Self-assembling colloidal particles in the cubic diamond crystal structure could potentially be used to make materials with a photonic bandgap1,2,3. Such materials are beneficial because they suppress spontaneous emission of light1 and are valued for their applications as optical waveguides, filters and laser resonators4, for improving light-harvesting technologies5,6,7 and for other applications4,8. Cubic diamond is preferred for these applications over more easily self-assembled structures, such as face-centred-cubic structures9,10, because diamond has a much wider bandgap and is less sensitive to imperfections11,12. In addition, the bandgap in diamond crystals appears at a refractive index contrast of about 2, which means that a photonic bandgap could be achieved using known materials at optical frequencies; this does not seem to be possible for face-centred-cubic crystals3,13. However, self-assembly of colloidal diamond is challenging. Because particles in a diamond lattice are tetrahedrally coordinated, one approach has been to self-assemble spherical particles with tetrahedral sticky patches14,15,16. But this approach lacks a mechanism to ensure that the patchy spheres select the staggered orientation of tetrahedral bonds on nearest-neighbour particles, which is required for cubic diamond15,17. Here we show that by using partially compressed tetrahedral clusters with retracted sticky patches, colloidal cubic diamond can be self-assembled using patch–patch adhesion in combination with a steric interlock mechanism that selects the required staggered bond orientation. Photonic bandstructure calculations reveal that the resulting lattices (direct and inverse) have promising optical properties, including a wide and complete photonic bandgap. The colloidal particles in the self-assembled cubic diamond structure are highly constrained and mechanically stable, which makes it possible to dry the suspension and retain the diamond structure. This makes these structures suitable templates for forming high-dielectric-contrast photonic crystals with cubic diamond symmetry.
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All data that support the findings are available from the corresponding authors on reasonable request.
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This research was primarily supported by the US Army Research Office under award number W911NF-17-1-0328. Additional funding was provided by the National Science Foundation under award number DMR-1610788. G.-R.Y. acknowledges support from the NRF (South Korea) under award number 2017M3A7B8065528. We acknowledge the use of shared facilities provided through the Materials Research Science and Engineering Center (MRSEC) programme of the National Science Foundation under award number DMR-1420073. The computational work was supported in part through the NYU IT High Performance Computing resources, services and staff expertise.
The authors declare no competing interests.
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Extended data figures and tables
a–c, The compression ratio of clusters can be changed by adding differing amounts of THF in the deformation step: a, no THF; b, 18 vol% THF; c, 30 vol% THF. d–f, The size ratio can be controlled by using different surfactants in the polymerization step: d, 0.05 wt% F-127; e, 0.05 wt% F-127 + 0.05 wt% SDS; f, 0.05 wt% F-127 + 0.05 wt% Triton X-100. Scale bars, 1 μm.
DNA strands are fluorescently labelled. The image shows that the single-stranded DNA can be selectively functionalized onto the TPM patches and that the polystyrene surfaces are nearly bare. Note that the polystyrene surfaces need not be completely bare of DNA strands: the areal coverage of DNA just has to be much lower on the polystyrene surfaces than on the TPM patches, so that the DNA melting temperatures for the sphere–patch or sphere–sphere interactions are lower than for the patch–patch interaction. The melting temperatures for the polystyrene–polystyrene and polystyrene–TPM interactions are always 6–20 °C below that of the TPM–TPM interaction. Inset, illustration of DNA-coated compressed clusters: red, DNA-coated TPM patches; white, polystyrene spheres not coated with DNA. Scale bar, 5 μm.
a, Simulation data (diamond symbols) are obtained using the HOOMD-blue software package; experimental data (circles) are superimposed. A typical simulation run is performed with 216–8,000 particles in a box with periodic boundaries at a volume fraction of 5%. The system is slowly cooled in the vicinity of the aggregation temperature. The final system is analysed to detect and characterize the formation of a potential crystalline phase. The red diamonds represent where the particles crystallize into cubic diamond; the grey diamonds represents where the system condenses into amorphous structures. The attractive DNA interaction is modelled by a Lennard–Jones potential that has its minimum at 1.03b. Using a shorter-range attractive potential between patches moves the region where cubic diamond crystals form to larger size ratios; a longer-range potential does the opposite. The grey line shows the locus of size and compression ratios where all three spherical lobes and the patch on neighbouring particles simultaneously touch in the staggered conformation. The blue circles represent experimental samples that either crystallized in the cubic diamond structure (closed circles; error bars ±0.02 in both directions) or formed random aggregates (open circles; similar uncertainties but with the error bars suppressed). b, A snapshot of the simulated system where the compressed clusters crystallized into cubic diamond crystals (dcc/(2a) = 0.70).
a–d, Optical microscope bright-field images of two-particle (a) and four-particle (b) aggregates, the 110 plane of a small crystal (c) and the 111 plane of the crystal (d). e–h, Corresponding computer-generated images. Scale bars, 1 μm.
a, Structure for a compression ratio of 0.76. The size ratio is chosen so that patches just touch. The volume fraction of solid material is 0.32. b, Same as in a, but made using a protective oxide layer with a thickness of 10% of the radius of the spherical lobe of a cluster. The volume fraction of solid material is 0.20. c, Band diagram for an inverse diamond lattice of clusters with a compression ratio of 0.76 (the structure shown in a), showing a complete photonic bandgap with a relative width of 0.12 between the second and third bands (highlighted in blue). The vertical axis is the dimensionless frequency fa/c, where f is frequency, a is lattice constant and c is the speed of light in vacuum. Only the first five bands are shown, but the first 50 were calculated and no other bandgaps were found. d, Minimum index nmin at which a bandgap opens for a range of compression ratios: direct lattice, blue; inverse lattice, red.
Illustration of the free rotation of a single bond between patchy particles. For spherical patchy particles, there is no preferred conformation: the staggered conformation, eclipsed conformation, and all the conformations in between are equally likely. Moreover, the bond angle between patchy particles is flexible, which makes the formation of four-, five-, six-, and seven-membered rings possible.
Unit cell of a direct lattice of colloidal cubic diamond of compressed clusters.
Confocal microscope z-stack taken along the 110 plane of colloidal diamond crystals. The TPM is fluorescently labelled. The z-stack step size is 500 nm.
Confocal microscope z-stack taken along the 111 plane of colloidal diamond crystals. The TPM is fluorescently labeled. The z-stack step size is 500 nm.
A unit cell of the inverse lattice of colloidal diamond by compressed clusters. The compression ratio is 0.74.
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He, M., Gales, J.P., Ducrot, É. et al. Colloidal diamond. Nature 585, 524–529 (2020). https://doi.org/10.1038/s41586-020-2718-6
Nature Communications (2021)