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Chin. Phys. B, 2021, Vol. 30(12): 124701    DOI: 10.1088/1674-1056/ac306c

Phase behavior of rotationally asymmetric Brownian kites containing 90° internal angles

Huaqing Liu(柳华清)1,†, Yiwu Zong(宗奕吾)1,†, Zhanglin Hou(侯章林)2, Thomas G. Mason3,4,‡, and Kun Zhao(赵坤)1,5,§
1 Key Laboratory of Systems Bioengineering(Ministry of Education), School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China;
2 Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou 325001, China;
3 Department of Physics and Astronomy, University of California-Los Angeles, Los Angeles, CA 90095, USA;
4 Department of Chemistry and Biochemistry, University of California-Los Angeles, Los Angeles, CA 90095, USA;
5 Physics Department, Tianjin University, Tianjin 300072, China
Abstract  Previous Monte Carlo simulations have shown that ordered tetratic phases can emerge in a dense two-dimensional Brownian system of rotationally asymmetric hard kites having 90° internal angles. However, there have been no experimental investigations yet to compare with these simulation results. Here, we have fabricated two types of micron-sized kites having internal angles of 72°-90°-108°-90° and 72°-99°-90°-99°, respectively, and we have experimentally studied their phase behavior in two-dimensional systems. Interestingly and in contrast to the Monte Carlo simulations, the experimental results show a phase sequence of isotropic fluid-hexagonal rotator crystal-square crystal as the area fraction φA increases for both types of kites. The observed square crystal displays not only a quasi-long-range translational order but also (quasi-)long-range 4-fold bond- and molecular-orientational order; these characteristics confirm that tetratic order can emerge even in dense Brownian systems of rotationally asymmetric particles. A model based on local polymorphic configurations (LPCs) is proposed to understand the origin of the square lattice order in these dense kite systems. The results in this study provide a new route to realize custom-designed self-assembly of colloids by controlling LPCs.
Keywords:  tetratic order      colloidal kites      two-dimentional system      phase behavior  
Received:  11 September 2021      Revised:  08 October 2021      Accepted manuscript online:  18 October 2021
PACS:  47.57.J- (Colloidal systems)  
  03.65.Vf (Phases: geometric; dynamic or topological)  
  75.40.Cx (Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.))  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11874277 and 21621004, and 11704276) and the Natural Science Foundation of Tianjin, China (Grant No. 19JCQNJC14900).
Corresponding Authors:  Thomas G. Mason, Kun Zhao     E-mail:;

Cite this article: 

Huaqing Liu(柳华清), Yiwu Zong(宗奕吾), Zhanglin Hou(侯章林), Thomas G. Mason, and Kun Zhao(赵坤) Phase behavior of rotationally asymmetric Brownian kites containing 90° internal angles 2021 Chin. Phys. B 30 124701

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