Abstract

Non-spherical colloidal building blocks introduce new design principles for self-assembly, making it possible to realize optical structures that could not be assembled previously. With this added complexity, the phase space expands enormously so that computer simulation becomes a valuable tool to design and assemble structures with useful optical properties. We recently demonstrated that tetrahedral clusters and spheres, interacting through a DNA-mediated short-range attractive interaction, self-assemble into a superlattice of interpenetrating diamond and pyrochlore sublattices, but only if the clusters consist of partially overlapping spheres. Here we show how the domain of crystallization can be extended by implementing a longer range potential and consider how the resultant structures affect the photonic band gaps of the underlying pyrochlore sublattice. We show that with the proper design, using clusters of overlapping spheres lead to larger photonic band gaps that open up at lower optical contrast.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. A. Imhof and D. Pine, “Ordered macroporous materials by emulsion templating,” Nature 389, 948–951 (1997).
    [Crossref]
  2. J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of Photonic Crystals Made of Air Spheres in Titania,” Science 281, 802–804 (1998).
    [Crossref] [PubMed]
  3. B. T. Holland, C. F. Blanford, and A. Stein, “Synthesis of macroporous minerals with highly ordered three-dimensional arrays of spheroidal voids,” Science 281, 538–540 (1998).
    [Crossref] [PubMed]
  4. H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
    [Crossref]
  5. Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
    [Crossref] [PubMed]
  6. K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
    [Crossref]
  7. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
    [Crossref] [PubMed]
  8. A. Garcia-Adeva, “Band gap atlas for photonic crystals having the symmetry of the kagomé and pyrochlore lattices,” New J. Phys. 8, 86 (2006).
    [Crossref]
  9. K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond structure with a 3d photonic band gap,” Phys. Rev. Lett. 100, 1–4 (2008).
    [Crossref]
  10. A.-P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and Alfons van Blaaderen, “Self-assembly route for photonic crystals with a bandgap in the visible region,” Nat. Mater. 6, 202–205 (2007).
    [Crossref] [PubMed]
  11. T. Dasgupta and M. Dijkstra, “Towards the colloidal Laves phase from binary hard-sphere mixtures via sedimentation,” Soft Matter (2018).
    [Crossref]
  12. E. Ducrot, M. He, G.-R. Yi, and D. J. Pine, “Colloidal alloys with preassembled clusters and spheres,” Nat. Mater. 16, 652–657 (2017).
    [Crossref] [PubMed]
  13. I.-S. Jo, J. Suk Oh, S.-H. Kim, D. J. Pine, and G.-R. Yi, “Compressible colloidal clusters from Pickering emulsions and their DNA functionalization,” Chem. Commun. 54, 8328–8331 (2018).
    [Crossref]
  14. Y. Wang, Y. Wang, X. Zheng, É. Ducrot, M.-G. Lee, G.-R. Yi, M. Weck, and D. J. Pine, “Synthetic strategies toward dna-coated colloids that crystallize,” J. Am. Chem. Soc. 137, 10760–10766 (2015).
    [Crossref] [PubMed]
  15. Z. Zeravcic, V. N. Manoharan, and M. P. Brenner, “Size limits of self-assembled colloidal structures made using specific interactions,” Proc. Natl. Acad. Sci. 111, 15918–15923 (2014).
    [Crossref] [PubMed]
  16. W. B. Rogers and J. C. Crocker, “Direct measurements of DNA-mediated colloidal interactions and their quantitative modeling,” Proc. Natl. Acad. Sci. United States Am. 108, 15687–15692 (2011).
    [Crossref]
  17. S. Angioletti-Uberti, B. M. Mognetti, and D. Frenkel, “Theory and simulation of DNA-coated colloids: a guide for rational design,” Phys. Chem. Chem. Phys. 18, 6373–6393 (2016).
    [Crossref] [PubMed]
  18. M. B. Zanjani, J. C. Crocker, and T. Sinno, “Self-assembly with colloidal clusters: facile crystal design using connectivity landscape analysis,” Soft Matter 13, 7098–7105 (2017).
    [Crossref] [PubMed]
  19. Y. Wang, Y. Wang, X. Zheng, É. Ducrot, J. S. Yodh, M. Weck, and D. J. Pine, “Crystallization of dna-coated colloids,” Nat. Commun. 67253 (2015).
  20. J. S. Oh, Y. Wang, D. J. Pine, and G.-R. Yi, “High-density peo-b-dna brushes on polymer particles for colloidal superstructures,” Chem. Mater. 27, 8337–8344 (2015).
    [Crossref]
  21. Y. Kim, R. J. Macfarlane, M. R. Jones, and C. A. Mirkin, “Transmutable nanoparticles with reconfigurable surface ligands,” Science 351, 579–582 (2016).
    [Crossref] [PubMed]
  22. T. Chen, Y. Hong, and B. M. Reinhard, “Probing dna stiffness through optical fluctuation analysis of plasmon rulers,” Nano Lett. 15, 5349–5357 (2015).
    [Crossref] [PubMed]
  23. J. A. Anderson, C. D. Lorenz, and A. Travesset, “General purpose molecular dynamics simulations fully implemented on graphics processing units,” J. Comput. Phys. 227, 5342–5359 (2008).
    [Crossref]
  24. J. Glaser, T. D. Nguyen, J. A. Anderson, P. Lui, F. Spiga, J. A. Millan, D. C. Morse, and S. C. Glotzer, “Strong scaling of general-purpose molecular dynamics simulations on GPUs,” Comput. Phys. Commun. 192, 97–107 (2015).
    [Crossref]
  25. D. Chandler, J. D. Weeks, and H. C. Andersen, “Van der Waals picture of liquids, solids, and phase transformations,” Science 220, 787–794 (1983).
    [Crossref] [PubMed]
  26. T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, “Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast,” Appl. Phys. Lett. 88, 241920 (2006).
    [Crossref]
  27. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
    [Crossref] [PubMed]
  28. J. S. King, E. Graugnard, and C. J. Summers, “TiO2 Inverse Opals Fabricated Using Low-Temperature Atomic Layer Deposition,” Adv. Mater. 17, 1010–1013 (2005).
    [Crossref]

