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Colloidal interactions: From effective potentials to structure

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In this paper we present an overview of some key theoretical tools employed for the investigations of the equilibrium structure and thermodynamics of complex fluids. We place our focus on the most common systems of soft-matter science, namely dispersions of colloidal particles, which may be hard or soft, and which may carry electric charge. The concept of the effective Hamiltonian, which plays the key role in these coarse-grained approaches is introduced, and it is given a precise mathematical definition. Its properties as well as key approximations involved in deriving effective potentials are discussed. Thereafter, the ways in which the effective interactions can be combined with tools from the theory of fluids and statistical mechanics are presented, putting emphasis on Density Functional Theory. The general principles are combined with extensive exposures from currently active research fields, and applications to interfacial and wetting behavior of complex mixtures as well as to crystallization and cluster formation are discussed. Appendix A serves as a mini-course on functionals and functional differentiation.

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References

  1. Ashcroft N. W. and Mermin N. D., Solid State Physics (Holt Saunders, Philadelphia) 1976.

    MATH  Google Scholar 

  2. Hunter R. J., Foundations of Colloid Science, Vol. I (Clarendon Press, Oxford) 1986.

    Google Scholar 

  3. Russel W. B., Saville D. A. and Schowalter W. R., Colloidal Dispersions (Cambridge University Press, Cambridge) 1989.

    Book  MATH  Google Scholar 

  4. Vanderhoff J. W., van den Hul H. J., Tausk R. J. M. and Overbeek J. T. G., in Clean Surfaces: Their Preparation and Characterization for Interfacial Studies, edited by G. Goldfinger (Dekker, New York) 1970.

  5. Goodwin J. W., Hearn J., Ho C. C. and Otewill R. H., Br. Polymer J., 5 (1973) 347.

    Article  Google Scholar 

  6. Iler R. K., Surface and Colloid Science, edited by E. Matijevic, Vol. 5 (Wiley, New York) 1973.

    Google Scholar 

  7. Iler R. K., The Chemistry of Silica (Wiley, New York) 1979.

    Google Scholar 

  8. Barrett K. E. J., Dispersion Polymerization in Organic Media (Wiley, London) 1975.

    Google Scholar 

  9. Antl L., Goodwin J. W., Hill R. D., Otewill R. H., Owens S. M., Papworth S. and Waters J. A., Colloids Surf., 17 (1986) 67.

    Article  Google Scholar 

  10. Pusey P. N. Les Houches, Session LI, Liquids, Freezing and Glass Transition, edited by J.-P. Hansen, D. Levesque and J. Zinn-Justin (North-Holland, Amsterdam) 1991.

    Google Scholar 

  11. Hansen J.-P. and Löwen H., Ann. Rev. Phys. Chem., 51 (2000) 209.

    Article  ADS  Google Scholar 

  12. Belloni L., J. Phys.: Condens. Matter, 12 (2000) R549.

    ADS  Google Scholar 

  13. Bianchi E., Largo J., Tartaglia P., Zaccarelli E. and Sciortino F., Phys. Rev. Lett., 97 (2006) 168301.

  14. Sciortino F., Giacometti A. and Pastore G., Phys. Rev. Lett., 103 (2006) 237801.

    Article  ADS  Google Scholar 

  15. Russo J., Tavares J. M., Teixeira P. I. C., Telo da Gama M. M. and Sciortino F., Phys. Rev. Lett., 106 (2011) 085703.

    Article  ADS  Google Scholar 

  16. Kretzschmar I. and Pawar Amar B., Langmuir, 24 (2008) 355.

    Article  Google Scholar 

  17. Kretzschmar I. and Pawar Amar B., Langmuir, 25 (2009) 9057.

    Article  Google Scholar 

  18. Bianchi E., Blaak R. and Likos C. N., Phys. Chem. Chem. Phys., 13 (2011) 6397.

    Article  Google Scholar 

  19. Grest G. S., Fetters L. J., Huang J. S. and Richter D., Adv. Chem. Phys., 94 (1996) 67.

    Google Scholar 

  20. Likos C. N., Löwen H., Watzlawek M., Abbas B., Jucknischke O., Allgaier J. and Richter D., Phys. Rev. Lett., 80 (1998) 4450.

    Article  ADS  Google Scholar 

  21. Watzlawek M., Likos C. N. and Löwen H., Phys. Rev. Lett., 82 (1999) 5289.

    Article  ADS  Google Scholar 

  22. McMillan W. G. and Mayer J. E., J. Chem. Phys., 13 (1945) 276.

    Article  ADS  Google Scholar 

  23. Kirkwood J. G. and Buff F. P., J. Chem. Phys., 19 (1951) 774.

    Article  ADS  MathSciNet  Google Scholar 

  24. van Megen W. and Snook I., Adv. Coll. Interface Sci., 21 (1984) 119.

