Abstract
Aggregation and crystallization of colloidal particles deposited from suspensions on glass surfaces were studied. Trajectories of individual particles are tracked and recorded. Statistics over large amount of particles were made to measure the mean square displacement (MSD), <r 2>, as functions of time, t. Isolated particles diffuse normally along the solid surface in a two dimensional random manner. A power law of <r 2 >~t α is obeyed both by short and long time scale MSDs of particles with neighbors. However, the exponent values are quite different. When the particle area fraction f ≤ 80 %, the particles diffuse normally at the short time scale with a retarded diffusion coefficient. While at the long time scale, a superdiffusive behavior of the particles is detected due to collective motion of particles. When f > 80 %, a spatial confinement effect shows in addition. The retarded particle dynamics and the collective particle movements both originate from the many-body hydrodynamic interaction enhanced by the quasi-two dimensional geometric conditions due to the existence of the substrate and the neighbor particles. If the substrate surface condition is favorable and the hydrodynamic interaction dominates, the long-range hydrodynamic interaction can lead particles in dense particle aggregations to self-assemble into long particle chains. This chaining behavior finally results in a phase transition taking place gradually over a large range of the particle area fraction.
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References
Beysens D, Narayanan T (1999) Wetting-induced aggregation of colloids. J Stat Phys 95:997–1008
Tomilov A, Videcoq A, Cerbelaud M, Piechowiak MA, Chartier T, Ala-Nissila T, Bochicchio D, Ferrando R (2013) Aggregation in colloidal suspensions: Evaluation of the role of hydrodynamic interactions by means of numerical simulations. J Phys Chem B 117:14509–14517
Cates ME, Tailleur J (2013) When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation. EPL (Europhys Lett 101:20010
Furukawa A, Tanaka H (2010) Key role of hydrodynamic interactions in colloidal gelation. Phys Rev Lett 104:245702
Denkov N, Velev O, Kralchevski P, Ivanov I, Yoshimura H, Nagayama K (1992) Mechanism of formation of two-dimensional crystals from latex particles on substrates. Langmuir 8:3183–3190
Pusey PN, Van Megen W (1986) Phase behaviour of concentrated suspensions of nearly hard colloidal spheres. Nature 320:340–342
Palberg T (1997) Colloidal crystallization dynamics. Curr Opin Colloid Interface Sci 2:607–614
Mikhael J, Roth J, Helden L, Bechinger C (2008) Archimedean-like tiling on decagonal quasicrystalline surfaces. Nature 454:501–504
Dong A, Chen J, Vora PM, Kikkawa JM, Murray CB (2010) Binary nanocrystal superlattice membranes self-assembled at the liquid-air interface. Nature 466:474–477
Velev OD, Kaler EW (2000) Structured porous materials via colloidal crystal templating: from inorganic oxides to metals. Adv Mater 12:531–534
Stein A, Schroden RC (2001) Colloidal crystal templating of three-dimensionally ordered macroporous solids: Materials for photonics and beyond. Curr Opin Solid State Mater Sci 5:553–564
Zharov I, Khabibullin A (2014) Surface-modified silica colloidal crystals: Nanoporous films and membranes with controlled ionic and molecular transport. Acc Chem Res 47:440–449
Ding H, Liu C, Gu H, Zhao Y, Wang B, Gu Z (2014) Responsive colloidal crystal for spectrometer grating. ACS Photonics 1:121–126
Yang D, Qin Y, Ye S, Ge J (2014) Polymerization-induced colloidal assembly and photonic crystal multilayer for coding and decoding. Adv Funct Mater 24:817–825
Xue J-Z, Wu X-L, Pine D, Chaikin P (1992) Hydrodynamic interactions in hard-sphere suspensions. Phys Rev A 45:989–993
Mittal J, Hummer G (2012) Pair diffusion, hydrodynamic interactions, and available volume in dense fluids. J Chem Phys 137:034110
Lele PP, Swan JW, Brady JF, Wagner NJ, Furst EM (2011) Colloidal diffusion and hydrodynamic screening near boundaries. Soft Matter 7:6844
Goddard BD, Nold A, Savva N, Pavliotis GA, Kalliadasis S (2013) Proceedings of the European Conference on Complex Systems 2012. In: Gilbert T, Kirkilionis M, Nicolis G (eds) Springer Proceedings in Complexity; Springer International Publishing: Cham
Nagar H, Roichman Y (2013) Collective Excitations of Hydrodynamically Coupled Driven Colloidal Particles. arXiv Prepr. arXiv1312.6576, 5
Bleibel J, Domínguez A, Günther F, Harting J, Oettel M (2014) Hydrodynamic interactions induce anomalous diffusion under partial confinement. Soft Matter 10:2945–2948
Yu J, Gao L, Yan Q, Shen D, Wong CC (2011) In-situ microscope observation of the growth of 2D colloidal crystals in a sessile drop. J Cryst Growth 318:1129–1133
Tanaka H, Araki T (2000) Simulation method of colloidal suspensions with hydrodynamic interactions: Fluid particle dynamics. Phys Rev Lett 85:1338–1341
Li Y, Farrher G, Kimmich R (2006) Sub- and superdiffusive molecular displacement laws in disordered porous media probed by nuclear magnetic resonance. Phys Rev E Stat Nonlinear Soft Matter Phys 74:066309
Sokolov Y, Frydel D, Grier DG, Diamant H, Roichman Y (2011) Hydrodynamic pair attractions between driven colloidal particles. Phys Rev Lett 107:158302
Beatus T, Bar-Ziv R, Tlusty T (2007) Anomalous microfluidic phonons induced by the interplay of hydrodynamic screening and incompressibility. Phys Rev Lett 99:124502
Shani I, Beatus T, Bar-Ziv RH, Tlusty T (2014) Long-range orientational order in two-dimensional microfluidic dipoles. Nat Phys 10:140–144
Acknowledgments
This work was supported by the National Natural Science Foundation of China (51205082), the State Key Lab of Advanced Welding and Joining, Harbin Institute of Technology (AWPTZ12-02), and Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (HIT.NSRIF.2011106). The authors would like to extend sincere thanks to Prof. Clemens Bechinger of 2. Physikalisches Institut, Universität Stuttgart, Germany for sharing softwares used in this research and giving useful comments and suggestions.
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Li, Y., Huo, Y. & Zhang, Y. Two dimensional colloidal crystals formed by particle self-assembly due to hydrodynamic interaction. Colloid Polym Sci 293, 2575–2583 (2015). https://doi.org/10.1007/s00396-015-3636-2
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DOI: https://doi.org/10.1007/s00396-015-3636-2