2018 (1)

I.-S. Jo, J. Suk Oh, S.-H. Kim, D. J. Pine, and G.-R. Yi, “Compressible colloidal clusters from Pickering emulsions and their DNA functionalization,” Chem. Commun. 54, 8328–8331 (2018).
[Crossref]

2017 (2)

E. Ducrot, M. He, G.-R. Yi, and D. J. Pine, “Colloidal alloys with preassembled clusters and spheres,” Nat. Mater. 16, 652–657 (2017).
[Crossref] [PubMed]

M. B. Zanjani, J. C. Crocker, and T. Sinno, “Self-assembly with colloidal clusters: facile crystal design using connectivity landscape analysis,” Soft Matter 13, 7098–7105 (2017).
[Crossref] [PubMed]

2016 (2)

S. Angioletti-Uberti, B. M. Mognetti, and D. Frenkel, “Theory and simulation of DNA-coated colloids: a guide for rational design,” Phys. Chem. Chem. Phys. 18, 6373–6393 (2016).
[Crossref] [PubMed]

Y. Kim, R. J. Macfarlane, M. R. Jones, and C. A. Mirkin, “Transmutable nanoparticles with reconfigurable surface ligands,” Science 351, 579–582 (2016).
[Crossref] [PubMed]

2015 (5)

T. Chen, Y. Hong, and B. M. Reinhard, “Probing dna stiffness through optical fluctuation analysis of plasmon rulers,” Nano Lett. 15, 5349–5357 (2015).
[Crossref] [PubMed]

J. Glaser, T. D. Nguyen, J. A. Anderson, P. Lui, F. Spiga, J. A. Millan, D. C. Morse, and S. C. Glotzer, “Strong scaling of general-purpose molecular dynamics simulations on GPUs,” Comput. Phys. Commun. 192, 97–107 (2015).
[Crossref]

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, J. S. Yodh, M. Weck, and D. J. Pine, “Crystallization of dna-coated colloids,” Nat. Commun. 67253 (2015).

J. S. Oh, Y. Wang, D. J. Pine, and G.-R. Yi, “High-density peo-b-dna brushes on polymer particles for colloidal superstructures,” Chem. Mater. 27, 8337–8344 (2015).
[Crossref]

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, M.-G. Lee, G.-R. Yi, M. Weck, and D. J. Pine, “Synthetic strategies toward dna-coated colloids that crystallize,” J. Am. Chem. Soc. 137, 10760–10766 (2015).
[Crossref] [PubMed]

2014 (1)

Z. Zeravcic, V. N. Manoharan, and M. P. Brenner, “Size limits of self-assembled colloidal structures made using specific interactions,” Proc. Natl. Acad. Sci. 111, 15918–15923 (2014).
[Crossref] [PubMed]

2011 (1)

W. B. Rogers and J. C. Crocker, “Direct measurements of DNA-mediated colloidal interactions and their quantitative modeling,” Proc. Natl. Acad. Sci. United States Am. 108, 15687–15692 (2011).
[Crossref]

2008 (2)

K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond structure with a 3d photonic band gap,” Phys. Rev. Lett. 100, 1–4 (2008).
[Crossref]

J. A. Anderson, C. D. Lorenz, and A. Travesset, “General purpose molecular dynamics simulations fully implemented on graphics processing units,” J. Comput. Phys. 227, 5342–5359 (2008).
[Crossref]

2007 (1)

A.-P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and Alfons van Blaaderen, “Self-assembly route for photonic crystals with a bandgap in the visible region,” Nat. Mater. 6, 202–205 (2007).
[Crossref] [PubMed]

2006 (2)

A. Garcia-Adeva, “Band gap atlas for photonic crystals having the symmetry of the kagomé and pyrochlore lattices,” New J. Phys. 8, 86 (2006).
[Crossref]

T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, “Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast,” Appl. Phys. Lett. 88, 241920 (2006).
[Crossref]

2005 (1)

