Spontaneous formation of ordered structures—self-assembly—is ubiquitous in nature and observed on different length scales, ranging from atomic and molecular systems to micrometre-scale objects and living matter1. Self-ordering in molecular and biological systems typically involves short-range hydrophobic and van der Waals interactions2,3. Here we introduce an approach to micrometre-scale self-assembly based on the joint action of attractive Casimir and repulsive electrostatic forces arising between charged metallic nanoflakes in an aqueous solution. This system forms a self-assembled optical Fabry–Pérot microcavity with a fundamental mode in the visible range (long-range separation distance about 100–200 nanometres) and a tunable equilibrium configuration. Furthermore, by placing an excitonic material in the microcavity region, we are able to realize hybrid light–matter states (polaritons4,5,6), whose properties, such as coupling strength and eigenstate composition, can be controlled in real time by the concentration of ligand molecules in the solution and light pressure. These Casimir microcavities could find future use as sensitive and tunable platforms for a variety of applications, including opto-mechanics7, nanomachinery8 and cavity-induced polaritonic chemistry9.
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The set of experimental and calculated optical spectra, SEM images, optical images and numerical codes are available through figshare.com with the identifier https://doi.org/10.6084/m9.figshare.14883024.v2. Additional data are available from T.O.S. upon request.
Whitesides, G. M. & Grzybowski, B. Self-assembly at all scales. Science 295, 2418–2421 (2002).
Min, Y., Akbulut, M., Kristiansen, K., Golan, Y. & Israelachvili, J. in Nanoscience and Technology: a Collection of Reviews from Nature Journals (ed. Rodgers, P.) 38–49 (World Scientific/Nature Publishing Group, 2010).
Batista, C. A. S., Larson, R. G. & Kotov, N. A. Nonadditivity of nanoparticle interactions. Science 350, 1242477 (2015).
Khitrova, G., Gibbs, H., Kira, M., Koch, S. W. & Scherer, A. Vacuum Rabi splitting in semiconductors. Nat. Phys. 2, 81–90 (2006).
Törmä, P. & Barnes, W. L. Strong coupling between surface plasmon polaritons and emitters: a review. Rep. Prog. Phys. 78, 013901 (2015).
Baranov, D. G., Wersäll, M., Cuadra, J., Antosiewicz, T. J. & Shegai, T. Novel nanostructures and materials for strong light-matter interactions. ACS Photon. 5, 24–42 (2018).
Eichenfield, M., Camacho, R., Chan, J., Vahala, K. J. & Painter, O. A picogram- and nanometre-scale photonic-crystal optomechanical cavity. Nature 459, 550–555 (2009).
Zhao, R. et al. Stable Casimir equilibria and quantum trapping. Science 364, 984–987 (2019).
Thomas, A. et al. Ground-state chemical reactivity under vibrational coupling to the vacuum electromagnetic field. Angew. Chem. Int. Edn 55, 11462–11466 (2016).
Casimir, H. B. G. On the attraction between two perfectly conducting plates. Kon. Ned. Akad. Wetensch. Proc. 51, 793–795 (1948).
Rodriguez, A. W. et al. Classical and fluctuation-induced electromagnetic interactions in micron-scale systems: designer bonding, antibonding, and Casimir forces. Ann. Phys. 527, 45–80 (2015).
Derjaguin, B. V. & Landau, L. D. Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes. Acta Physicochim. URSS 14, 633–662 (1941).
Verwey, E. J. W. Theory of the stability of lyophobic colloids. J. Phys. Chem. 51, 631–636 (1947).
Lifshitz, E. M. The theory of molecular attractive forces between solids. Sov. Phys. JETP 2, 73–83 (1956).
Dzyaloshinskii, I. E., Lifshitz, E. M. & Pitaevskii, L. P. The general theory of van der Waals forces. Adv. Phys. 10, 165–209 (1961).
van Blokland, P. H. & Overbeek, J. T. G. Van der Waals forces between objects covered with a chromium layer. J. Chem. Soc. Faraday Trans. I 74, 2637–2651 (1978).
Lamoreaux, S. K. Demonstration of the Casimir force in the 0.6 to 6 μm range. Phys. Rev. Lett. 78, 5–8 (1997).
Bressi, G., Carugno, G., Onofrio, R. & Ruoso, G. Measurement of the Casimir force between parallel metallic surfaces. Phys. Rev. Lett. 88, 041804 (2002).
Munday, J. N., Capasso, F. & Parsegian, V. A. Measured long-range repulsive Casimir–Lifshitz forces. Nature 457, 170–173 (2009).
Munday, J. & Capasso, F. Repulsive Casimir and van der Waals forces: from measurements to future technologies. Int. J. Mod. Phys. A 25, 2252–2259 (2010).
Tang, L. et al. Measurement of non-monotonic Casimir forces between silicon nanostructures. Nat. Photon. 11, 97–101 (2017).
Cho, Y. K., Wartena, R., Tobias, S. M. & Chiang, Y.-M. Self-assembling colloidal-scale devices: selecting and using short-range surface forces between conductive solids. Adv. Funct. Mater. 17, 379–389 (2007).
