Advertisement

Simulation of Charged Colloids in Solution

  • Per LinseEmail author
Chapter
Part of the Advances in Polymer Science book series (POLYMER, volume 185)

Abstract

Physicochemical properties of solutions of charged colloids are often dominated by the electrostatic interactions present in such systems. A full determination of these properties constitutes a highly nontrivial many-body problem involving long-range interactions. In electrostatically strongly coupled systems, it is essential to explicitly include both the charged colloids and the small ions in the model. The present review describes recent advances in performing Metropolis Monte Carlo simulations of such systems modeled within the primitive model of electrolytes. Four representative colloidal systems are systematically used in combination with three different boundary conditions. First, the spherical cell model is considered, and it is used primarily to examine the distribution of the counterions near a colloid. Second, the cylindrical cell model containing two colloids is presented, and it is employed to calculate the mean force and/ or the potential of mean force acting on one of the colloids. Several methods are utilized and their merits are compared. Finally, full structural and thermodynamic properties are presented by using a cubic simulation box with periodic boundary conditions applied. An account of the system size convergence, the convergence of the Ewald summation, including an estimate of truncation errors and practical guidelines, and the ability to increase the simulation efficiency by using cluster trial displacements is provided.

Charged colloids Monte Carlo simulation Mean force Ewald summation Cluster trial move 