J. S. King, E. Graugnard, and C. J. Summers, “TiO2 Inverse Opals Fabricated Using Low-Temperature Atomic Layer Deposition,” Adv. Mater. 17, 1010–1013 (2005).
[Crossref]

2001 (2)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref] [PubMed]

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[Crossref] [PubMed]

1998 (3)

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[Crossref]

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of Photonic Crystals Made of Air Spheres in Titania,” Science 281, 802–804 (1998).
[Crossref] [PubMed]

B. T. Holland, C. F. Blanford, and A. Stein, “Synthesis of macroporous minerals with highly ordered three-dimensional arrays of spheroidal voids,” Science 281, 538–540 (1998).
[Crossref] [PubMed]

1997 (1)

A. Imhof and D. Pine, “Ordered macroporous materials by emulsion templating,” Nature 389, 948–951 (1997).
[Crossref]

1992 (1)

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[Crossref]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref] [PubMed]

1983 (1)

D. Chandler, J. D. Weeks, and H. C. Andersen, “Van der Waals picture of liquids, solids, and phase transformations,” Science 220, 787–794 (1983).
[Crossref] [PubMed]

Andersen, H. C.

D. Chandler, J. D. Weeks, and H. C. Andersen, “Van der Waals picture of liquids, solids, and phase transformations,” Science 220, 787–794 (1983).
[Crossref] [PubMed]

Anderson, J. A.

J. Glaser, T. D. Nguyen, J. A. Anderson, P. Lui, F. Spiga, J. A. Millan, D. C. Morse, and S. C. Glotzer, “Strong scaling of general-purpose molecular dynamics simulations on GPUs,” Comput. Phys. Commun. 192, 97–107 (2015).
[Crossref]

J. A. Anderson, C. D. Lorenz, and A. Travesset, “General purpose molecular dynamics simulations fully implemented on graphics processing units,” J. Comput. Phys. 227, 5342–5359 (2008).
[Crossref]

Angioletti-Uberti, S.

S. Angioletti-Uberti, B. M. Mognetti, and D. Frenkel, “Theory and simulation of DNA-coated colloids: a guide for rational design,” Phys. Chem. Chem. Phys. 18, 6373–6393 (2016).
[Crossref] [PubMed]

Blanford, C. F.

B. T. Holland, C. F. Blanford, and A. Stein, “Synthesis of macroporous minerals with highly ordered three-dimensional arrays of spheroidal voids,” Science 281, 538–540 (1998).
[Crossref] [PubMed]

Bo, X.-Z.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[Crossref] [PubMed]

Brenner, M. P.

Z. Zeravcic, V. N. Manoharan, and M. P. Brenner, “Size limits of self-assembled colloidal structures made using specific interactions,” Proc. Natl. Acad. Sci. 111, 15918–15923 (2014).
[Crossref] [PubMed]

Busch, K.

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[Crossref]

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref] [PubMed]

Chandler, D.

D. Chandler, J. D. Weeks, and H. C. Andersen, “Van der Waals picture of liquids, solids, and phase transformations,” Science 220, 787–794 (1983).
[Crossref] [PubMed]

Chen, T.

T. Chen, Y. Hong, and B. M. Reinhard, “Probing dna stiffness through optical fluctuation analysis of plasmon rulers,” Nano Lett. 15, 5349–5357 (2015).
[Crossref] [PubMed]

Crocker, J. C.

M. B. Zanjani, J. C. Crocker, and T. Sinno, “Self-assembly with colloidal clusters: facile crystal design using connectivity landscape analysis,” Soft Matter 13, 7098–7105 (2017).
[Crossref] [PubMed]

W. B. Rogers and J. C. Crocker, “Direct measurements of DNA-mediated colloidal interactions and their quantitative modeling,” Proc. Natl. Acad. Sci. United States Am. 108, 15687–15692 (2011).
[Crossref]

Dasgupta, T.

T. Dasgupta and M. Dijkstra, “Towards the colloidal Laves phase from binary hard-sphere mixtures via sedimentation,” Soft Matter (2018).
[Crossref]

Dijkstra, M.

A.-P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and Alfons van Blaaderen, “Self-assembly route for photonic crystals with a bandgap in the visible region,” Nat. Mater. 6, 202–205 (2007).
[Crossref] [PubMed]

T. Dasgupta and M. Dijkstra, “Towards the colloidal Laves phase from binary hard-sphere mixtures via sedimentation,” Soft Matter (2018).
[Crossref]

Ducrot, E.

E. Ducrot, M. He, G.-R. Yi, and D. J. Pine, “Colloidal alloys with preassembled clusters and spheres,” Nat. Mater. 16, 652–657 (2017).
[Crossref] [PubMed]

Ducrot, É.

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, M.-G. Lee, G.-R. Yi, M. Weck, and D. J. Pine, “Synthetic strategies toward dna-coated colloids that crystallize,” J. Am. Chem. Soc. 137, 10760–10766 (2015).
[Crossref] [PubMed]

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, J. S. Yodh, M. Weck, and D. J. Pine, “Crystallization of dna-coated colloids,” Nat. Commun. 67253 (2015).