Biggs, S. & Mulvaney, P. Measurement of the forces between gold surfaces in water by atomic force microscopy. J. Chem. Phys. 100, 8501–8505 (1994).
Israelachvili, J. N. Intermolecular and Surface Forces (Academic, 2015).
Chen, S. et al. Rapid seedless synthesis of gold nanoplates with microscaled edge length in a high yield and their application in SERS. Nano-Micro Lett. 8, 328–335 (2016).
Li, R. et al. Study on the assembly structure variation of cetyltrimethylammonium bromide on the surface of gold nanoparticles. ACS Omega 5, 4943–4952 (2020).
Liu, Y., Tourbin, M., Lachaize, S. & Guiraud, P. Silica nanoparticles separation from water: aggregation by cetyltrimethylammonium bromide (CTAB). Chemosphere 92, 681–687 (2013).
Chen, F., Mohideen, U., Klimchitskaya, G. & Mostepanenko, V. Demonstration of the lateral Casimir force. Phys. Rev. Lett. 88, 101801 (2002).
Chen, F., Mohideen, U., Klimchitskaya, G. & Mostepanenko, V. Experimental and theoretical investigation of the lateral Casimir force between corrugated surfaces. Phys. Rev. A 66, 032113 (2002).
Rodrigues, R. B., Neto, P. A. M., Lambrecht, A. & Reynaud, S. Lateral Casimir force beyond the proximity-force approximation. Phys. Rev. Lett. 96, 100402 (2006).
Meyer, M., Le Ru, E. & Etchegoin, P. Self-limiting aggregation leads to long-lived metastable clusters in colloidal solutions. J. Phys. Chem. B 110, 6040–6047 (2006).
Junginger, A. et al. Tunable strong coupling of two adjacent optical λ/2 Fabry-Pérot microresonators. Opt. Express 28, 485–493 (2020).
Berkhout, A., Wolterink, T. A. & Koenderink, A. F. Strong coupling to generate complex birefringence: metasurface in the middle etalons. ACS Photon. 7, 2799 (2020).
Li, Y. et al. Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2. Phys. Rev. B 90, 205422 (2014).
Gatemala, H., Pienpinijtham, P., Thammacharoen, C. & Ekgasit, S. Rapid fabrication of silver microplates under an oxidative etching environment consisting of O2/Cl−, NH4OH/H2O2, and H2O2. CrystEngComm 17, 5530–5537 (2015).
Castellanos-Gomez, A. et al. Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping. 2D Mater. 1, 011002 (2014).
Shegai, T., Brian, B., Miljkovic, V. D. & Käll, M. Angular distribution of surface-enhanced Raman scattering from individual au nanoparticle aggregates. ACS Nano 5, 2036–2041 (2011).
Lifshitz, E. M. et al. in Perspectives in Theoretical Physics (ed. Pitaevski, L. P.) 329–349 (Elsevier, 1992).
Johnson, P. B. & Christy, R.-W. Optical constants of the noble metals. Phys. Rev. B 6, 4370 (1972).
Segelstein, D. The Complex Refractive Index of Water. MSc thesis, Univ. Missouri (1981).
Kadirov, M. K., Litvinov, A. I., Nizameev, I. R. & Zakharova, L. Y. Adsorption and premicellar aggregation of CTAB molecules and fabrication of nanosized platinum lattice on the glass surface. J. Phys. Chem. C 118, 19785–19794 (2014).
The authors acknowledge K. Eliasson for help with Raman measurements, as well as E. Tornéus, A. B. Yankovich, P. Erhart and M. Käll for stimulating discussions. The authors acknowledge financial support from the Swedish Research Council (under the VR Miljö project, grant no. 2016-06059 to T.O.S; and the VR project, grant no. 2017-04545 to T.O.S), the Knut and Alice Wallenberg Foundation (project no. 2019.0140 to T.O.S.), and the Chalmers Excellence Initiative Nano.
The authors declare no competing interests.
Peer review information Nature thanks Jeremy Munday and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.
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This file contains Supplementary Notes 1 – 5, Supplementary Text, Supplementary Figures 1 – 25, Supplementary Tables 1 – 3, legends for Supplementary Videos 1 – 6 and Supplementary References.
A stable gold nanoflake dimer as well as formation of a dimer.
Relative displacement of top and bottom nanoflakes within a self-assembled dimer along x and y directions as a function of time. Note that while flakes can move and rotate with respect to each other, their relative displacement is always small in comparison to the lateral size of the flakes. This indicated the dimer stability not only in vertical, but also in lateral directions.
A stable gold nanoflake trimer.
Relative displacement of top, middle, and bottom nanoflakes within a trimer along x and y directions as a function of time. This video shows that the self-assembled trimer exhibits an equilibrium not only in vertical direction, but also in lateral directions.
Additional examples of stable self-assembled multi-stacks of gold nanoflakes.
Additional examples of stable self-assembled multi-stacks of gold nanoflakes.
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Munkhbat, B., Canales, A., Küçüköz, B. et al. Tunable self-assembled Casimir microcavities and polaritons. Nature 597, 214–219 (2021). https://doi.org/10.1038/s41586-021-03826-3