    Article  Google Scholar 

  25. Likos C. N., Phys. Rep., 348 (2001) 267.

    Article  ADS  Google Scholar 

  26. Dijkstra M., van Roij R. and Evans R., Phys. Rev. E, 59 (1999) 5744.

    Article  ADS  Google Scholar 

  27. Likos C. N., Phys. Rep., 348 (2001) 267.

    Article  ADS  Google Scholar 

  28. van Roij R. and Hansen J.-P., Phys. Rev. Lett., 79 (1997) 3082.

    Article  ADS  Google Scholar 

  29. van Roij R., Dijkstra M. and Hansen J.-P., Phys. Rev. E, 59 (1999) 2010.

    Article  ADS  Google Scholar 

  30. Witten T. A. and Pincus P. A., Macromolecules, 19 (1986) 2509.

    Article  ADS  Google Scholar 

  31. Attard P., J. Chem. Phys., 91 (1989) 3083.

    Article  ADS  Google Scholar 

  32. Dzubiella J., Likos C. N. and Löwen H., J. Chem. Phys., 116 (2002) 9518.

    Article  ADS  Google Scholar 

  33. Hoffmann N., Likos C. N. and Hansen J.-P., Mol. Phys., 102 (2004) 857.

    Article  ADS  Google Scholar 

  34. Bianchi E., Kahl G. and Likos C. N., Soft Matter, 7 (2011) 8313.

    Article  ADS  Google Scholar 

  35. Badia M., Benhamou M., Derouiche A. and Bretonnet J. L., Colloid Polym. Sci., 279 (2001) 763.

    Article  Google Scholar 

  36. Daoud M. and Cotton J. P., J. Phys. (Paris), 43 (1982) 531.

    Article  Google Scholar 

  37. Likos C. N., Soft Matter, 2 (2006) 478.

    Article  ADS  Google Scholar 

  38. Hansen J.-P. and McDonald I. R., Theory of Simple Liquids, 3rd Edition (Academic Press, London) 2006.

    MATH  Google Scholar 

  39. Higgins J. S. and Benoît H. C., Polymers and Neutron Scattering (Clarendon Press, Oxford) 1994.

    Google Scholar 

  40. Rosenfeld Y. and Ashcroft N. W., Phys. Rev. A, 20 (1979) 1208.

    Article  ADS  Google Scholar 

  41. Rogers F. A. and Young D. A., Phys. Rev. A, 30 (1984) 999.

    Article  ADS  Google Scholar 

  42. Hutchinson P. and Conkie W. R., Mol. Phys., 24 (1972) 567.

    Article  ADS  Google Scholar 

  43. Hall D. S. and Conkie W. R., Mol. Phys., 40 (1980) 907.

    Article  ADS  Google Scholar 

  44. Verlet L., Mol. Phys., 42 (1981) 1291.

    Article  ADS  Google Scholar 

  45. Munakata T., Phys. Rev. E, 50 (1994) 2347.

    Article  ADS  Google Scholar 

  46. Araki J. and Munakata T., Phys. Rev. E, 52 (1995) 2577.

    Article  ADS  Google Scholar 

  47. Dean D. S., J. Phys. A, 29 (1996) L613.

    Article  ADS  Google Scholar 

  48. Marconi U. M. B. and Tarazona P., J. Chem. Phys., 110 (1999) 8032.

    Article  ADS  Google Scholar 

  49. Archer A. J. and Rauscher M., J. Phys. A, 37 (2004) 9325.

    Article  ADS  MathSciNet  Google Scholar 

  50. Dzubiella J. and Likos C. N., J. Phys.: Condens. Matter, 15 (2003) L147.

    ADS  Google Scholar 

  51. Archer A. J. and Evans R., J. Chem. Phys., 121 (2004) 4246.

    Article  ADS  Google Scholar 