Edagawa, K.

K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond structure with a 3d photonic band gap,” Phys. Rev. Lett. 100, 1–4 (2008).
[Crossref]

Frenkel, D.

S. Angioletti-Uberti, B. M. Mognetti, and D. Frenkel, “Theory and simulation of DNA-coated colloids: a guide for rational design,” Phys. Chem. Chem. Phys. 18, 6373–6393 (2016).
[Crossref] [PubMed]

Garcia-Adeva, A.

A. Garcia-Adeva, “Band gap atlas for photonic crystals having the symmetry of the kagomé and pyrochlore lattices,” New J. Phys. 8, 86 (2006).
[Crossref]

Ghebrebrhan, M.

T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, “Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast,” Appl. Phys. Lett. 88, 241920 (2006).
[Crossref]

Glaser, J.

J. Glaser, T. D. Nguyen, J. A. Anderson, P. Lui, F. Spiga, J. A. Millan, D. C. Morse, and S. C. Glotzer, “Strong scaling of general-purpose molecular dynamics simulations on GPUs,” Comput. Phys. Commun. 192, 97–107 (2015).
[Crossref]

Glotzer, S. C.

J. Glaser, T. D. Nguyen, J. A. Anderson, P. Lui, F. Spiga, J. A. Millan, D. C. Morse, and S. C. Glotzer, “Strong scaling of general-purpose molecular dynamics simulations on GPUs,” Comput. Phys. Commun. 192, 97–107 (2015).
[Crossref]

Graugnard, E.

J. S. King, E. Graugnard, and C. J. Summers, “TiO2 Inverse Opals Fabricated Using Low-Temperature Atomic Layer Deposition,” Adv. Mater. 17, 1010–1013 (2005).
[Crossref]

Haus, J. W.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[Crossref]

He, M.

E. Ducrot, M. He, G.-R. Yi, and D. J. Pine, “Colloidal alloys with preassembled clusters and spheres,” Nat. Mater. 16, 652–657 (2017).
[Crossref] [PubMed]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref] [PubMed]

Holland, B. T.

B. T. Holland, C. F. Blanford, and A. Stein, “Synthesis of macroporous minerals with highly ordered three-dimensional arrays of spheroidal voids,” Science 281, 538–540 (1998).
[Crossref] [PubMed]

Hong, Y.

T. Chen, Y. Hong, and B. M. Reinhard, “Probing dna stiffness through optical fluctuation analysis of plasmon rulers,” Nano Lett. 15, 5349–5357 (2015).
[Crossref] [PubMed]

Hynninen, A.-P.

A.-P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and Alfons van Blaaderen, “Self-assembly route for photonic crystals with a bandgap in the visible region,” Nat. Mater. 6, 202–205 (2007).
[Crossref] [PubMed]

Imhof, A.

A. Imhof and D. Pine, “Ordered macroporous materials by emulsion templating,” Nature 389, 948–951 (1997).
[Crossref]

Inguva, R.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[Crossref]

Jo, I.-S.

I.-S. Jo, J. Suk Oh, S.-H. Kim, D. J. Pine, and G.-R. Yi, “Compressible colloidal clusters from Pickering emulsions and their DNA functionalization,” Chem. Commun. 54, 8328–8331 (2018).
[Crossref]

Joannopoulos, J. D.

T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, “Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast,” Appl. Phys. Lett. 88, 241920 (2006).
[Crossref]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref] [PubMed]

John, S.

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[Crossref]

Johnson, S. G.

Jones, M. R.

Y. Kim, R. J. Macfarlane, M. R. Jones, and C. A. Mirkin, “Transmutable nanoparticles with reconfigurable surface ligands,” Science 351, 579–582 (2016).
[Crossref] [PubMed]

Kanoko, S.

K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond structure with a 3d photonic band gap,” Phys. Rev. Lett. 100, 1–4 (2008).
[Crossref]

Kim, S.-H.

I.-S. Jo, J. Suk Oh, S.-H. Kim, D. J. Pine, and G.-R. Yi, “Compressible colloidal clusters from Pickering emulsions and their DNA functionalization,” Chem. Commun. 54, 8328–8331 (2018).
[Crossref]

Kim, Y.

Y. Kim, R. J. Macfarlane, M. R. Jones, and C. A. Mirkin, “Transmutable nanoparticles with reconfigurable surface ligands,” Science 351, 579–582 (2016).
[Crossref] [PubMed]

King, J. S.

J. S. King, E. Graugnard, and C. J. Summers, “TiO2 Inverse Opals Fabricated Using Low-Temperature Atomic Layer Deposition,” Adv. Mater. 17, 1010–1013 (2005).
[Crossref]

Lee, M.-G.

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, M.-G. Lee, G.-R. Yi, M. Weck, and D. J. Pine, “Synthetic strategies toward dna-coated colloids that crystallize,” J. Am. Chem. Soc. 137, 10760–10766 (2015).
[Crossref] [PubMed]

Liddell, C. M.

