胶体排空相互作用理论与计算

马红孺

doi:10.7498/aps.65.184701

摘要

胶体悬浮液由1 nm到1 m大小的颗粒悬浮在液体中构成. 胶体颗粒之间具有体积排斥相互作用和其他相互作用，体积排斥导致排空效应. 当大硬球处于小球构成的胶体中时，大球周围有小球中心不能进入的排空层. 在大的硬球相互接近时，其排空层重合，使小球的自由体积增加，从而熵增加，导致大球之间的等效相互作用，这个相互作用称为排空相互作用. 本文介绍了胶体排空相互作用的概念和图像，简要介绍了计算硬球排空相互作用的接受比率方法、Wang-Landau方法、密度泛函理论方法等数值方法；以Asakura-Oosawa模型为例，介绍了Derjaguin近似方法. 利用这个近似方法，推导了小硬球胶体中一对硬球、硬球和硬墙之间的排空相互作用，以及一对硬球在细棒胶体和薄盘胶体中的排空相互作用的近似公式.

关键词:

胶体 /
排空相互作用

Abstract

Colloidal suspension is composed of particles with sizes between 1 nm and 1 m, suspended in liquid phase. The interaction between the particles consists of a hard core repulsive interaction and other kinds of repulsive and attractive interacions. Hard interaction forbids the particles from occupying the same places, resulting in a depletion effect. When big colloid particles are immersed in a colloid of small particles, each big particle has a depletion layer where the small particles cannot enter due to the hard interaction. The depletion layers of two big particles overlap when they are close enough so that extra free volume of the small particles increases and therefore the entropy of the small particles increase, thus an effective interaction between big particles is induced. This effective interaction is the so-called depletion interaction. In this review the concepts and an intuitive explanation of depletion interaction of colloidal suspensions are presented. The numerical calculation methods, including the acceptance ratio method, Wang-Landau-type method, and density functional theory method, are briefly reviewed. Several useful analytic approximations are presented. Stating from the depletion interaction between two flat plates, the Derjaguin approximation is introduced through the Asakura- Oosawa model. With this approximation, the approximate formulas of depletion interaction between two hard spheres, between a hard sphere and a hard wall, and between a hard sphere and curved hard walls in a small hard sphere colloid are derived. The depletion interaction between two hard spheres in a thin rod colloid and a thin disk colloid are also derived in the Derjaguin approximation.

Keywords:

colloids /
depletion interaction

作者及机构信息

马红孺^1,2

1.
上海交通大学机械与动力工程学院, 上海 200240;

2.
上海交通大学, 人工结构及量子调控教育部重点实验室, 上海 200240

通信作者: 马红孺, hrma@sjtu.edu.cn

基金项目: 国家自然科学基金（批准号：11304169）资助的课题.

Authors and contacts

Ma Hong-Ru^1,2

1.
School of Mechanical Engineering, Shanghai Jiaotong University, Shanghai 200240, China;

2.
Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shanghai Jiaotong University, Shanghai 200240, China

Corresponding author: Ma Hong-Ru, hrma@sjtu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11304169).

参考文献

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[55]	Mao Y, Cates M E, Lekkerkerker H N W 1995 Phys. Rev. Lett. 75 4548
[56]	Mao Y, Cates M E, Lekkerkerker H N W 1997 J. Chem. Phys. 106 3721
[57]	Mao Y, Bladon P, Lekkerkerker H N W, Cates M E 1997 Molec. Phys. 92 151
[58]	Piech M, Walz J Y 2000 J. Colloid Interf. Sci. 232 86
[59]	Oversteegen S M, Lekkerkerker H N W 2004 Physica A 341 23
[60]	Henderson J R 2002 Physica A 313 321