  52. Rex M., Löwen H. and Likos C. N., Phys. Rev. E, 72 (2005) 021404.

    Article  ADS  Google Scholar 

  53. Evans R., Adv. Phys., 28 (1979) 143.

    Article  ADS  Google Scholar 

  54. Percus J. K., Phys. Rev. Lett., 8 (2006) 462.

    Article  ADS  Google Scholar 

  55. Ramakrishnan T. V. and Yussouff M., Phys. Rev. B, 19 (1979) 2775.

    Article  ADS  Google Scholar 

  56. Evans R., in Fundamentals of Inhomogeneous Fluids, edited by Henderson D. (Dekker, New York) 1992.

  57. Rosenfeld Y., J. Chem. Phys., 98 (1993) 8126.

    Article  ADS  Google Scholar 

  58. Schmidt M., J. Phys.: Condens. Matter, 15 (2003) S101.

    ADS  Google Scholar 

  59. Louis A. A., Bolhuis P. G., Hansen J.-P. and Meijer E. J., Phys. Rev. Lett., 85 (2000) 2522.

    Article  ADS  Google Scholar 

  60. Konieczny M., Likos C. N. and Löwen H., J. Chem. Phys., 121 (2004) 4913.

    Article  ADS  Google Scholar 

  61. Likos C. N., Schmidt M., Löwen H., Ballauff M. and Pötschke D., Macromolecules, 34 (2001) 2914.

    Article  ADS  Google Scholar 

  62. Likos C. N., Rosenfeldt S., Dingenouts N., Ballauf M., Lindner P., Werner N. and Vögtle F., J. Chem. Phys., 117 (2002) 1869.

    Article  ADS  Google Scholar 

  63. Götze I. O., Harreis H. M. and Likos C. N., J. Chem. Phys., 120 (2004) 7761.

    Article  ADS  Google Scholar 

  64. Jusufi A., Dzubiella J., Likos C. N., Von Ferber C. and Löwen H., J. Phys.: Condens. Matter, 13 (2001) 6177.

    ADS  Google Scholar 

  65. Gottwald D., Likos C. N., Kahl G. and Löwen H., Phys. Rev. Lett., 92 (2004) 068301.

    Article  ADS  Google Scholar 

  66. Gottwald D., Likos C. N., Kahl G. and Löwen H., J. Chem. Phys., 122 (2005) 074903.

    Article  ADS  Google Scholar 

  67. Jusufi A., Likos C. N. and Löwen H., Phys. Rev. Lett., 88 (2002) 018301.

    Article  ADS  Google Scholar 

  68. Jusufi A., Likos C. N. and Löwen H., J. Chem. Phys., 116 (2002) 11011.

    Article  ADS  Google Scholar 

  69. Lang A., Likos C. N., Watzlawek M. and Löwen H., J. Phys.: Condens. Matter, 12 (2000) 5087.

    ADS  Google Scholar 

  70. Likos C. N., Lang A., Watzlawek M. and Löwen H., Phys. Rev. E, 63 (2001) 031206.

  71. Louis A. A., Bolhuis P. G. and Hansen J.-P., Phys. Rev. E, 62 (2000) 7961.

    Article  ADS  Google Scholar 

  72. Archer A. J. and Evans R., Phys. Rev. E, 64 (2001) 041501.

    Article  ADS  Google Scholar 

  73. Archer A. J. and Evans R., J. Phys.: Condens. Matter, 14 (2002) 1131.

    ADS  Google Scholar 

  74. Archer A. J., Likos C. N. and Evans R., J. Phys.: Condens. Matter, 14 (2002) 12031.

    ADS  Google Scholar 

  75. Acedo L. and Santos A., Phys. Lett. A, 323 (2004) 427.

    Article  ADS  Google Scholar 

  76. Dietrich S., in Phase Transitions and Critical Phenomena, edited by Domb C. and Lebowitz J. L., Vol. 12 (Academic, London) 1988, p. 1.