T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, “Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast,” Appl. Phys. Lett. 88, 241920 (2006).
[Crossref]

Lorenz, C. D.

J. A. Anderson, C. D. Lorenz, and A. Travesset, “General purpose molecular dynamics simulations fully implemented on graphics processing units,” J. Comput. Phys. 227, 5342–5359 (2008).
[Crossref]

Lui, P.

J. Glaser, T. D. Nguyen, J. A. Anderson, P. Lui, F. Spiga, J. A. Millan, D. C. Morse, and S. C. Glotzer, “Strong scaling of general-purpose molecular dynamics simulations on GPUs,” Comput. Phys. Commun. 192, 97–107 (2015).
[Crossref]

Macfarlane, R. J.

Y. Kim, R. J. Macfarlane, M. R. Jones, and C. A. Mirkin, “Transmutable nanoparticles with reconfigurable surface ligands,” Science 351, 579–582 (2016).
[Crossref] [PubMed]

Manoharan, V. N.

Z. Zeravcic, V. N. Manoharan, and M. P. Brenner, “Size limits of self-assembled colloidal structures made using specific interactions,” Proc. Natl. Acad. Sci. 111, 15918–15923 (2014).
[Crossref] [PubMed]

Millan, J. A.

J. Glaser, T. D. Nguyen, J. A. Anderson, P. Lui, F. Spiga, J. A. Millan, D. C. Morse, and S. C. Glotzer, “Strong scaling of general-purpose molecular dynamics simulations on GPUs,” Comput. Phys. Commun. 192, 97–107 (2015).
[Crossref]

Mirkin, C. A.

Y. Kim, R. J. Macfarlane, M. R. Jones, and C. A. Mirkin, “Transmutable nanoparticles with reconfigurable surface ligands,” Science 351, 579–582 (2016).
[Crossref] [PubMed]

Mognetti, B. M.

S. Angioletti-Uberti, B. M. Mognetti, and D. Frenkel, “Theory and simulation of DNA-coated colloids: a guide for rational design,” Phys. Chem. Chem. Phys. 18, 6373–6393 (2016).
[Crossref] [PubMed]

Morse, D. C.

J. Glaser, T. D. Nguyen, J. A. Anderson, P. Lui, F. Spiga, J. A. Millan, D. C. Morse, and S. C. Glotzer, “Strong scaling of general-purpose molecular dynamics simulations on GPUs,” Comput. Phys. Commun. 192, 97–107 (2015).
[Crossref]

Ngo, T. T.

T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, “Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast,” Appl. Phys. Lett. 88, 241920 (2006).
[Crossref]

Nguyen, T. D.

J. Glaser, T. D. Nguyen, J. A. Anderson, P. Lui, F. Spiga, J. A. Millan, D. C. Morse, and S. C. Glotzer, “Strong scaling of general-purpose molecular dynamics simulations on GPUs,” Comput. Phys. Commun. 192, 97–107 (2015).
[Crossref]

Norris, D. J.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[Crossref] [PubMed]

Notomi, M.

K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond structure with a 3d photonic band gap,” Phys. Rev. Lett. 100, 1–4 (2008).
[Crossref]

Oh, J. S.

J. S. Oh, Y. Wang, D. J. Pine, and G.-R. Yi, “High-density peo-b-dna brushes on polymer particles for colloidal superstructures,” Chem. Mater. 27, 8337–8344 (2015).
[Crossref]

Pine, D.

A. Imhof and D. Pine, “Ordered macroporous materials by emulsion templating,” Nature 389, 948–951 (1997).
[Crossref]

Pine, D. J.

I.-S. Jo, J. Suk Oh, S.-H. Kim, D. J. Pine, and G.-R. Yi, “Compressible colloidal clusters from Pickering emulsions and their DNA functionalization,” Chem. Commun. 54, 8328–8331 (2018).
[Crossref]

E. Ducrot, M. He, G.-R. Yi, and D. J. Pine, “Colloidal alloys with preassembled clusters and spheres,” Nat. Mater. 16, 652–657 (2017).
[Crossref] [PubMed]

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, M.-G. Lee, G.-R. Yi, M. Weck, and D. J. Pine, “Synthetic strategies toward dna-coated colloids that crystallize,” J. Am. Chem. Soc. 137, 10760–10766 (2015).
[Crossref] [PubMed]

J. S. Oh, Y. Wang, D. J. Pine, and G.-R. Yi, “High-density peo-b-dna brushes on polymer particles for colloidal superstructures,” Chem. Mater. 27, 8337–8344 (2015).
[Crossref]

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, J. S. Yodh, M. Weck, and D. J. Pine, “Crystallization of dna-coated colloids,” Nat. Commun. 67253 (2015).

Reinhard, B. M.

T. Chen, Y. Hong, and B. M. Reinhard, “Probing dna stiffness through optical fluctuation analysis of plasmon rulers,” Nano Lett. 15, 5349–5357 (2015).
[Crossref] [PubMed]

Rogers, W. B.

