搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

有限尺寸胶体体系的二维结晶

贝帮坤 王华光 张泽新

引用本文:
Citation:

有限尺寸胶体体系的二维结晶

贝帮坤, 王华光, 张泽新

Two-dimensional crystallization in finite-sized colloidal systems

Bei Bang-Kun, Wang Hua-Guang, Zhang Ze-Xin
PDF
HTML
导出引用
  • 从工业上的大尺寸晶体生长到实验室中受限小体系的结晶, 结晶是普遍存在的物理现象, 也一直是物理学中的重要研究课题. 与大尺度结晶相变的研究相比, 对于有限小尺度体系结晶过程的研究相对较少. 本文通过设计具有吸引相互作用的胶体体系, 在实验上研究了有限小尺寸胶体体系的二维结晶相变. 通过计算和分析径向分布函数、泰森多边形以及取向序参量, 发现有限小尺寸体系的结晶过程是从中央高密度区域开始, 随着结晶的进行, 周围液相减小而晶相增加, 最后完全转变为晶态的过程. 体系结晶速率呈现两个阶段: 在结晶初期中央区域是高密度的亚稳态液体, 会降低结晶自由能能垒, 使得体系快速结晶; 随后晶相长大, 亚稳态液体消失, 体系结晶速率变慢. 此外, 通过统计有序度参量的分布发现: 在结晶过程中, 序参量出现双峰分布, 分别对应液相和晶相, 与大尺度胶体体系的二维结晶行为一致, 说明序参量分布的变化规律是二维结晶相变的重要特征.
    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.
      通信作者: 张泽新, zhangzx@suda.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11574222, 11704269, 21522404)和江苏省高等学校自然科学研究项目(批准号: 17KJB140020)资助的课题.
      Corresponding author: Zhang Ze-Xin, zhangzx@suda.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11574222, 11704269, 21522404) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No.17KJB140020).
    [1]

    Löwen H 1994 Phys. Rep. 237 249Google Scholar

    [2]

    Kosterlitz J M, Thouless D J 1973 J. Phys. C 6 1181Google Scholar

    [3]

    Nelson D R, Halperin B 1979 Phys. Rev. B 19 2457Google Scholar

    [4]

    Young A 1979 Phys. Rev. B 19 1855Google Scholar

    [5]

    Gasser U 2009 J. Phys.: Condes. Matter 21 203101Google Scholar

    [6]

    Dinsmore A D, Crocker J C, Yodh A G 1998 Curr. Opin. Colloid Interface Sci. 3 5Google Scholar

    [7]

    Gast A P, Russel W B 1998 Phys. Today 51 24Google Scholar

    [8]

    Pieranski P 1983 Contemp. Phys. 24 25Google Scholar

    [9]

    Gasser U, Weeks E R, Schofield A, Pusey P, Weitz D 2001 Science 292 258Google Scholar

    [10]

    Kegel W K, van Blaaderen A 2000 Science 287 290Google Scholar

    [11]

    Wu Y L, Derks D, van Blaaderen A, Imhof A 2009 Proc. Natl. Acad. Sci. U.S.A. 106 10564Google Scholar

    [12]

    Hynninen A P, Thijssen J H, Vermolen E C, Dijkstra M, van Blaaderen A 2007 Nat. Mater. 6 202Google Scholar

    [13]

    Wang Z, Alsayed A M, Yodh A G, Han Y 2010 J. Chem. Phys. 132 154501Google Scholar

    [14]

    Wang Z, Qi W, Peng Y, Alsayed A M, Chen Y, Tong P, Han Y 2011 J. Chem. Phys. 134 034506Google Scholar

    [15]

    Savage J, Blair D, Levine A, Guyer R, Dinsmore A 2006 Science 314 795Google Scholar

    [16]

    Savage J, Dinsmore A 2009 Phys. Rev. Lett. 102 198302Google Scholar

    [17]

    Moore L J, Dear R D, Summers M D, Dullens R P, Ritchie G A 2010 Nano Lett. 10 4266Google Scholar

    [18]

    Tanaka S, Oki Y, Kimura Y 2014 Phys. Rev. E 89 052305Google Scholar

    [19]

    Bonn D, Otwinowski J, Sacanna S, Guo H, Wegdam G, Schall P 2009 Phys. Rev. Lett. 103 156101Google Scholar

    [20]

    Zhang Z, Yunker P J, Habdas P, Yodh A G 2011 Phys. Rev. Lett. 107 208303Google Scholar

    [21]

    Xiao Y S, Yang L, Tian H Z, Yu Q M, Zhang Z X 2013 Langmuir 29 7216Google 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 230Google Scholar