Abbreviations

DLVO

Derjaguin--Landau--Verwey--Overbeek

MI

minimum image

MC

Monte Carlo

PB

Poisson--Boltzmann

SC

spherical cutoff

pmf

potential of mean force

RDF

radial distribution function

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Evans DF, Wennerström H (1994) The colloidal domain where physics, chemistry, biology, and technology meet. VCH, New York Google Scholar
  2. 2.
    Arora AK, Tata BVR (1996) In: Rajagopalan R (ed) Complex fluids and fluid microstructures. VCH, New York Google Scholar
  3. 3.
    Derjaguin BV, Landau L (1941) Acta Physiochim (USSR) 14:633 Google Scholar
  4. 4.
    Verwey EJ, Overbeek JTG (1948) Theory of the stability of lyophobic colloids. Elsevier, Amsterdam Google Scholar
  5. 5.
    Khan A, Fontell K, Lindman B (1984) J Colloid Interface Sci 101:193 CrossRefGoogle Scholar
  6. 6.
    Kang C, Khan A (1993) J Colloid Interface Sci 156:218 CrossRefGoogle Scholar
  7. 7.
    Tata BVR, Rajalakshmi M, Arora AK (1992) Phys Rev Lett 69:3778 CrossRefGoogle Scholar
  8. 8.
    Ito K, Yoshida H, Ise H (1994) Science 263:66 Google Scholar
  9. 9.
    Larsen AE, Grier DG (1997) Nature 385:230 CrossRefGoogle Scholar
  10. 10.
    Grier DG (1998) Nature 393:621 CrossRefGoogle Scholar
  11. 11.
    Vlachy V (1999) Annu Rev Phys Chem 50:145 CrossRefGoogle Scholar
  12. 12.
    Hansen J-P, Löwen H (2000) Annu Rev Phys Chem 51:209 CrossRefGoogle Scholar
  13. 13.
    Belloni L (2000) J Phys Condens Matter 12:R549 Google Scholar
  14. 14.
    Bhuiyan LB, Vlachy V, Outhwaite CW (2002) Int Rev Phys Chem 21:1 CrossRefGoogle Scholar
  15. 15.
    Allahyarov E, D'Amico I, Löwen H (1998) Phys Rev Lett 81:1334 CrossRefGoogle Scholar
  16. 16.
    Grønbech-Jensen N, Beardmore KM, Pincus P (1998) Physica A 261:74 CrossRefGoogle Scholar
  17. 17.
    Wu J, Bratko D, Prausnitz JM (1998) Proc Natl Acad Sci 95:15169 CrossRefGoogle Scholar
  18. 18.
    Linse P, Lobaskin V (1999) Phys Rev Lett 83:4208 CrossRefGoogle Scholar
  19. 19.
    Wu J, Bratko D, Blanch HW, Prausnitz JM (1999) J Chem Phys 111:7084 CrossRefGoogle Scholar
  20. 20.
    Linse P, Lobaskin V (2000) J Chem Phys 112:3917 CrossRefGoogle Scholar
  21. 21.
    Hribar B, Vlachy V (2000) Biophys J 78:694 Google Scholar
  22. 22.
    Linse P (2000) J Chem Phys 113:4359 CrossRefGoogle Scholar
  23. 23.
    Messina R, Holm C, Kremer K (2000) Phys Rev Lett 85:872 CrossRefGoogle Scholar
  24. 24.
    Messina R, Holm C, Kremer K (2000) Europhys Lett 51:461 CrossRefGoogle Scholar
  25. 25.
    Belloni L (2002) J Phys Condens Matter 14:9323 Google Scholar
  26. 26.
    Linse P (2002) J Phys Condens Matter 14:13449 Google Scholar
  27. 27.
    Lobaskin V, Qamhieh K (2003) J Phys Chem B 107:8022 CrossRefGoogle Scholar
  28. 28.
    Angelescu DG, Linse P (2003) Langmuir 19:9661 CrossRefGoogle Scholar
  29. 29.
    Kjellander R, Marcelja S (1984) Chem Phys Lett 112:49 CrossRefGoogle Scholar
  30. 30.
    Outhwaite CW, Molero M (1992) Chem Phys Lett 197:643 CrossRefGoogle Scholar
  31. 31.
    Rouzina I, Bloomfield VA (1996) J Phys Chem 100:9977 CrossRefGoogle Scholar
  32. 32.
    van Roij R, Hansen J-P (1997) Phys Rev Lett 79:3082 CrossRefGoogle Scholar
