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Growth strategy for solution-phase growth of two-dimensional nanomaterials via a unified model


Two-dimensional (2D) materials prepared by a solution-phase growth route exhibit many unique properties and are promising for use in various fields. However, simple, rational and green fabrication of target materials remains challenging due to the lack of guiding principles. Here we propose a universal qualitative model for 2D materials grown for layered and non-layered crystal structures by a solution-phase growth route; both theoretical simulation and experimental results confirm the model’s validity. This model demonstrates that 2D growth can be controlled by only tuning the reaction concentration and temperature, and has been applied to fabricate more than 30 different 2D nanomaterials in water at room temperature and in the absence of additives. Furthermore, the model shows promise for optimizing the experimental design of numerous other 2D nanomaterials.

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Fig. 1: Theoretical simulation results.
Fig. 2: Theoretical simulation results and the relationship between the possible materials and the corresponding parameters.
Fig. 3: Schematic representation of the formation mechanism for 2D nanomaterials.
Fig. 4: TEM images of 2D nanomaterials.

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Data availability

The data supporting the findings of this study are available within the article and its Supplementary Information. Source data are provided with this paper.

Code availability

The codes used for the findings of this study and README files are freely available for download at The included README files describe the detailed information for smoothly running our codes, including the required software and the installation guide, the programs covered by our codes and the instructions for operation performed by our codes.


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The authors thank the Particle Analysis Center of SFB 1214 at the University of Konstanz for measurements. The authors acknowledge J. Boneberg from the University of Konstanz for assistance with AFM measurements. Z.C. was funded by a Chinese Scholarship Council stipend. R.S. and P.N. gratefully acknowledge the computing time granted by the John von Neumann Institute for Computing (NIC) and provided on supercomputers JURECA and JUWELS at Jülich Supercomputing Center (JSC). This work was financially supported by the Sino-German Center for Research Promotion (grants GZ 1351, M.H. and H.C.), the Deutsche Forschungsgemeinschaft (DFG) within the framework of the collaborative research centre SFB 1214 (H.C., R.S. and P.N.) projects A4 and B1 and the National Natural Science Foundation of China (21775142, M.H.).

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Authors and Affiliations



Z.C., M.H. and H.C. conceived the concept, designed the experiments and wrote the manuscript. Z.C. synthesized and characterized the samples. Z.C. and X.W. performed data analysis. R.S. and P.N. developed the theoretical simulation part, performed theoretical simulations and data analysis and wrote the manuscript. M.F., Q.F. and E.S. contributed to the characterization. Z.H. contributed to the calculation of surface energy.

Corresponding authors

Correspondence to Minghua Huang, Peter Nielaba or Helmut Cölfen.

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The authors declare no competing interests.

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Nature Synthesis thanks Jianhua Hao and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Peter Seavill, in collaboration with the Nature Synthesis team.

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Supplementary Information

Experimental details, Supplementary sections 1–4, Figs. 2-1 to 3-12-4 and Tables 1–4.

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Chen, Z., Schmid, R., Wang, X. et al. Growth strategy for solution-phase growth of two-dimensional nanomaterials via a unified model. Nat. Synth 2, 670–677 (2023).

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