    [24]

    Ten Wolde P R, Frenkel D 1997 Science 277 1975Google Scholar

    [25]

    Zhang K, Liu X 2004 Nature 429 739Google Scholar

    [26]

    Lutsko J F, Nicolis G 2006 Phys. Rev. Lett. 96 046102Google Scholar

    [27]

    Han Y, Ha N, Alsayed A, Yodh A 2008 Phys. Rev. E 77 041406

  • 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

    Fig. 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)

    Fig. 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)

    Fig. 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

    Fig. 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)

    Fig. 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

    Fig. 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

    Fig. 7.  The distribution of orientational order parameter at different crystallization times.

  • [1]

    Löwen H 1994 Phys. Rep. 237 249Google Scholar

    [2]

    Kosterlitz J M, Thouless D J 1973 J. Phys. C 6 1181Google Scholar

    [3]

    Nelson D R, Halperin B 1979 Phys. Rev. B 19 2457Google Scholar

    [4]

    Young A 1979 Phys. Rev. B 19 1855Google Scholar

    [5]

    Gasser U 2009 J. Phys.: Condes. Matter 21 203101Google Scholar

    [6]

    Dinsmore A D, Crocker J C, Yodh A G 1998 Curr. Opin. Colloid Interface Sci. 3 5Google Scholar

    [7]

    Gast A P, Russel W B 1998 Phys. Today 51 24Google Scholar

    [8]

    Pieranski P 1983 Contemp. Phys. 24 25Google Scholar

    [9]

    Gasser U, Weeks E R, Schofield A, Pusey P, Weitz D 2001 Science 292 258Google Scholar

    [10]

    Kegel W K, van Blaaderen A 2000 Science 287 290Google Scholar

    [11]

    Wu Y L, Derks D, van Blaaderen A, Imhof A 2009 Proc. Natl. Acad. Sci. U.S.A. 106 10564Google Scholar

    [12]

    Hynninen A P, Thijssen J H, Vermolen E C, Dijkstra M, van Blaaderen A 2007 Nat. Mater. 6 202Google Scholar

    [13]

    Wang Z, Alsayed A M, Yodh A G, Han Y 2010 J. Chem. Phys. 132 154501Google Scholar

    [14]

    Wang Z, Qi W, Peng Y, Alsayed A M, Chen Y, Tong P, Han Y 2011 J. Chem. Phys. 134 034506Google Scholar

    [15]

    Savage J, Blair D, Levine A, Guyer R, Dinsmore A 2006 Science 314 795Google Scholar

    [16]

    Savage J, Dinsmore A 2009 Phys. Rev. Lett. 102 198302Google Scholar

    [17]

    Moore L J, Dear R D, Summers M D, Dullens R P, Ritchie G A 2010 Nano Lett. 10 4266Google Scholar

    [18]

    Tanaka S, Oki Y, Kimura Y 2014 Phys. Rev. E 89 052305Google Scholar

    [19]

    Bonn D, Otwinowski J, Sacanna S, Guo H, Wegdam G, Schall P 2009 Phys. Rev. Lett. 103 156101Google Scholar

    [20]

    Zhang Z, Yunker P J, Habdas P, Yodh A G 2011 Phys. Rev. Lett. 107 208303Google Scholar

    [21]

    Xiao Y S, Yang L, Tian H Z, Yu Q M, Zhang Z X 2013 Langmuir 29 7216Google 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 230Google Scholar

    [24]

    Ten Wolde P R, Frenkel D 1997 Science 277 1975Google Scholar

    [25]

    Zhang K, Liu X 2004 Nature 429 739Google Scholar

    [26]

    Lutsko J F, Nicolis G 2006 Phys. Rev. Lett. 96 046102Google Scholar

    [27]

