packing within the ordered phase. Moreover, the core dynamics are frozen as revealed by the value of the dynamic order parameters and the reduced strength of dipolar relaxation. The kinetics of phase transformation from the isotropic to the ordered phase proceeds via a nucleation and growth mechanism, and the rates are dominated by the nucleation barrier. Within the isotropic phase the core dynamics display strong temperature dependence with rates that depend on the number of methylene units in the alkyl chains.