W. B. Rogers and J. C. Crocker, “Direct measurements of DNA-mediated colloidal interactions and their quantitative modeling,” Proc. Natl. Acad. Sci. United States Am. 108, 15687–15692 (2011).
[Crossref]

Sinno, T.

M. B. Zanjani, J. C. Crocker, and T. Sinno, “Self-assembly with colloidal clusters: facile crystal design using connectivity landscape analysis,” Soft Matter 13, 7098–7105 (2017).
[Crossref] [PubMed]

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref] [PubMed]

Sözüer, H. S.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[Crossref]

Spiga, F.

J. Glaser, T. D. Nguyen, J. A. Anderson, P. Lui, F. Spiga, J. A. Millan, D. C. Morse, and S. C. Glotzer, “Strong scaling of general-purpose molecular dynamics simulations on GPUs,” Comput. Phys. Commun. 192, 97–107 (2015).
[Crossref]

Stein, A.

B. T. Holland, C. F. Blanford, and A. Stein, “Synthesis of macroporous minerals with highly ordered three-dimensional arrays of spheroidal voids,” Science 281, 538–540 (1998).
[Crossref] [PubMed]

Sturm, J. C.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[Crossref] [PubMed]

Suk Oh, J.

I.-S. Jo, J. Suk Oh, S.-H. Kim, D. J. Pine, and G.-R. Yi, “Compressible colloidal clusters from Pickering emulsions and their DNA functionalization,” Chem. Commun. 54, 8328–8331 (2018).
[Crossref]

Summers, C. J.

J. S. King, E. Graugnard, and C. J. Summers, “TiO2 Inverse Opals Fabricated Using Low-Temperature Atomic Layer Deposition,” Adv. Mater. 17, 1010–1013 (2005).
[Crossref]

Thijssen, J. H. J.

A.-P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and Alfons van Blaaderen, “Self-assembly route for photonic crystals with a bandgap in the visible region,” Nat. Mater. 6, 202–205 (2007).
[Crossref] [PubMed]

Travesset, A.

J. A. Anderson, C. D. Lorenz, and A. Travesset, “General purpose molecular dynamics simulations fully implemented on graphics processing units,” J. Comput. Phys. 227, 5342–5359 (2008).
[Crossref]

van Blaaderen, Alfons

A.-P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and Alfons van Blaaderen, “Self-assembly route for photonic crystals with a bandgap in the visible region,” Nat. Mater. 6, 202–205 (2007).
[Crossref] [PubMed]

Vermolen, E. C. M.

A.-P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and Alfons van Blaaderen, “Self-assembly route for photonic crystals with a bandgap in the visible region,” Nat. Mater. 6, 202–205 (2007).
[Crossref] [PubMed]

Vlasov, Y. A.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[Crossref] [PubMed]

Vos, W. L.

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of Photonic Crystals Made of Air Spheres in Titania,” Science 281, 802–804 (1998).
[Crossref] [PubMed]

Wang, Y.

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, J. S. Yodh, M. Weck, and D. J. Pine, “Crystallization of dna-coated colloids,” Nat. Commun. 67253 (2015).

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, J. S. Yodh, M. Weck, and D. J. Pine, “Crystallization of dna-coated colloids,” Nat. Commun. 67253 (2015).

J. S. Oh, Y. Wang, D. J. Pine, and G.-R. Yi, “High-density peo-b-dna brushes on polymer particles for colloidal superstructures,” Chem. Mater. 27, 8337–8344 (2015).
[Crossref]

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, M.-G. Lee, G.-R. Yi, M. Weck, and D. J. Pine, “Synthetic strategies toward dna-coated colloids that crystallize,” J. Am. Chem. Soc. 137, 10760–10766 (2015).
[Crossref] [PubMed]

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, M.-G. Lee, G.-R. Yi, M. Weck, and D. J. Pine, “Synthetic strategies toward dna-coated colloids that crystallize,” J. Am. Chem. Soc. 137, 10760–10766 (2015).
[Crossref] [PubMed]

Weck, M.

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, M.-G. Lee, G.-R. Yi, M. Weck, and D. J. Pine, “Synthetic strategies toward dna-coated colloids that crystallize,” J. Am. Chem. Soc. 137, 10760–10766 (2015).
[Crossref] [PubMed]

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, J. S. Yodh, M. Weck, and D. J. Pine, “Crystallization of dna-coated colloids,” Nat. Commun. 67253 (2015).

Weeks, J. D.

D. Chandler, J. D. Weeks, and H. C. Andersen, “Van der Waals picture of liquids, solids, and phase transformations,” Science 220, 787–794 (1983).
[Crossref] [PubMed]

Wijnhoven, J. E. G. J.

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of Photonic Crystals Made of Air Spheres in Titania,” Science 281, 802–804 (1998).
[Crossref] [PubMed]

Yi, G.-R.

