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2022 | OriginalPaper | Chapter

7. Dynamics of Soft-Matter Quasicrystals with 12-Fold Symmetry

Authors : Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun

Published in: Generalized Dynamics of Soft-Matter Quasicrystals

Publisher: Springer Nature Singapore

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Abstract

The discussion in the first 6 chapters provides preparation for the subsequent study. We aim to explore the structures and dynamic properties of soft-matter quasicrystals.

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Literature
1.
go back to reference Fan, T.Y.: Equation system of generalized hydrodynamics of soft-matter quasicrystals. Appl. Math. Mech. 37, 331–347 (2016), in Chinese (2016); arXiv: 1908.06425[cond-mat.soft]. 15 Oct 2019 Fan, T.Y.: Equation system of generalized hydrodynamics of soft-matter quasicrystals. Appl. Math. Mech. 37, 331–347 (2016), in Chinese (2016); arXiv: 1908.06425[cond-mat.soft]. 15 Oct 2019
2.
go back to reference Fan, T.Y.: Generalized hydrodynamics of second two-dimensional soft-matter quasicrystals. Appl. Math. Mech. 38, 189–199 (2017), in Chinese (2017); arXiv: 1908.06430[cond-mat.soft], 15 Oct 2019 Fan, T.Y.: Generalized hydrodynamics of second two-dimensional soft-matter quasicrystals. Appl. Math. Mech. 38, 189–199 (2017), in Chinese (2017); arXiv: 1908.06430[cond-mat.soft], 15 Oct 2019
3.
go back to reference Fan, T.Y., Z.Y.: Three-dimensional generalized dynamics of soft-matter quasicrystals. Appl. Math. Mech. 38, 2017, 1195–1207, in Chinese (2017); Adv. Mat. Sci. Eng. 2020, Article 1D 4875854 (2020) Fan, T.Y., Z.Y.: Three-dimensional generalized dynamics of soft-matter quasicrystals. Appl. Math. Mech. 38, 2017, 1195–1207, in Chinese (2017); Adv. Mat. Sci. Eng. 2020, Article 1D 4875854 (2020)
4.
go back to reference Zeng, X., Ungar, G., Liu, Y., Percec, V., Dulcey, A.S.E., Hobbs, J.K.: Supermolecular dentritic liquid quasicrystals. Nature 428, 157–160 (2004) Zeng, X., Ungar, G., Liu, Y., Percec, V., Dulcey, A.S.E., Hobbs, J.K.: Supermolecular dentritic liquid quasicrystals. Nature 428, 157–160 (2004)
5.
go back to reference Takano, K.: A mesoscopic Archimedian tiling having a complexity in polymeric stars. J. Polym. Sci. Pol. Phys. 43, 2427–2432 (2005)ADSCrossRef Takano, K.: A mesoscopic Archimedian tiling having a complexity in polymeric stars. J. Polym. Sci. Pol. Phys. 43, 2427–2432 (2005)ADSCrossRef
6.
go back to reference Hayashida, K., Dotera, T., Takano, A., Matsushita, Y.: Polymeric quasicrystal: mesoscopic quasicrystalline tiling in ABC star polymers. Phys. Rev. Lett. 98, 195502 (2007) Hayashida, K., Dotera, T., Takano, A., Matsushita, Y.: Polymeric quasicrystal: mesoscopic quasicrystalline tiling in ABC star polymers. Phys. Rev. Lett. 98, 195502 (2007)
7.
go back to reference Talapin, V.D., Shevechenko, E.V., Bodnarchuk, M.I., Ye, X.C., Chen, J., Murray, C.B.: Quasicrystalline order in self-assembled binary nanoparticle superlattices. Nature 461, 964–967 (2009)ADSCrossRef Talapin, V.D., Shevechenko, E.V., Bodnarchuk, M.I., Ye, X.C., Chen, J., Murray, C.B.: Quasicrystalline order in self-assembled binary nanoparticle superlattices. Nature 461, 964–967 (2009)ADSCrossRef
8.