  33. 33.
    Tokuyama M (1999) Phys Rev E 59:R2550 CrossRefGoogle Scholar
  34. 34.
    Levin Y (1999) Physica A 265:432 CrossRefGoogle Scholar
  35. 35.
    van Roij R, Dijkstra M, Hansen J-P (1999) Phys Rev E 59:2010 CrossRefGoogle Scholar
  36. 36.
    Warren PB (2000) J Chem Phys 112:4683 CrossRefGoogle Scholar
  37. 37.
    Naji A, Netz RR (2004) Eur Phys J E 13:43 CrossRefGoogle Scholar
  38. 38.
    Guldbrand L, Jönsson B, Wennerström H, Linse P (1984) J Chem Phys 80:2221 CrossRefGoogle Scholar
  39. 39.
    Moreira AG, Netz RR (2001) Phys Rev Lett 87:078301 CrossRefGoogle Scholar
  40. 40.
    Moreira AG, Netz RR (2002) Eur Phys J E 8:33 Google Scholar
  41. 41.
    Guldbrand L, Nilsson LG, Nordenskiöld L (1986) J Chem Phys 85:6686 CrossRefGoogle Scholar
  42. 42.
    Grønbech-Jensen N, Mashl RJ, Bruinsma RF, Gelbart WM (1997) Phys Rev Lett 78:2477 CrossRefGoogle Scholar
  43. 43.
    Ha B-Y, Liu AJ (1997) Phys Rev Lett 79:1289 CrossRefGoogle Scholar
  44. 44.
    Ha B-Y, Liu AJ (1998) Phys Rev Lett 81:1011 CrossRefGoogle Scholar
  45. 45.
    Podgornik R, Parsegian VA (1998) Phys Rev Lett 80:1560 CrossRefGoogle Scholar
  46. 46.
    Shklovskii BI (1999) Phys Rev Lett 82:3268 CrossRefGoogle Scholar
  47. 47.
    Solis FJ, Olverade la Cruz M (1999) Phys Rev E 60:4496 CrossRefGoogle Scholar
  48. 48.
    Deserno M, Arnold A, Holm C (2003) Macromolecules 2003:249 CrossRefGoogle Scholar
  49. 49.
    Stevens MJ (1999) Phys Rev Lett 82:101 CrossRefGoogle Scholar
  50. 50.
    Stevens MJ, Kremer K (1995) J Chem Phys 103:1669 CrossRefGoogle Scholar
  51. 51.
    Winkler RG, Gold M, Reineker P (1998) Phys Rev Lett 80:3731 CrossRefGoogle Scholar
  52. 52.
    Khan MO, Jönsson B (1999) Biopolymers 49:121 CrossRefGoogle Scholar
  53. 53.
    Pais AACC, Miguel MG, Linse P, Lindman B (2002) J Chem Phys 117:1385 CrossRefGoogle Scholar
  54. 54.
    Orkoulas G, Kumar SK, Panagiotopoulos AZ (2003) Phys Rev Lett 90:048303 CrossRefGoogle Scholar
  55. 55.
    Stevens MJ (2001) Biophys J 80:130 Google Scholar
  56. 56.
    Yan Q, de Pablo JJ (2003) Phys Rev Lett 67:061803 Google Scholar
  57. 57.
    Schneider S, Linse P (2004) Macromolecules 37:3850 CrossRefGoogle Scholar
  58. 58.
    Linse P (1990) J Chem Phys 93:1376 CrossRefGoogle Scholar
  59. 59.
    Ewald P (1921) Ann Phys 64:253 Google Scholar
  60. 60.
    Gordon HL, Valleau JP (1995) Mol Simul 14:361 Google Scholar
  61. 61.
    Linse P, Lobaskin V (2000) In: Engquist B, Johnsson L, Hammill M, Short F (eds) Simulation and Visualization on the Grid. Lecture Notes in Computational Science and Engineering, vol 13. Springer, Berlin Heidelberg New York, p 165 Google Scholar
  62. 62.
    McMillan WG, Mayer JE (1945) J Chem Phys 13:276 CrossRefGoogle Scholar
  63. 63.
    Hill TL (1960 and 1986) An Introduction to Statistical Thermodynamics. Dover, New York Google Scholar
  64. 64.
    Allen MP, Tildelsley DJ (1987) Computer simulation of liquids. Oxford, New York Google Scholar
  65. 65.
    Frenkel D, Smit B (1996) Understanding Molecular Simulation: From Algorithms to Applications. Academic, San Diego Google Scholar
  66. 66.
