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Critical Casimir Forces in Colloidal Suspensions

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Abstract

Some time ago, Fisher and de Gennes pointed out that long-ranged correlations in a fluid close to its critical point T c cause distinct effective forces between immersed colloidal particles which can even lead to flocculation [C. R. Acad. Sc. Paris B 287:207 (1978)]. Here we calculate such forces between pairs of spherical particles as function of both relevant thermodynamic variables, i.e., the reduced temperature t=(T−T c )/T c and the field h conjugate to the order parameter. This provides the basis for specific predictions concerning the phase behavior of a suspension of colloidal particles in a near-critical solvent.

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REFERENCES

  1. M. E. Fisher and P. G. de Gennes, C. R. Acad. Sc. Paris B 287:207(1978).

    Google Scholar 

  2. This conjecture has been worked out in more detail in P. G. de Gennes, C. R. Acad. Sci. Ser. II 292:701(1981).

    Google Scholar 

  3. D. Beysens and D. Estève, Phys. Rev. Lett. 54:2123(1985); for a review, see, D. Beysens, J.-M. Petit, T. Narayanan, A. Kumar, and M. L. Broide, Ber. Bunsenges. Phys. Chem. 98:382(1994).

    Google Scholar 

  4. P. D. Gallagher, M. L. Kurnaz, and J. V. Maher, Phys. Rev. A 46:7750(1992)

    Google Scholar 

  5. M. L. Kurnaz and J. V. Maher, Phys. Rev. E 51:5916(1995).

    Google Scholar 

  6. B. M. Law, J.-M. Petit, and D. Beysens, Phys. Rev. E 57:5782(1998)

    Google Scholar 

  7. J.-M. Petit, B. M. Law, and D. Beysens, J. Colloid Interface Sci. 202:441(1998).

    Google Scholar 

  8. T. Narayanan, A. Kumar, E. S. R. Gopal, D. Beysens, P. Guenoun, and G. Zalczer, Phys. Rev. E 48:1989(1993).

    Google Scholar 

  9. Y. Jayalakshmi and E. W. Kaler, Phys. Rev. Lett. 78:1379(1997).

    Google Scholar 

  10. H. Grüll and D. Woermann, Ber. Bunsenges. Phys. Chem. 101:814(1997).

    Google Scholar 

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

    Google Scholar 

  12. Colloid Physics, Proceedings of the Workshop on Colloid Physics held at the University of Konstanz, Germany, November 30-December 2, 1995, Physica A 235 (1997).

  13. F. Schlesener, A. Hanke, R. Klimpel, and S. Dietrich, Phys. Rev. E 63:041803(2001).

    Google Scholar 

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

    Google Scholar 

  15. H. Löwen, Phys. Rev. Lett. 74:1028(1995)

    Google Scholar 

  16. H. LöwenZ. Phys. B 97:269(1995).

    Google Scholar 

  17. T. Bieker and S. Dietrich, Physica A 252:85(1998); and references therein.

    Google Scholar 

  18. C. Bauer, T. Bieker, and S. Dietrich, Phys. Rev. E 62:5324(2000).

    Google Scholar 

  19. U. Brodatzki and K. Mecke, preprint cond-mat/0112009.

  20. H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51:793(1948).

    Google Scholar 

  21. S. K. Lamoreaux, Am. J. Phys. 67:850(1999).

    Google Scholar 

  22. U. Mohideen and A. Roy, Phys. Rev. Lett. 81:4549(1998).

    Google Scholar 

  23. G. Bressi, G. Carugno, R. Onofrio, and G. Ruoso, Phys. Rev. Lett. 88:041804(2002).

    Google Scholar 

  24. P. Ziherl, R. Podgornik, and S. Žumer, Phys. Rev. Lett. 82:1189(1999)

    Google Scholar 

  25. A. Borštnik, H. Stark, and S. Žumer, Phys. Rev. E 61:2831(2000).

    Google Scholar 

  26. N. Uchida, Phys. Rev. Lett. 87:216101(2001).

    Google Scholar 

  27. K. Symanzik, Nucl. Phys. B 190:1(1981)

    Google Scholar 

  28. M. Lüscher, K. Symanzik, and P. Weisz, Nucl. Phys. B 171:365(1980).

    Google Scholar 

  29. P. Ziherl and I. MuŠevič, Liq. Cryst. 28:1057(2001).

    Google Scholar 

  30. J. O. Indekeu, M. P. Nightingale, and W. V. Wang, Phys. Rev. B 34:330(1986).

    Google Scholar 

  31. M. Krech and S. Dietrich, Phys. Rev. Lett. 66:245(1991); 67:1055(1991); Phys. Rev. A 46:1922(1992);46:1886(1992); J. Low Temp. Phys.89:145(1992).

