ABSTRACT
Bifurcations in kinetic pathways decide the evolution of a system. An example is crystallization, in which the thermodynamically stable polymorph may not form due to kinetic hindrance. Here, we use confined self-assembly to investigate the interplay of thermodynamics and kinetics in the crystallization pathways of finite clusters. We report the observation of decahedral clusters from colloidal particles in emulsion droplets and show that these decahedral clusters can be thermodynamically stable, just like icosahedral clusters. Our hard sphere simulations reveal how the development of the early nucleus shape passes through a bifurcation that decides the cluster symmetry. A geometric argument explains why decahedral clusters are kinetically hindered and why icosahedral clusters can be dominant even if they are not in the thermodynamic ground state.
ABSTRACT
Supraparticles are spherical colloidal crystals prepared by confined self-assembly processes. A particularly appealing property of these microscale structures is the structural color arising from interference of light with their building blocks. Here, we assemble supraparticles with high structural order that exhibit coloration from uniform, polyhedral metal-organic framework (MOF) particles. We analyse the structural coloration as a function of the size of these anisotropic building blocks and their internal structure. We attribute the angle-dependent coloration of the MOF supraparticles to the presence of ordered, onion-like layers at the outermost regions. Surprisingly, even though different shapes of the MOF particles have different propensities to form these onion layers, all supraparticle dispersions show well-visible macroscopic coloration, indicating that local ordering is sufficient to generate interference effects.
ABSTRACT
The structure of finite self-assembling systems depends sensitively on the number of constituent building blocks. Recently, it was demonstrated that hard sphere-like colloidal particles show a magic number effect when confined in emulsion droplets. Geometric construction rules permit a few dozen magic numbers that correspond to a discrete series of completely filled concentric icosahedral shells. Here, we investigate the free energy landscape of these colloidal clusters as a function of the number of their constituent building blocks for system sizes up to several thousand particles. We find that minima in the free energy landscape, arising from the presence of filled, concentric shells, are significantly broadened, compared to their atomic analogues. Colloidal clusters in spherical confinement can flexibly accommodate excess particles by ordering icosahedrally in the cluster center while changing the structure near the cluster surface. In between these magic number regions, the building blocks cannot arrange into filled shells. Instead, we observe that defects accumulate in a single wedge and therefore only affect a few tetrahedral grains of the cluster. We predict the existence of this wedge by simulation and confirm its presence in experiment using electron tomography. The introduction of the wedge minimizes the free energy penalty by confining defects to small regions within the cluster. In addition, the remaining ordered tetrahedral grains can relax internal strain by breaking icosahedral symmetry. Our findings demonstrate how multiple defect mechanisms collude to form the complex free energy landscape of colloidal clusters.
ABSTRACT
Clusters in systems as diverse as metal atoms, virus proteins, noble gases, and nucleons have properties that depend sensitively on the number of constituent particles. Certain numbers are termed 'magic' because they grant the system with closed shells and exceptional stability. To this point, magic number clusters have been exclusively found with attractive interactions as present between atoms. Here we show that magic number clusters exist in a confined soft matter system with negligible interactions. Colloidal particles in an emulsion droplet spontaneously organize into a series of clusters with precisely defined shell structures. Crucially, free energy calculations demonstrate that colloidal clusters with magic numbers possess higher thermodynamic stability than those off magic numbers. A complex kinetic pathway is responsible for the efficiency of this system in finding its minimum free energy configuration. Targeting similar magic number states is a strategy towards unique configurations in finite self-organizing systems across the scales.