go back to reference Fischer, S., Exner, A., Zielske, K., Perlich, J., Deloudi, S., Steuer, W., Linder, P., Foestor, S.: Colloidal quasicrystals with 12-fold and 18-fold symmetry. Proc. Nat. Acad. Sci 108, 1810–1814 (2011)ADSCrossRef Fischer, S., Exner, A., Zielske, K., Perlich, J., Deloudi, S., Steuer, W., Linder, P., Foestor, S.: Colloidal quasicrystals with 12-fold and 18-fold symmetry. Proc. Nat. Acad. Sci 108, 1810–1814 (2011)ADSCrossRef
9.
go back to reference Yue, K., Huang, M.J., Marson, R., He, J.L., Huang, J.H., Zhou, Z., Liu, C., Yan, X.S., Wu, K., Wang, J., Guo, Z.H., Liu, H., Zhang, W., Ni, P.H., Wesdemiotis, C., Wen-Bin Zhang, W.B., Sharon, Glotzer, S.C., Cheng, S.Z.D.: Geometry induced sequence of nanoscale Frank-Kasper and quasicrystal mesophases in giant surfactants. Proc. Nat. Acad. Sci. 113, 1392–1400 (2016) Yue, K., Huang, M.J., Marson, R., He, J.L., Huang, J.H., Zhou, Z., Liu, C., Yan, X.S., Wu, K., Wang, J., Guo, Z.H., Liu, H., Zhang, W., Ni, P.H., Wesdemiotis, C., Wen-Bin Zhang, W.B., Sharon, Glotzer, S.C., Cheng, S.Z.D.: Geometry induced sequence of nanoscale Frank-Kasper and quasicrystal mesophases in giant surfactants. Proc. Nat. Acad. Sci. 113, 1392–1400 (2016)
10.
go back to reference Lubensky, T.C., Ramaswamy, S., Toner, J.: Hydrodynamics of icosahedral quasicrystals. Phys. Rev. B 32, 7444–7452 (1985)ADSCrossRef Lubensky, T.C., Ramaswamy, S., Toner, J.: Hydrodynamics of icosahedral quasicrystals. Phys. Rev. B 32, 7444–7452 (1985)ADSCrossRef
11.
go back to reference Fan, T.Y.: Mathematical theory of elasticity of quasicrystals and its applications, Science Press, Beijing/Springer-Verlag, Heidelberg, 1st edition, 2010; 2nd edition, 2016, in which the more detailed discussion on symmetry groups of quasicrystals, refer to Hu, C.Z., Wang, R.H., Ding, D.H.: Symmetry groups, physical constant tensors, elasticity and dislocations. Rep. Prog. Phys. 63, 1–39 (2000); the dislocation solution of phason field was obtained firstly by Ding, D.H., refer to Yang, S.H., Ding, D.H.: Foundation of Theory of Crystal Dislocations, vol. 2, Science Press. Beijing (1998), in Chinese Fan, T.Y.: Mathematical theory of elasticity of quasicrystals and its applications, Science Press, Beijing/Springer-Verlag, Heidelberg, 1st edition, 2010; 2nd edition, 2016, in which the more detailed discussion on symmetry groups of quasicrystals, refer to Hu, C.Z., Wang, R.H., Ding, D.H.: Symmetry groups, physical constant tensors, elasticity and dislocations. Rep. Prog. Phys. 63, 1–39 (2000); the dislocation solution of phason field was obtained firstly by Ding, D.H., refer to Yang, S.H., Ding, D.H.: Foundation of Theory of Crystal Dislocations, vol. 2, Science Press. Beijing (1998), in Chinese
12.
go back to reference Sleozkin, N.A.: Incompressible Viscous Fluid Dynamics. Gostehizdat Press, Moscow, in Russian (1959) Sleozkin, N.A.: Incompressible Viscous Fluid Dynamics. Gostehizdat Press, Moscow, in Russian (1959)
13.
go back to reference Oseen, C.W.: Ueber die Stokes’sche Formel und ueber eine verwandte Aufgabe in der Hydrodynamik, Ark Math Astronom Fys. 6 (1910) Oseen, C.W.: Ueber die Stokes’sche Formel und ueber eine verwandte Aufgabe in der Hydrodynamik, Ark Math Astronom Fys. 6 (1910)
14.
go back to reference Oseen, C.W.: Neuere Methoden und Ergibnisse in der Hydrodynamik. Akademische Verlagsgesellschaft, Leipzig (1927)MATH Oseen, C.W.: Neuere Methoden und Ergibnisse in der Hydrodynamik. Akademische Verlagsgesellschaft, Leipzig (1927)MATH
15.