    Sokal AD (1996) Lectures at the Cargèse Summer School on “Functional Integration: Basis and Applications” Google Scholar
  67. 67.
    Mille M (1977) J Colloid Interface Sci 59:211 CrossRefGoogle Scholar
  68. 68.
    Frahm J, Diekmann S (1979) J Colloid Interface Sci 70:440 CrossRefGoogle Scholar
  69. 69.
    Bentz J (1981) J Colloid Interface Sci 80:179 CrossRefGoogle Scholar
  70. 70.
    Linse P, Gunnarsson G, Jönsson B (1982) J Phys Chem 86:413 CrossRefGoogle Scholar
  71. 71.
    Lampert MA, Martinelli RU (1985) Chem Phys Lett 121:121 CrossRefGoogle Scholar
  72. 72.
    Amaro ML, Bhuiyan LB, Outhwaite CW (1995) Mol Phys 86:725 CrossRefGoogle Scholar
  73. 73.
    Degreve L, Lozada-Cassou M (1995) Mol Phys 86:758 Google Scholar
  74. 74.
    Rebolj N, Kristl J, Kalyuzhnyi YV, Vlachy V (1997) Langmuir 13:3646 CrossRefGoogle Scholar
  75. 75.
    Bell GM (1964) J Trans Faraday Soc 60:1752 CrossRefGoogle Scholar
  76. 76.
    Bell GM, Dunning AJ (1970) J Trans Faraday Soc 66:500 CrossRefGoogle Scholar
  77. 77.
    Bratko D, Lindman B (1985) J Phys Chem 89:1437 CrossRefGoogle Scholar
  78. 78.
    Jönsson B, Wennerström H, Nilsson PG, Linse P (1986) Colloid Polym Sci 264:77 CrossRefGoogle Scholar
  79. 79.
    Gunnarsson G, Jönsson B, Wennerström H (1980) J Phys Chem 84:3114 CrossRefGoogle Scholar
  80. 80.
    Jönsson B, Wennerström H (1981) J Colloid Interface Sci 80:482 CrossRefGoogle Scholar
  81. 81.
    Wennerström H, Jönsson B, Linse P (1982) J Chem Phys 76:4665 CrossRefGoogle Scholar
  82. 82.
    Marcus RA (1955) J Chem Phys 23:1057 CrossRefGoogle Scholar
  83. 83.
    da Silva FLB, Bogren D, Söderman O, Åkesson T, Jönsson B (2002) J Phys Chem B 106:3515 CrossRefGoogle Scholar
  84. 84.
    Messina R, Holm C, Kremer K (2001) Eur Phys J D 4:363 Google Scholar
  85. 85.
    Messina R (2002) Physica A 308:57 CrossRefGoogle Scholar
  86. 86.
    Linse S, Jönsson B, Chazin WJ (1995) Proc Natl Acad Sci USA 92:4748 CrossRefGoogle Scholar
  87. 87.
    Linse P (1986) J Phys Chem 90:6821 CrossRefGoogle Scholar
  88. 88.
    Messina R (2002) J Chem Phys 117:11062 CrossRefGoogle Scholar
  89. 89.
    von Grünberg HH, Belloni L (2000) Phys Rev E 62:2493 CrossRefGoogle Scholar
  90. 90.
    Wallin T, Linse P (1996) J Phys Chem 100:17873 CrossRefGoogle Scholar
  91. 91.
    Wallin T, Linse P (1996) Langmuir 12:305 CrossRefGoogle Scholar
  92. 92.
    Wallin T, Linse P (1997) J Phys Chem B 101:5506 CrossRefGoogle Scholar
  93. 93.
    Mateescu EM, Jeppesen C, Pincus P (1999) Europhys Lett 46:493 CrossRefGoogle Scholar
  94. 94.
    Nguyen TT, Shklovskii BI (2001) Physica A 293:324 CrossRefGoogle Scholar
  95. 95.
    Akinchina A, Linse P (2002) Macromolecules 35:5183 CrossRefGoogle Scholar
  96. 96.
    Akinchina A, Linse P (2003) Macromolecules 107:8011 Google Scholar
  97. 97.
    Woodward C, Jönsson B, Åkesson T (1988) J Chem Phys 89:5145 CrossRefGoogle Scholar
  98. 98.
    Granfeldt MK, Jönsson B, Woodward CE (1991) J Phys Chem 95:4819 CrossRefGoogle Scholar
  99. 99.
    Striolo A, Bratko D, Wu JZ, Elvassore N, Blanch HW, Prausnitz JM (2002) J Chem Phys 116:7733 CrossRefGoogle Scholar