    Google Scholar 

  32. M. Krech, The Casimir Effect in Critical Systems (World Scientific, Singapore, 1994)

    Google Scholar 

  33. M. KrechJ. Phys.: Condens. Matter 11:R391(1999).

    Google Scholar 

  34. M. Krech, Phys. Rev. E 56:1642(1997).

    Google Scholar 

  35. M. Kardar and R. Golestanian, Rev. Mod. Phys. 71:1233(1999)

    Google Scholar 

  36. R. Golestanian, Phys. Rev. E 62, 5242(2000).

    Google Scholar 

  37. A. Mukhopadhyay and B. M. Law, Phys. Rev. Lett. 83:772(1999).

    Google Scholar 

  38. R. Garcia and M. H. W. Chan, Phys. Rev. Lett. 83:1187(1999)

    Google Scholar 

  39. R. Garcia and M. H. W. ChanPhysica B 280:55(2000)

    Google Scholar 

  40. R. Garcia and M. H. W. ChanJ. Low Temp. Phys. 121:495(2000)

    Google Scholar 

  41. R. Garcia and M. H. W. ChanPhys. Rev. Lett. 88:086101(2002).

    Google Scholar 

  42. The same holds for one-or two-component fluids near their liquid-vapor critical points.

  43. K. Binder, in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (Academic, London, 1983), Vol. 8, p. 1.

    Google Scholar 

  44. H. W. Diehl, in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (Academic, London, 1986), Vol. 10, p. 75

    Google Scholar 

  45. H. W. Diehl, Int. J. Mod. Phys. B 11:3503(1997).

    Google Scholar 

  46. A. J. Liu and M. E. Fisher, Phys. Rev. A 40:7202(1989).

    Google Scholar 

  47. J. L. Cardy, Phys. Rev. Lett. 65:1443(1990).

    Google Scholar 

  48. H. W. Diehl and M. Smock, Phys. Rev. B 47:5841(1993)

    Google Scholar 

  49. H. W. Diehl and M. Smock, Phys. Rev. B 48:6740(1993).

    Google Scholar 

  50. E. Eisenriegler and M. Stapper, Phys. Rev. B 50:10009(1994).

    Google Scholar 

  51. G. Flöter and S. Dietrich, Z. Phys. B 97:213(1995).

    Google Scholar 

  52. For a review, see, B. M. Law, Prog. Surf. Sci. 66:159(2001).

    Google Scholar 

  53. A. Hanke and S. Dietrich, Phys. Rev. E 59:5081(1999).

    Google Scholar 

  54. A. Hanke, Phys. Rev. Lett. 84:2180(2000).

    Google Scholar 

  55. H. W. Diehl and M. Smock, Physica A 281:268(2000)

    Google Scholar 

  56. H. W. Diehl and M. SmockEur. Phys. J. B 21:567(2001).

    Google Scholar 

  57. A. Hanke and M. Kardar, Phys. Rev. Lett. 86:4596(2001)

    Google Scholar 

  58. A. Hanke and M. KardarPhys. Rev. E 65, 046121(2002).

    Google Scholar 

  59. T. W. Burkhardt and E. Eisenriegler, Phys. Rev. Lett. 74:3189(1995)

    Google Scholar 

  60. T. W. Burkhardt and E. Eisenriegler, Phys. Rev. Lett. 78:2867(1997).

    Google Scholar 

  61. R. Netz, Phys. Rev. Lett. 76:3646(1996).

    Google Scholar 

  62. A. Hanke, F. Schlesener, E. Eisenriegler, and S. Dietrich, Phys. Rev. Lett. 81:1885(1998).

    Google Scholar 

  63. T. W. Burkhardt and E. Eisenriegler, J. Phys. A 18:L83(1985).

    Google Scholar 

  64. S. Gnutzmann and U. Ritschel, Z. Phys. B 96:391(1995).

    Google Scholar 

  65. E. Eisenriegler and U. Ritschel, Phys. Rev. B 51:13717(1995).

    Google Scholar 

  66. M. E. Fisher, Rev. Mod. Phys. 46:597(1974)

    Google Scholar 

  67. M. E. Fisher, Rev. Mod. Phys. 70:653(1998).