    Han Y, Ha N, Alsayed A, Yodh A 2008 Phys. Rev. E 77 041406

  • [1] 亢玉彬, 唐吉龙, 李科学, 李想, 侯效兵, 楚学影, 林逢源, 王晓华, 魏志鹏. Be, Si掺杂调控GaAs纳米线结构相变及光学特性. 物理学报, 2021, 70(20): 207804. doi: 10.7498/aps.70.20210782
    [2] 刘心卓, 王华光. 椭球胶体在圆球胶体体系中扩散行为的实验研究. 物理学报, 2020, 69(23): 238201. doi: 10.7498/aps.69.20201301
    [3] 杨俊升, 朱子亮, 曹启龙. 预取向半晶态高分子片晶结构形成微观机理及其应力-应变响应特性的分子动力学模拟. 物理学报, 2020, 69(3): 038101. doi: 10.7498/aps.69.20191191
    [4] 马红孺. 胶体排空相互作用理论与计算. 物理学报, 2016, 65(18): 184701. doi: 10.7498/aps.65.184701
    [5] 张天辉, 曹镜声, 梁颖, 刘向阳. 胶体在基础物理研究中的应用. 物理学报, 2016, 65(17): 176401. doi: 10.7498/aps.65.176401
    [6] 王理林, 王志军, 林鑫, 王锦程, 黄卫东. 冷却速率对温敏聚N-异丙基丙烯酰胺胶体结晶过程的影响. 物理学报, 2016, 65(10): 106403. doi: 10.7498/aps.65.106403
    [7] 王东明, 吕业刚, 宋三年, 王苗, 沈祥, 王国祥, 戴世勋, 宋志棠. Cu对用于高速相变存储器的Sb2Te薄膜的结构及相变的影响研究. 物理学报, 2015, 64(15): 156102. doi: 10.7498/aps.64.156102
    [8] 孙景阳, 王东明, 吕业刚, 王苗, 汪伊曼, 沈祥, 王国祥, 戴世勋. 应用于相变存储器的Cu-Ge3Sb2Te5薄膜的结构及相变特性研究. 物理学报, 2015, 64(1): 016103. doi: 10.7498/aps.64.016103
    [9] 曲艳东, 孔祥清, 李晓杰, 闫鸿浩. 热处理对爆轰合成的纳米TiO2混晶的结构相变的影响. 物理学报, 2014, 63(3): 037301. doi: 10.7498/aps.63.037301
    [10] 邢雪, 王小飞, 张庆礼, 孙贵花, 刘文鹏, 孙敦陆, 殷绍唐. LuTaO4相变及结构. 物理学报, 2014, 63(24): 248107. doi: 10.7498/aps.63.248107
    [11] 刘本琼, 谢雷, 段晓溪, 孙光爱, 陈波, 宋建明, 刘耀光, 汪小琳. 铀的结构相变及力学性能的第一性原理计算. 物理学报, 2013, 62(17): 176104. doi: 10.7498/aps.62.176104
    [12] 周平, 王新强, 周木, 夏川茴, 史玲娜, 胡成华. 第一性原理研究硫化镉高压相变及其电子结构与弹性性质. 物理学报, 2013, 62(8): 087104. doi: 10.7498/aps.62.087104
    [13] 卢志鹏, 祝文军, 卢铁城, 孟川民, 徐亮, 李绪海. 高温高压下过渡金属Ru的结构相变. 物理学报, 2013, 62(17): 176402. doi: 10.7498/aps.62.176402
    [14] 李建华, 崔元顺, 曾祥华, 陈贵宾. ZnS结构相变、电子结构和光学性质的研究. 物理学报, 2013, 62(7): 077102. doi: 10.7498/aps.62.077102
    [15] 王军国, 刘福生, 李永宏, 张明建, 张宁超, 薛学东. 在石英界面处液态水的冲击结构相变. 物理学报, 2012, 61(19): 196201. doi: 10.7498/aps.61.196201
    [16] 董丽芳, 杨玉杰, 范伟丽, 岳晗, 王帅, 肖红. 介质阻挡放电中放电丝结构相变过程研究. 物理学报, 2010, 59(3): 1917-1922. doi: 10.7498/aps.59.1917
    [17] 季正华, 曾祥华, 岑洁萍, 谭明秋. ZnSe相变、电子结构的第一性原理计算. 物理学报, 2010, 59(2): 1219-1224. doi: 10.7498/aps.59.1219
    [18] 崔新林, 祝文军, 邓小良, 李英骏, 贺红亮. 冲击波压缩下含纳米孔洞单晶铁的结构相变研究. 物理学报, 2006, 55(10): 5545-5550. doi: 10.7498/aps.55.5545
    [19] 王震遐, 王 森, 胡建刚, 俞国军. 多壁碳纳米管在循环相变过程中结构变化初探. 物理学报, 2005, 54(9): 4263-4268. doi: 10.7498/aps.54.4263
    [20] 汪金芝, 方庆清. 纳米Zn0.6CoxFe2.4-xO4晶粒的结构相变与磁性研究. 物理学报, 2004, 53(9): 3186-3190. doi: 10.7498/aps.53.3186
计量
  • 文章访问数:  6180
  • PDF下载量:  82
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-03-05
  • 修回日期:  2019-03-18
  • 上网日期:  2019-05-01
  • 刊出日期:  2019-05-20

/

返回文章
返回