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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.
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Keywords:
- colloids /
- depletion interaction
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[7] Hong L, Jiang S, Granick S 2006 Langmuir 22 9495
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[21] Asakura S, Oosawa F 1954 J. Chem. Phys. 22 1255
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[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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[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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