  77. Alder B. J. and Wainwright T. E., J. Chem. Phys., 27 (1957) 1208.

    Article  ADS  Google Scholar 

  78. Wood W. W. and Jacobson J. D., J. Chem. Phys., 27 (1957) 1207.

    Article  ADS  Google Scholar 

  79. Alder B. J., Hoover W. G. and Young D. A., J. Chem. Phys., 49 (1968) 3688.

    Article  ADS  Google Scholar 

  80. Hoover W. G. and Ree F. H., J. Chem. Phys., 49 (1968) 3609.

    Article  ADS  Google Scholar 

  81. Haymet A. D. J. and Oxtoby D., J. Chem. Phys., 84 (1986) 1769.

    Article  ADS  Google Scholar 

  82. Bolhuis P., Frenkel D., Mau S. C. and Huse D. A., Nature, 388 (1997) 235.

    Article  ADS  Google Scholar 

  83. Likos C. N. and Ashcroft N. W., Phys. Rev. Lett., 69 (1992) 316.

    Article  ADS  Google Scholar 

  84. Archer A. J., Phys. Rev. E, 72 (2005) 051501.

    Article  ADS  Google Scholar 

  85. Ballauff M. and Likos C. N., Ang. Chem. Int. Ed., 43 (2004) 2998.

    Article  Google Scholar 

  86. Mladek B. M., Kahl G. and Likos C. N., Phys. Rev. Lett., 100 (2008) 028301.

    Article  ADS  Google Scholar 

  87. Likos C. N., Mladek B. M., Gottwald D. and Kahl G., J. Chem. Phys., 126 (2007) 224502.

    Article  ADS  Google Scholar 

  88. Mladek B. M., Gottwald D., Kahl G., Neumann M. and Likos C. N., Phys. Rev. Lett., 96 (2006) 045701.

    Article  ADS  Google Scholar 

  89. Mladek B. M., Gottwald D., Kahl G., Neumann M. and Likos C. N., J. Phys. Chem. B, 111 (2007) 12799.

    Article  Google Scholar 

  90. Mladek B. M., Charbonneau P. and Frenkel D., Phys. Rev. Lett., 99 (2007) 235702.

    Article  ADS  Google Scholar 

  91. Mladek B. M., Charbonneau P., Likos C. N., Kahl G. and Frenkel D., J. Phys.: Condens. Matter, 20 (2008) 494245.

    Google Scholar 

  92. Moreno A. J. and Likos C. N., Phys. Rev. Lett., 99 (2007) 107801.

    Article  ADS  Google Scholar 

  93. Coslovich D., Strauss L. and Kahl G., Soft Matter, 7 (2011) 2127.

  94. Neuhaus T. and Likos C. N., J. Phys.: Condens. Matter, 23 (2011) 234112.

    ADS  Google Scholar 

  95. Zhang K., Charbonneau P. and Mladek B. M., Phys. Rev. Lett., 105 (2010) 245701.

    Article  ADS  Google Scholar 

  96. Nikoubashman A., Kahl G. and Likos C. N., Phys. Rev. Lett., 107 (2011) 068302.

    Article  ADS  Google Scholar 

  97. Nikoubashman A., Kahl G. and Likos C. N., Soft Matter, 8 (2012) 4121.

    Article  ADS  Google Scholar 

  98. Lenz D. A., Blaak R., Likos C. N. and Mladek B. M., Phys. Rev. Lett., 109 (2012) 228301.

    Article  ADS  Google Scholar 

  99. Glaser M. A., Grason G. M., Kamien R. D., Košmrlj A., Santangelo C. D. and Ziherl P., EPL, 78 (2007) 46004.

    Article  ADS  Google Scholar 

  100. Ziherl P. and Kamien R. D., J. Phys. Chem. B, 115 (2011) 7200.

    Article  Google Scholar 

  101. Ziherl P. and Kamien R. D., Phys. Rev. Lett., 85 (2001) 3528.

    Article  ADS  Google Scholar 

  102. Ziherl P. and Kamien R. D., J. Phys. Chem. B, 105 (2001) 10147.

    Article  Google Scholar 

  103. Yethiraj A. and Woodward C. E., J. Chem. Phys., 102 (1995) 5499.

    Article  ADS  Google Scholar 

  104. Wu J. and Li Z., Annu. Rev. Phys. Chem., 58 (2008) 85.

    Article  ADS  Google Scholar 

  105. Yu Y.-X. and Wu J., J. Chem. Phys., 117 (2002) 2368.

    Article  ADS  Google Scholar 

  106. Egorov S. A., Phys. Rev. E, 72 (2005) 010401.

    Article  ADS  Google Scholar 

  107. Li Z., Cao D. and Wu J., J. Chem. Phys., 122 (2005) 174708.

    Article  ADS  Google Scholar 

  108. Wang L., Liang H. and Wu J., J. Chem. Phys., 133 (2010) 044906.

    Article  ADS  Google Scholar 

  109. Chandler D. and Pratt L. R., J. Chem. Phys., 65 (1976) 2925.

    Article  ADS  Google Scholar 

  110. Zhou Y. Q. and Stell G., J. Chem. Phys., 96 (1992) 1507.

    Article  ADS  Google Scholar 

  111. Wertheim M. S., J. Chem. Phys., 87 (1987) 7323.

    Article  ADS  Google Scholar 

  112. Binney J. J., Dowrick N. J., Fischer A. J. and Newman M. E. J., The Theory of Critical Phenomena: An Introduction to the Renormalization Group (Oxford University Press, Oxford) 1992.

    MATH  Google Scholar 

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  1. Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090, Vienna, Austria

    C. N. Likos

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Reproduced from Proceedings of the International School of Physics “Enrico Fermi”, Course 184, Physics of Complex Colloids, edited by C. Bechinger, F. Sciortino and P. Ziherl (IOS Press, Amsterdam and SIF, Bologna) 2013, pp. 1–60.

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Likos, C.N. Colloidal interactions: From effective potentials to structure. Riv. Nuovo Cim. 37, 125–180 (2014). https://doi.org/10.1393/ncr/i2014-10098-1

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