施引文献

[1]	Graham T 1861 Philosophical Transactions of the Royal Society of London 151 183
[2]	Brown R 1828 Philosophical Magazine Series 2 4 161
[3]	Einstein A 1905 Annalen der Physik 17 549
[4]	Matijevic E 1986 Langmuir 2 12
[5]	Matijevic E 1994 Langmuir 10 8
[6]	Snoeks E, van Blaaderen A, van Dillen T, van Kats C M, Brongersma M L, Polman A 2000 Adv. Mater. 12 1511
[7]	Hong L, Jiang S, Granick S 2006 Langmuir 22 9495
[8]	Jiang S, Chen Q, Tripathy M, Luijten E, Schweizer K S, Granick S 2010 Adv. Mater. 22 1060
[9]	Pusey P N (In Hansen J P, Levesque D, Zinn-Justin J editors) 1991 Liquids, Freezing and Glass Transition. II, chapter 10 (Amsterdam: North-Holland) p763
[10]	Dhont J K G 1996 An Introduction to Dynamics of Colloids. Studies in Interface Science (Amsterdam: Elsevier Science)
[11]	Nägele G 1996 Phys. Reports 272 215
[12]	Klein R 1997 The Physics of Complex Systems (In Mallamace F, Stanley H E, Ed.) (Amsterdam: IOS Press) pp301-345
[13]	Likos C N 2001 Phys. Reports 348 267
[14]	Hansen J, McDonald I R 2013 Theory of Simple Liquids: With Applications to Soft Matter (New York: Academic Press)
[15]	Lekkerkerker H N W, Tuinier R 2011 Colloids and the Depletion Interaction (Heidelberg: Springer)
[16]	Derjaguin B V, Landau L 1941 Acta Physicochim. URSS 14 633
[17]	Verwey E F, Overbeek J T G 1948 Theory of the Stability of Lyophobic Colloids (Amsterdam: Elsevier)
[18]	London F 1930 Z. Phys. Chem. 11 222
[19]	Eisenschitz R, London F 1930 Zeitschrift fr Physik 60 491
[20]	Israelachvili J N 2011 Intermolecular and Surface Forces (3rd Ed.) (New York: Academic Press)
[21]	Asakura S, Oosawa F 1954 J. Chem. Phys. 22 1255
[22]	Vrij A 1976 Pure Appl. Chem. 48 471
[23]	Dinsmore A D, Warren P B, Poon W C K, Yodh A G 1997 EPL 40 337
[24]	Bartlett P, Ottewill R H, Pusey P N 1992 Phys. Rev. Lett. 68 3801
[25]	Eldridge M D, Madden P A, Frenkel D 1993 Molec. Phys. 79 105
[26]	Dinsmore A D, Yodh A G, Pine D J 1996 Nature 383 239
[27]	Onsager L 1933 Chem. Rev. 13 73
[28]	Onsager L 1949 Ann. NY Acad. Sci. 51 627
[29]	Attard P 1989 J. Chem. Phys. 91 3083
[30]	Götzelmann B, Evans R, Dietrich S 1998 Phys. Rev. E 57 6785
[31]	Bennett C H 1976 J. Comp. Phys. 22 245
[32]	Allen M P, Tildesley D J 1994 Computer Simulation of Liquids (Oxford: Clarendon Press)
[33]	Li W H, Xue S, Ma H R 2001 J. Shanghai Jiao Tong Univ. E-6 126
[34]	Li W H, Ma H R 2002 Phys. Rev. E 66 061407
[35]	Li W H, Ma H R 2003 Eur. Phys. J. E 12 321
[36]	Li W H, Ma H R 2003 J. Chem. Phys. 119 585
[37]	Li W H, Yang T, Ma H R 2008 J. Chem. Phys. 128 044910
[38]	Wang F G, Landau D P 2001 Phys. Rev. Lett. 86 2050
[39]	Wang F G, Landau D P 2001 Phys. Rev. E 64 056101
[40]	Miao H, Li Y, Ma H R 2014 J. Chem. Phys. 140 154904
[41]	Hohenberg P, Kohn W 1964 Phys. Rev. 136 B864
[42]	Mermin N D 1965 Phys. Rev. 137 A1441
[43]	Rosenfeld Y 1989 Phys. Rev. Lett. 63 980
[44]	Kierlik E, Rosinberg M L 1990 Phys. Rev. A 42 3382
[45]	Tarazona P 2000 Phys. Rev. Lett. 84 694
[46]	Derjaguin B 1934 Kolloid-Zeitschrift 69 155
[47]	Glandt E D 1980 J. Colloid Interf. Sci. 77 512
[48]	Mao Y, Cates M E, Lekkerkerker H N W 1995 Physica A 222 10
[49]	Walz J Y, Sharma A 1994 J. Colloid Interf. Sci. 168 485
[50]	Biben T, Bladon P, Frenkel D 1996 J. Phys. Condensed Mat. 8 10799
[51]	Fisher I Z 1964 Statistical Theory of Liquids (Chicago: The University of Chicago Press)
[52]	Henderson J R 1986 Molec. Phys. 59 89
[53]	Holyst R 1989 Molec. Phys. 68 391
[54]	Asakura S, Oosawa F 1958 J. Polym. Sci. 33 183
[55]	Mao Y, Cates M E, Lekkerkerker H N W 1995 Phys. Rev. Lett. 75 4548
[56]	Mao Y, Cates M E, Lekkerkerker H N W 1997 J. Chem. Phys. 106 3721
[57]	Mao Y, Bladon P, Lekkerkerker H N W, Cates M E 1997 Molec. Phys. 92 151
[58]	Piech M, Walz J Y 2000 J. Colloid Interf. Sci. 232 86
[59]	Oversteegen S M, Lekkerkerker H N W 2004 Physica A 341 23
[60]	Henderson J R 2002 Physica A 313 321

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