Fabrication of Colloidal Laves Phases via Hard Tetramers and Hard Spheres: Bulk Phase Diagram and Sedimentation Behavior

Abstract

Colloidal photonic crystals display peculiar optical properties that make them particularly suitable for application in different fields. However, the low packing fraction of the targeted structures usually poses a real challenge in the fabrication stage. Here, we propose a route to colloidal photonic crystals via a binary mixture of hard tetramers and hard spheres. By combining theory and computer simulations, we calculate the phase diagram as well as the stacking diagram of the mixture and show that a colloidal analogue of the MgCu2 Laves phase—which can serve as a precursor of a photonic band-gap structure—is a thermodynamically stable phase in a large region of the phase diagram. Our findings show a relatively large coexistence region between the fluid and the Laves phase, which is potentially accessible by experiments. Furthermore, we determine the sedimentation behavior of the suggested mixture, by identifying several stacking sequences in the sediment. Our work uncovers a self-assembly path toward a photonic structure with a band gap in the visible region.

Novel Pyrochlorelike Crystal with a Photonic Band Gap Self-Assembled Using Colloids with a Simple Interaction Potential

“…In the case of the pyrochlore structure, a fabrication method involving an arduous layer-by-layer growth procedure was proposed [13]. A less laborious alternative to these is the directed self-assembly of the colloidal analogue of the MgCu 2 Laves phase from a binary colloidal dispersion [4,14,15]. One of the components of the Laves phase can then be selectively removed to obtain either the diamond or the pyrochlore lattice.…”

“…We found that the system exhibited the formation of tetrahedral clusters at δ ≥ 1.95σ HS . We, then, proceeded to a detailed study of the phase behavior of the HCSS system at a constant shoulder width of δ ¼ 2.10σ HS and studied the formation of a pyrochlore lattice, which can be considered to be composed of tetrahedral clusters [14,39]. To this end, we perform Monte Carlo simulations using a system of N particles in a cubic box of volume V with periodic boundary conditions in the canonical (NVT) and isothermal-isobaric (NPT) ensembles.…”

Colloidal crystals with diamond symmetry at optical lengthscales

“…Metamaterials, typically consisting of optical wavelength-sized building blocks arranged in periodic arrays, promise the creation of unique photonic technologies 1 . A particularly favourable three-dimensional metamaterial consists of transparent spheres arranged on a cubic diamond lattice 2 , which has led to a multi-decade effort to form diamond structures using lithography 3 , micromanipulation 4 or holography 5 as well as self-assembly approaches based upon liquid crystals 6 , nanoparticles 7 8 9 or colloidal crystallization 10 11 12 13 14 15 . The notorious difficulty of forming a diamond lattice using colloidal crystallization is due to the structure's low filling fraction and mechanical instability; colloids with short-ranged and isotropic attractive interactions will favour a denser and more highly coordinated structure.…”

“…One example is isomorphic to the MgCu 2 Laves phase 12 21 ( Fig. 1c ), in which the ‘scaffold' consists of smaller ‘Cu' spheres 11 arranged into a second diamond lattice of tetrahedral clusters of spheres 15 (also known as the pyrochlore lattice).…”

Role of local assembly in the hierarchical crystallization of associating colloidal hard hemispheres

“…It was recently suggested that for self-assembly of complex colloidal crystals, one can pre-assemble the local structures to help the hierarchical crystallization [19][20][21]. However, the role of the local assembly for the hierarchical crystallization remains unclear.…”