I.-S. Jo, J. Suk Oh, S.-H. Kim, D. J. Pine, and G.-R. Yi, “Compressible colloidal clusters from Pickering emulsions and their DNA functionalization,” Chem. Commun. 54, 8328–8331 (2018).
[Crossref]

E. Ducrot, M. He, G.-R. Yi, and D. J. Pine, “Colloidal alloys with preassembled clusters and spheres,” Nat. Mater. 16, 652–657 (2017).
[Crossref] [PubMed]

J. S. Oh, Y. Wang, D. J. Pine, and G.-R. Yi, “High-density peo-b-dna brushes on polymer particles for colloidal superstructures,” Chem. Mater. 27, 8337–8344 (2015).
[Crossref]

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, M.-G. Lee, G.-R. Yi, M. Weck, and D. J. Pine, “Synthetic strategies toward dna-coated colloids that crystallize,” J. Am. Chem. Soc. 137, 10760–10766 (2015).
[Crossref] [PubMed]

Yodh, J. S.

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, J. S. Yodh, M. Weck, and D. J. Pine, “Crystallization of dna-coated colloids,” Nat. Commun. 67253 (2015).

Zanjani, M. B.

M. B. Zanjani, J. C. Crocker, and T. Sinno, “Self-assembly with colloidal clusters: facile crystal design using connectivity landscape analysis,” Soft Matter 13, 7098–7105 (2017).
[Crossref] [PubMed]

Zeravcic, Z.

Z. Zeravcic, V. N. Manoharan, and M. P. Brenner, “Size limits of self-assembled colloidal structures made using specific interactions,” Proc. Natl. Acad. Sci. 111, 15918–15923 (2014).
[Crossref] [PubMed]

Zheng, X.

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, M.-G. Lee, G.-R. Yi, M. Weck, and D. J. Pine, “Synthetic strategies toward dna-coated colloids that crystallize,” J. Am. Chem. Soc. 137, 10760–10766 (2015).
[Crossref] [PubMed]

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, J. S. Yodh, M. Weck, and D. J. Pine, “Crystallization of dna-coated colloids,” Nat. Commun. 67253 (2015).

Adv. Mater. (1)

J. S. King, E. Graugnard, and C. J. Summers, “TiO2 Inverse Opals Fabricated Using Low-Temperature Atomic Layer Deposition,” Adv. Mater. 17, 1010–1013 (2005).
[Crossref]

Appl. Phys. Lett. (1)

T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, “Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast,” Appl. Phys. Lett. 88, 241920 (2006).
[Crossref]

Chem. Commun. (1)

I.-S. Jo, J. Suk Oh, S.-H. Kim, D. J. Pine, and G.-R. Yi, “Compressible colloidal clusters from Pickering emulsions and their DNA functionalization,” Chem. Commun. 54, 8328–8331 (2018).
[Crossref]

Chem. Mater. (1)

J. S. Oh, Y. Wang, D. J. Pine, and G.-R. Yi, “High-density peo-b-dna brushes on polymer particles for colloidal superstructures,” Chem. Mater. 27, 8337–8344 (2015).
[Crossref]

Comput. Phys. Commun. (1)

J. Glaser, T. D. Nguyen, J. A. Anderson, P. Lui, F. Spiga, J. A. Millan, D. C. Morse, and S. C. Glotzer, “Strong scaling of general-purpose molecular dynamics simulations on GPUs,” Comput. Phys. Commun. 192, 97–107 (2015).
[Crossref]

J. Am. Chem. Soc. (1)

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, M.-G. Lee, G.-R. Yi, M. Weck, and D. J. Pine, “Synthetic strategies toward dna-coated colloids that crystallize,” J. Am. Chem. Soc. 137, 10760–10766 (2015).
[Crossref] [PubMed]

J. Comput. Phys. (1)

J. A. Anderson, C. D. Lorenz, and A. Travesset, “General purpose molecular dynamics simulations fully implemented on graphics processing units,” J. Comput. Phys. 227, 5342–5359 (2008).
[Crossref]

Nano Lett. (1)

T. Chen, Y. Hong, and B. M. Reinhard, “Probing dna stiffness through optical fluctuation analysis of plasmon rulers,” Nano Lett. 15, 5349–5357 (2015).
[Crossref] [PubMed]

Nat. Commun. (1)

Y. Wang, Y. Wang, X. Zheng, É. Ducrot, J. S. Yodh, M. Weck, and D. J. Pine, “Crystallization of dna-coated colloids,” Nat. Commun. 67253 (2015).

Nat. Mater. (2)

E. Ducrot, M. He, G.-R. Yi, and D. J. Pine, “Colloidal alloys with preassembled clusters and spheres,” Nat. Mater. 16, 652–657 (2017).
[Crossref] [PubMed]

A.-P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and Alfons van Blaaderen, “Self-assembly route for photonic crystals with a bandgap in the visible region,” Nat. Mater. 6, 202–205 (2007).
[Crossref] [PubMed]

Nature (2)

A. Imhof and D. Pine, “Ordered macroporous materials by emulsion templating,” Nature 389, 948–951 (1997).
[Crossref]

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[Crossref] [PubMed]

New J. Phys. (1)

A. Garcia-Adeva, “Band gap atlas for photonic crystals having the symmetry of the kagomé and pyrochlore lattices,” New J. Phys. 8, 86 (2006).
[Crossref]

