Abstract
Wedderburn–Etherington number patterns, which have inherent combinatorial rules, are ubiquitous in natural tree-like systems and are of significance for studying the assembly of single particles into branched superstructures. However, implementing these patterns at the micro- or nanoscale is still challenging. By controlling the sequential fusion of nanodroplets, these patterns can be reproduced in nanometre-sized branched mesoporous silica structures. Anisotropic mesoporous silica nanoparticles, possessing exposed reaction-active droplet surfaces, are initially synthesized and then assembled following Wedderburn–Etherington number patterns (1, 1, 1, 2, 3, 6, 11, and so on), forming branched nanotrees containing dimers to multimers. This assembly is achieved by using ligand-grafted palladium nanocrystals as an adhesive, which can fuse the droplets exposed on one side of the preformed nanoparticles. The formed dimers have a Y-shaped architecture with two fused branches (length, ∼395 nm; outer diameter, ∼157 nm) connected by an open tube that grows later, and the sequential fusion-growth style can further extend the Y-structure to multibranched structures. Statistics can predict the degree of branching at each assembly level. The types and configurations of branched structural isomers can also be calculated precisely and are specified by the Wedderburn–Etherington trees.
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Data availability
Data supporting the findings of this study are available within the article and the associated Supplementary Information Section. Source data are provided with this paper.
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Acknowledgements
This work was supported by the National Key R&D Program of China (2018YFA0209402 (D.Z.)), the National Natural Science Foundation of China (22088101 (D.Z.), 21875043 (X.L.), 22075049 (X.L.), 21733003 (D.Z.), 51961145403 (D.Z.), 21833008 (Z.L.)), the Key Basic Research Program of Science and Technology Commission of Shanghai Municipality (22JC1410200 (D.Z.)), the Shanghai Rising-Star Program (20QA1401200 (X.L.)), the Shanghai Pilot Program for Basic Research-Fudan University (22TQ004 (X.L.)) and the Natural Science Foundation of Shanghai (22ZR1404600, 18ZR1404600, 20490710600 (X.L.)). This publication was made possible by NPRP grant number NPRP 12S-0309-190268 (X.L.) from the Qatar National Research Fund (a member of the Qatar Foundation), the ‘Junma’ Program of Inner Mongolia University (23600-5233709 (Y.M.)) and the Inner Mongolia Natural Science Foundation Youth Fund (2023QN02013 (Y.M.)). The statements made herein are solely the responsibility of the authors.
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Contributions
D.Z., X.L. and Y.M. contributed to the study conception and writing of the paper. Y.M. performed all material syntheses, characterizations, data collection and analysis. Y.A., B.M., K.L., C.W., W.Z., J.J. and J.Z. assisted Y.M. with the synthesis of materials and the data collection and analysis. Z.L, Y.-L.Z. and R.L. performed the simulation of the fusion process and distribution of products, and A.D. and L.D. were involved in partial analysis of the fusion mechanism. All authors read and commented on the paper.
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Nature Synthesis thanks Hongyu Chen and Ming-Yong Han for their contribution to the peer review of this work. Primary Handling Editor: Alexandra Groves, in collaboration with the Nature Synthesis team.
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Supplementary information
Supplementary Information
Table of contents, Supplementary methods, Figs. 1–34, Table 1 and refs.1–9.
Supplementary Video 1
Movie 1 Dynamic fusion angle.
Supplementary Video 2
Movie 2 Dynamic fusion process.
Supplementary Video 3
Movie 3 Pairwise fusion.
Supplementary Data Fig. 2a
Droplet size distribution at different times.
Supplementary Data Figure 5d
Variation of estimated exposed surface areas at different times.
Supplementary Data Figure 9
SAXS pattern, N2 sorption isotherms, pore-size distribution, and (d) X-ray diffraction pattern of the samples.
Supplementary Data Figure 11a, b
Fourier-transform infrared spectra of palladium nanocrystals and zeta potential changes of CTAB solution at different times.
Supplementary Data Figure 13e-g
Variation of product yield with different palladium concentrations.
Supplementary Data Figure 23c
Calculated main products at each level.
Supplementary Data Figure 33
Curvature hot spot distribution at different times.
Source data
Source Data Fig. 1
Statistical source data Fig. 1e.
Source Data Fig. 2
Statistical source data Fig. 2b,d,f,h,j.
Source Data Fig. 4
Statistical source data Fig. 4c.
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Ma, Y., Zhu, YL., Lin, R. et al. Synthesis of branched silica nanotrees using a nanodroplet sequential fusion strategy. Nat. Synth 3, 236–244 (2024). https://doi.org/10.1038/s44160-023-00434-z
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DOI: https://doi.org/10.1038/s44160-023-00434-z
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