  100. 100.
    Allahyarov E, Löwen H, Louis AA, Hansen JP (2002) Europhys Lett 57:731 CrossRefGoogle Scholar
  101. 101.
    Allahyarov E, Löwen H, Hansen JP, Louis AA (2003) Phys Rev E 67:051404 CrossRefGoogle Scholar
  102. 102.
    Lund M, Jönsson B (2003) Biophys J 85:2940 CrossRefGoogle Scholar
  103. 103.
    Linse P, Jönsson B (1983) J Chem Phys 78:3167 CrossRefGoogle Scholar
  104. 104.
    Vlachy V, Marshall CH, Haymet ADJ (1989) J Am Chem Soc 111:4160 CrossRefGoogle Scholar
  105. 105.
    Hribar B, Kalyuzhnyi YV, Vlachy V (1996) Mol Phys 87:1317 Google Scholar
  106. 106.
    Hribar B, Vlachy V (1997) J Phys Chem B 101:3457 CrossRefGoogle Scholar
  107. 107.
    Hribar B, Krienke H, Kalyuzhnyi YV, Vlachy V (1997) J Mol Liq 73–74:277 CrossRefGoogle Scholar
  108. 108.
    Lobaskin V, Linse P (1998) J Chem Phys 109:3530 CrossRefGoogle Scholar
  109. 109.
    Lobaskin V, Linse P (1999) J Chem Phys 111:4300 CrossRefGoogle Scholar
  110. 110.
    Neu JC (1999) Phys Rev E 82:1072 Google Scholar
  111. 111.
    Sader JE, Chan DYC (1999) J Colloid Interface Sci 203:268 CrossRefGoogle Scholar
  112. 112.
    Rescic J, Linse P (2000) J Phys Chem B 104:7852 CrossRefGoogle Scholar
  113. 113.
    Skepö M, Linse P (2002) J Phys Chem B 36:508 Google Scholar
  114. 114.
    Carlsson F, Malmsten M, Linse P (2003) J Am Chem Soc 125:3140 CrossRefGoogle Scholar
  115. 115.
    Jardat M, Cartailler T, Turq P (2001) J Chem Phys 115:1066 CrossRefGoogle Scholar
  116. 116.
    Landau LD, Lifshitz EM (1960) Electrodynamics of continuous media. Pergamon, Bristol Google Scholar
  117. 117.
    Russel WB, Saville DA, Schowalter WR (1989) Colloidal dispersions. Cambridge University Press, New York Google Scholar
  118. 118.
    Adams DJ (1979) Chem Phys Lett 62:329 CrossRefGoogle Scholar
  119. 119.
    Ceperly D (1980) NRCC Proc no 9. National Technical Information Service, Springfield, VA Google Scholar
  120. 120.
    de Leeuw SW, Perram JW, Smith ER (1980) Proc R Soc Lond A 373:27 Google Scholar
  121. 121.
    Romero-Enrique JM, Orkoulas G, Panagiotopoulos AZ, Fisher ME (2000) Phys Rev Lett 85:4558 CrossRefGoogle Scholar
  122. 122.
    de Leeuw SW, Perram JW, Smith ER (1980) Proc R Soc Lond A 373:57 CrossRefGoogle Scholar
  123. 123.
    Perram JW, Petersen HG, de Leeuw SW (1988) Mol Phys 65:875 CrossRefGoogle Scholar
  124. 124.
    Darden T, York D, Pedersen L (1993) J Chem Phys 98:10089 CrossRefGoogle Scholar
  125. 125.
    Essmann U, Perera L, Berkowitz ML, Darden T, Lee H, Pedersen LG (1995) J Chem Phys 103:8577 CrossRefGoogle Scholar
  126. 126.
    Petersen HG (1995) J Chem Phys 103:3668 CrossRefGoogle Scholar
  127. 127.
    Deserno M, Holm C (1998) J Chem Phys 109:7678 CrossRefGoogle Scholar
  128. 128.
    Kolafa J, Perram JW (1992) Molec Sim 9:351 Google Scholar
  129. 129.
    Linse P (1999) J Chem Phys 110:3493 CrossRefGoogle Scholar
  130. 130.
    Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) J Chem Phys 21:1087 CrossRefGoogle Scholar

Authors and Affiliations

  1. 1.Physical Chemistry 1Center for Chemistry and Chemical Engineering, Lund UniversityLundSweden

Personalised recommendations