    Google Scholar 

  68. A. Ciach and H. W. Diehl, Europhys. Lett. 12:635(1990)

    Google Scholar 

  69. H. W. Diehl and A. Ciach, Phys. Rev. B 44:6642(1991).

    Google Scholar 

  70. M. E. Fisher and P. J. Upton, Phys. Rev. Lett. 65:2402(1990).

    Google Scholar 

  71. M. E. Fisher and P. J. Upton, Phys. Rev. Lett. 65:3405(1990).

    Google Scholar 

  72. Z. Borjan and P. J. Upton, Phys. Rev. Lett. 81:4911(1998).

    Google Scholar 

  73. Z. Borjan and P. J. Upton, Phys. Rev. E 63:065102(2001).

    Google Scholar 

  74. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, London, 1965).

    Google Scholar 

  75. Our use of the conformal transformation should not lead to the misconception that conformal invariance holds in d=3 for Landau theory.

  76. M. E. Fisher and H. Au-Yang, Physica A 110:255(1980).

    Google Scholar 

  77. R. L. Burden and J. D. Faires, Numerical Analysis (PWS, Boston, 1993).

    Google Scholar 

  78. H. Späth, Eindimensionale Spline-Interpolations-Algorithmen (Oldenbourg, 1990)

  79. H. Späth, Zweidimensionale Spline-Interpolations-Algorithmen (Oldenbourg, 1991).

  80. L. S. Brown, Ann. of Phys. 126:135(1980).

    Google Scholar 

  81. B. V. Derjaguin, Kolloid Z. 69:155(1934).

    Google Scholar 

  82. E. Eisenriegler, A. Hanke, and S. Dietrich, Phys. Rev. E 54:1134(1996).

    Google Scholar 

  83. J. Chen and A. Anandarajah, J. Colloid Interface Sci. 180:519(1996).

    Google Scholar 

  84. B. Widom, J. Chem. Phys. 43:3898(1965).

    Google Scholar 

  85. H. B. Tarko and M. E. Fisher, Phys. Rev. Lett. 31:926(1973)

    Google Scholar 

  86. H. B. Tarko and M. E. FisherPhys. Rev. B 11, 1217(1975).

    Google Scholar 

  87. N. B. Wilding and M. Krech, Phys. Rev. E 57:5795(1998).

    Google Scholar 

  88. A. M. Ferrenberg, D. P. Landau, and K. Binder, Phys. Rev. E 58:3353(1998).

    Google Scholar 

  89. A. Drzewińzki, A. Maciołek, and R. Evans, Phys. Rev. Lett. 85:3079(2000); A. Maciołek, A. Drzewińzki, and R. Evans, Phys. Rev. E 64:056137(2001).

    Google Scholar 

  90. H. Nakanishi and M. E. Fisher, J. Chem. Phys. 78:3279(1983).

    Google Scholar 

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Authors and Affiliations

  1. Max-Planck-Institut für Metallforschung, Heisenbergstr. 1, D-70569, Stuttgart, Germany

    F. Schlesener & S. Dietrich

  2. Institut für Theoretische und Angewandte Physik, Universität Stuttgart, D-70550, Stuttgart, Germany

    F. Schlesener & S. Dietrich

  3. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139

    A. Hanke

  4. Department of Physics, Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, United Kingdom

    A. Hanke

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  1. F. Schlesener
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  3. S. Dietrich
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Schlesener, F., Hanke, A. & Dietrich, S. Critical Casimir Forces in Colloidal Suspensions. Journal of Statistical Physics 110, 981–1013 (2003). https://doi.org/10.1023/A:1022184508016

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