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The nature of crystallization is considered to be one of the most fundamental research problems in condensed matter physics. With single particle resolution offered by video microscopy, colloidal suspensions provide a novel model system for studying crystallization, melting and other phase transitions, where the structures and dynamics of the particles during the transitions can be quantitatively probed. Traditional systems for studying the crystallization typically focus on the infinitely large systems in order to obtain the equilibrium state. However, studies of the crystallization in finite-sized systems such as crystallization in thin films and porous media, are rare despite the fact that they are the common phenomena in natural world. In this paper, we experimentally investigate the crystallization in a finite-sized colloidal system with attractive interactions. The colloidal suspension is composed of polystyrene microspheres dispersed in a mixture of water and 2, 6-lutidine, in which the interaction between the particles can be tuned by adjusting the temperature. We increase the temperature to 34 °C to induce attractions between the particles and thus producing a cluster, and then reduce the temperature to 33 °C to tune off the attractions. Thus we obtain a finite-sized liquid cluster of the colloidal particles. Crystallization is triggered by increasing the temperature to 34 °C. The crystallization process is recorded by video microscopy and the video data are analyzed by a standard particle tracking algorithm. Through the analysis of radial distribution function, Voronoi diagram, and local order parameter, we find that the crystallization of the finite colloidal system starts from the central dense region of the liquid cluster. This leads to a crystalline phase in the center and a liquid phase on the edge of the cluster. As time elapses, the central crystalline region grows while outer liquid region shrinks. The crystallization process exhibits a two-step scenario: a fast crystallization initially and a slow crystallization at the later stage. At the initial stage, the center of the system forms a dense metastable liquid phase, which lowers the free-energy barrier of crystallization and results in a fast crystallization. As the crystalline region grows, the metastable phase disappears, and thus the crystallization rate decreases. Moreover, a bimodal distribution of the orientational order parameter is observed during the crystallization in our finite-sized colloidal system, which is consistent with that in a large system. This indicates that the bimodal distribution is a common feature of the two-dimensional crystallization.
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Keywords:
- colloids /
- crystallization /
- structure /
- phase transition
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图 1 二维有限尺寸胶体体系的明场显微镜照片 (a) t = 0 s时的液态; (b) t = 1300 s时的晶态, t为结晶时间, 图中标尺为10 μm
Figure 1. Bright-field micrographs of the finite-sized two-dimensional colloidal systems: (a) Liquid phase at t = 0 s; (b) crystal phase at t = 1300 s. t is the crystallization time. The scale bar is 10 μm.
图 2 不同结晶时刻的径向分布函数g(r)
Figure 2. Pair correlation function g(r) at different times of crystallization.
图 3 不同结晶时刻的泰森多边形分布图, 图中的色标表示粒子的最近邻粒子的个数(参见图标)
Figure 3. Snapshots of Voronoi diagram at different times. The color code indicates the number of nearest neighbors for the particles (see the legend).
图 4 近邻粒子数为6的粒子数占总粒子数的比例随结晶时间的变化, 两段不同斜率的红色线条表明, 体系结构变化大约分为两个阶段: 先快后慢
Figure 4. The fraction of particles with 6 nearest neighbors versus crystallization time. The red line is a guide to the eye.
图 5 体系取向序参量随时间分布图, 颜色代表粒子取向序参量
${\psi _{6}}$ 值(参见色带图)Figure 5. Snapshots of orientational order parameter
${\psi _{6}}$ at different times of crystallization. The color of particles represents the value of${\psi _{6}}$ (see the color bar).
图 6 粒子取向序参量的平均值随结晶时间的变化
Figure 6. The time-dependent averaged orientational order parameter,
${\psi _{6}}$ . The red line is a guide to the eye.
图 7 取向序参量的值在不同结晶时刻的分布
Figure 7. The distribution of orientational order parameter at different crystallization times.
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[1] Löwen H 1994 Phys. Rep. 237 249
Google Scholar
[2] Kosterlitz J M, Thouless D J 1973 J. Phys. C 6 1181
Google Scholar
[3] Nelson D R, Halperin B 1979 Phys. Rev. B 19 2457
Google Scholar
[4] Young A 1979 Phys. Rev. B 19 1855
Google Scholar
[5] Gasser U 2009 J. Phys.: Condes. Matter 21 203101
Google Scholar
[6] Dinsmore A D, Crocker J C, Yodh A G 1998 Curr. Opin. Colloid Interface Sci. 3 5
Google Scholar
[7] Gast A P, Russel W B 1998 Phys. Today 51 24
Google Scholar
[8] Pieranski P 1983 Contemp. Phys. 24 25
Google Scholar
[9] Gasser U, Weeks E R, Schofield A, Pusey P, Weitz D 2001 Science 292 258
Google Scholar
[10] Kegel W K, van Blaaderen A 2000 Science 287 290
Google Scholar
[11] Wu Y L, Derks D, van Blaaderen A, Imhof A 2009 Proc. Natl. Acad. Sci. U.S.A. 106 10564
Google Scholar
[12] Hynninen A P, Thijssen J H, Vermolen E C, Dijkstra M, van Blaaderen A 2007 Nat. Mater. 6 202
Google Scholar
[13] Wang Z, Alsayed A M, Yodh A G, Han Y 2010 J. Chem. Phys. 132 154501
Google Scholar
[14] Wang Z, Qi W, Peng Y, Alsayed A M, Chen Y, Tong P, Han Y 2011 J. Chem. Phys. 134 034506
Google Scholar
[15] Savage J, Blair D, Levine A, Guyer R, Dinsmore A 2006 Science 314 795
Google Scholar
[16] Savage J, Dinsmore A 2009 Phys. Rev. Lett. 102 198302
Google Scholar
[17] Moore L J, Dear R D, Summers M D, Dullens R P, Ritchie G A 2010 Nano Lett. 10 4266
Google Scholar
[18] Tanaka S, Oki Y, Kimura Y 2014 Phys. Rev. E 89 052305
Google Scholar
[19] Bonn D, Otwinowski J, Sacanna S, Guo H, Wegdam G, Schall P 2009 Phys. Rev. Lett. 103 156101
Google Scholar
[20] Zhang Z, Yunker P J, Habdas P, Yodh A G 2011 Phys. Rev. Lett. 107 208303
Google Scholar
[21] Xiao Y S, Yang L, Tian H Z, Yu Q M, Zhang Z X 2013 Langmuir 29 7216
Google Scholar
[22] 王华光, 张泽新 2016 物理学报 65 219
Wang H G, Zhang Z Z 2016 Acta Phys. Sin. 65 219
[23] Zhang Z, Xu N, Chen D T N, Yunker P, Alsayed A M, Aptowicz K B, Habdas P, Liu A J, Nagel S R, Yodh A G 2009 Nature 459 230
Google Scholar
[24] Ten Wolde P R, Frenkel D 1997 Science 277 1975
Google Scholar
[25] Zhang K, Liu X 2004 Nature 429 739
Google Scholar
[26] Lutsko J F, Nicolis G 2006 Phys. Rev. Lett. 96 046102
Google Scholar
[27] Han Y, Ha N, Alsayed A, Yodh A 2008 Phys. Rev. E 77 041406
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