Opt. Express (1)

Phys. Chem. Chem. Phys. (1)

S. Angioletti-Uberti, B. M. Mognetti, and D. Frenkel, “Theory and simulation of DNA-coated colloids: a guide for rational design,” Phys. Chem. Chem. Phys. 18, 6373–6393 (2016).
[Crossref] [PubMed]

Phys. Rev. B (1)

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[Crossref]

Phys. Rev. E (1)

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[Crossref]

Phys. Rev. Lett. (2)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref] [PubMed]

K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond structure with a 3d photonic band gap,” Phys. Rev. Lett. 100, 1–4 (2008).
[Crossref]

Proc. Natl. Acad. Sci. (1)

Z. Zeravcic, V. N. Manoharan, and M. P. Brenner, “Size limits of self-assembled colloidal structures made using specific interactions,” Proc. Natl. Acad. Sci. 111, 15918–15923 (2014).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. United States Am. (1)

W. B. Rogers and J. C. Crocker, “Direct measurements of DNA-mediated colloidal interactions and their quantitative modeling,” Proc. Natl. Acad. Sci. United States Am. 108, 15687–15692 (2011).
[Crossref]

Science (4)

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of Photonic Crystals Made of Air Spheres in Titania,” Science 281, 802–804 (1998).
[Crossref] [PubMed]

B. T. Holland, C. F. Blanford, and A. Stein, “Synthesis of macroporous minerals with highly ordered three-dimensional arrays of spheroidal voids,” Science 281, 538–540 (1998).
[Crossref] [PubMed]

D. Chandler, J. D. Weeks, and H. C. Andersen, “Van der Waals picture of liquids, solids, and phase transformations,” Science 220, 787–794 (1983).
[Crossref] [PubMed]

Y. Kim, R. J. Macfarlane, M. R. Jones, and C. A. Mirkin, “Transmutable nanoparticles with reconfigurable surface ligands,” Science 351, 579–582 (2016).
[Crossref] [PubMed]

Soft Matter (1)

M. B. Zanjani, J. C. Crocker, and T. Sinno, “Self-assembly with colloidal clusters: facile crystal design using connectivity landscape analysis,” Soft Matter 13, 7098–7105 (2017).
[Crossref] [PubMed]

Other (1)

T. Dasgupta and M. Dijkstra, “Towards the colloidal Laves phase from binary hard-sphere mixtures via sedimentation,” Soft Matter (2018).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Left: Tetrahedral clusters formed by four overlapping polystyrene spheres. The compression ratio rcc/2r0 defines the degree of inter-penetration of the constituent spheres. Here, polystyrene spheres are used with rcc/2r0 = 0.75. Scale bar: 500 nm. Right: Renderings of clusters with rcc/2r0 = 1, 0.75, and 0.5, from top to bottom.
Fig. 2
Fig. 2 Phase diagrams for different potentials. (a) Attractive potential UA(r) between spheres and clusters for various values of n in Eqs. (1) and (2). (b) Phase diagrams showing domains of compression ratios rcc/2r0 sphere ratios R/r0 where the MgCu2 lattice forms for different values of the exponent n, with the correspondence between color and n for both panels indicated in panel (b). For each value of n, the structure is amorphous outside its corresponding colored boundary.
Fig. 3
Fig. 3 Photonic band diagrams and renderings for four different crystals at an optical contrast m = 2.6, where f is the frequency, a is the lattice constant for the underlying FCC unit cell, and c the speed of light in vacuum. The presence of an omnidirectional photonic band gap is highlighted by the blue band. (a) The geometrically ideal pyrochlore lattice with no compression. (b) The geometrically ideal inverse pyrochlore lattice, for m = 2.6 this crystal does not have a complete photonic band gap. (c) The pyrochlore formed from compressed clusters with rcc/2r0 = 0.95. (d) The inverse of a pyrochlore formed from clusters with rcc/2r0 = 0.60. INSETS: Renderings of the corresponding lattices
Fig. 4
Fig. 4 (a) Minimum refractive index contrast mmin for which a band gap opens (i.e. Δf/fc > 0.0001) for the direct and inverse pyrochlore lattices built using compressed clusters. (b) Relative band gap δ = Δf/fc as a function of the compression ratio for various optical contrast m for direct (solid lines) and inverse (dashed lines) pyrochlore lattices.
Fig. 5
Fig. 5 Relative band width as a function of ratio rf/r0 for an inverse pyrochlore lattice constructed from clusters with rcc/2r0 = 0.65. INSET: rendering for the corresponding inverse lattice with rcc/2r0 = 0.65 and rf/r0 = 0.85.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

U A ( r ) = { 4 [ ( σ r ) 2 n ( σ r ) n ] for r < 2 n σ exp [ 1 2 ( r 2 n σ 2 ω ) 2 ] for r > 2 n σ with ω = σ ln 2 n
U R ( r ) = { 4 [ ( σ r ) 2 n ( σ r ) n + 1 4 ] for r < 2 n σ 0 for r > 2 n σ

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