go back to reference Cheng, H., Fan, T.Y., Tang, Z.Y.: Flow of compressible viscous fluid past a circular cylinder, unpublished work (2016) Cheng, H., Fan, T.Y., Tang, Z.Y.: Flow of compressible viscous fluid past a circular cylinder, unpublished work (2016)
16.
go back to reference Cheng, H., Fan, T.Y.: Flow of soft-matter quasicrystals with 12-fold symmetry past a circular cylinder, unpublished work (2017) Cheng, H., Fan, T.Y.: Flow of soft-matter quasicrystals with 12-fold symmetry past a circular cylinder, unpublished work (2017)
17.
go back to reference Kochin, N.E., Kibel’I, I.A., Roze, N.V.: Theoretical Hydrodynamics. Government Press of Phys-Math Literature, Moscow, in Russian (1953) Kochin, N.E., Kibel’I, I.A., Roze, N.V.: Theoretical Hydrodynamics. Government Press of Phys-Math Literature, Moscow, in Russian (1953)
18.
go back to reference Oleynikov, P., Dzugutov, M., Lidin, S.: A smectic quasicrystal. Soft Matter 12, 8869–8876 (2016)ADSCrossRef Oleynikov, P., Dzugutov, M., Lidin, S.: A smectic quasicrystal. Soft Matter 12, 8869–8876 (2016)ADSCrossRef
19.
go back to reference Brostow, W., Cunha, A.M., Quintanila, J., Simoes, R.: Crack formation and propagation of polymer-liquid crystals. Macromol. Theor. Simul. 11, 308–312 (2002)CrossRef Brostow, W., Cunha, A.M., Quintanila, J., Simoes, R.: Crack formation and propagation of polymer-liquid crystals. Macromol. Theor. Simul. 11, 308–312 (2002)CrossRef
20.
go back to reference Fan, T.Y.: A model of crack in smectic a liquid crystals. Philol. Mag. Lett. 92, 153–158 (2012)ADSCrossRef Fan, T.Y.: A model of crack in smectic a liquid crystals. Philol. Mag. Lett. 92, 153–158 (2012)ADSCrossRef
21.
go back to reference Fan, T.Y., Tang, Z.Y.: A model of crack based on dislocations in smectic A liquid crystals. Chin. Phys. B. 20, 106103 (2014) Fan, T.Y., Tang, Z.Y.: A model of crack based on dislocations in smectic A liquid crystals. Chin. Phys. B. 20, 106103 (2014)
22.
go back to reference Bohn, S., Pauchard, L., Couder, Y.: Hierarchical crack pattern as formed by successive domain divisions. I. Temporal and geometrical hierarchy. Phys. Rev. E 71, 046214 (2005) Bohn, S., Pauchard, L., Couder, Y.: Hierarchical crack pattern as formed by successive domain divisions. I. Temporal and geometrical hierarchy. Phys. Rev. E 71, 046214 (2005)
23.
go back to reference Tirumkudulu, M.S.: Cracking in drying latex films. Langmuir 21, 4938–4948 (2005)CrossRef Tirumkudulu, M.S.: Cracking in drying latex films. Langmuir 21, 4938–4948 (2005)CrossRef
24.
go back to reference Yow, H.N., Goikoetra, M., Goehring, L., Routh, A.F.: Effect of film thickness and particle size on cracking stresses in drying latex films. J. Colloid. Interface Sci. 352, 542–548 (2010)ADSCrossRef Yow, H.N., Goikoetra, M., Goehring, L., Routh, A.F.: Effect of film thickness and particle size on cracking stresses in drying latex films. J. Colloid. Interface Sci. 352, 542–548 (2010)ADSCrossRef
25.
go back to reference van der Kooij, H.M., Sprakel, J.: Watching paint dry; more exciting than it seems. Soft Matter 11, 6353–6359 (2015)ADSCrossRef van der Kooij, H.M., Sprakel, J.: Watching paint dry; more exciting than it seems. Soft Matter 11, 6353–6359 (2015)ADSCrossRef
Metadata
Title
Dynamics of Soft-Matter Quasicrystals with 12-Fold Symmetry
Authors
Tian-You Fan
Wenge Yang
Hui Cheng
Xiao-Hong Sun
Copyright Year
2022
Publisher
Springer Nature Singapore
DOI
https://doi.org/10.1007/978-981-16-6628-5_7

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