Skip to main content
SpringerLink
Log in

Simulation of Charged Colloids in Solution

  • Chapter
  • First Online:
Advanced Computer Simulation Approaches for Soft Matter Sciences II

Part of the book series: Advances in Polymer Science ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

References

  1. Evans DF, Wennerström H (1994) The colloidal domain where physics, chemistry, biology, and technology meet. VCH, New York

    Google Scholar 

  2. Arora AK, Tata BVR (1996) In: Rajagopalan R (ed) Complex fluids and fluid microstructures. VCH, New York

    Google Scholar 

  3. Derjaguin BV, Landau L (1941) Acta Physiochim (USSR) 14:633

    Google Scholar 

  4. Verwey EJ, Overbeek JTG (1948) Theory of the stability of lyophobic colloids. Elsevier, Amsterdam

    Google Scholar 

  5. Khan A, Fontell K, Lindman B (1984) J Colloid Interface Sci 101:193

    Article  CAS  Google Scholar 

  6. Kang C, Khan A (1993) J Colloid Interface Sci 156:218

    Article  CAS  Google Scholar 

  7. Tata BVR, Rajalakshmi M, Arora AK (1992) Phys Rev Lett 69:3778

    Article  CAS  Google Scholar 

  8. Ito K, Yoshida H, Ise H (1994) Science 263:66

    CAS  Google Scholar 

  9. Larsen AE, Grier DG (1997) Nature 385:230

    Article  CAS  Google Scholar 

  10. Grier DG (1998) Nature 393:621

    Article  CAS  Google Scholar 

  11. Vlachy V (1999) Annu Rev Phys Chem 50:145

    Article  CAS  Google Scholar 

  12. Hansen J-P, Löwen H (2000) Annu Rev Phys Chem 51:209

    Article  CAS  Google Scholar 

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

    CAS  Google Scholar 

  14. Bhuiyan LB, Vlachy V, Outhwaite CW (2002) Int Rev Phys Chem 21:1

    Article  CAS  Google Scholar 

  15. Allahyarov E, D'Amico I, Löwen H (1998) Phys Rev Lett 81:1334

    Article  CAS  Google Scholar 

  16. Grønbech-Jensen N, Beardmore KM, Pincus P (1998) Physica A 261:74

    Article  Google Scholar 

  17. Wu J, Bratko D, Prausnitz JM (1998) Proc Natl Acad Sci 95:15169

    Article  CAS  Google Scholar 

  18. Linse P, Lobaskin V (1999) Phys Rev Lett 83:4208

    Article  CAS  Google Scholar 

  19. Wu J, Bratko D, Blanch HW, Prausnitz JM (1999) J Chem Phys 111:7084

    Article  CAS  Google Scholar 

  20. Linse P, Lobaskin V (2000) J Chem Phys 112:3917

    Article  CAS  Google Scholar 

  21. Hribar B, Vlachy V (2000) Biophys J 78:694

    CAS  Google Scholar 

  22. Linse P (2000) J Chem Phys 113:4359

    Article  CAS  Google Scholar 

  23. Messina R, Holm C, Kremer K (2000) Phys Rev Lett 85:872

    Article  CAS  Google Scholar 

  24. Messina R, Holm C, Kremer K (2000) Europhys Lett 51:461

    Article  CAS  Google Scholar 

  25. Belloni L (2002) J Phys Condens Matter 14:9323

    CAS  Google Scholar 

  26. Linse P (2002) J Phys Condens Matter 14:13449

    CAS  Google Scholar 

  27. Lobaskin V, Qamhieh K (2003) J Phys Chem B 107:8022

    Article  CAS  Google Scholar 

  28. Angelescu DG, Linse P (2003) Langmuir 19:9661

    Article  CAS  Google Scholar 

  29. Kjellander R, Marcelja S (1984) Chem Phys Lett 112:49

    Article  CAS  Google Scholar 

  30. Outhwaite CW, Molero M (1992) Chem Phys Lett 197:643

    Article  CAS  Google Scholar 

  31. Rouzina I, Bloomfield VA (1996) J Phys Chem 100:9977

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  33. Tokuyama M (1999) Phys Rev E 59:R2550

    Article  CAS  Google Scholar 

  34. Levin Y (1999) Physica A 265:432

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  36. Warren PB (2000) J Chem Phys 112:4683

    Article  CAS  Google Scholar 

  37. Naji A, Netz RR (2004) Eur Phys J E 13:43

    Article  CAS  Google Scholar 

  38. Guldbrand L, Jönsson B, Wennerström H, Linse P (1984) J Chem Phys 80:2221

    Article  CAS  Google Scholar 

  39. Moreira AG, Netz RR (2001) Phys Rev Lett 87:078301

    Article  CAS  Google Scholar 

  40. Moreira AG, Netz RR (2002) Eur Phys J E 8:33

    CAS  Google Scholar 

  41. Guldbrand L, Nilsson LG, Nordenskiöld L (1986) J Chem Phys 85:6686

    Article  CAS  Google Scholar 

  42. Grønbech-Jensen N, Mashl RJ, Bruinsma RF, Gelbart WM (1997) Phys Rev Lett 78:2477

    Article  Google Scholar 

  43. Ha B-Y, Liu AJ (1997) Phys Rev Lett 79:1289

    Article  CAS  Google Scholar 

  44. Ha B-Y, Liu AJ (1998) Phys Rev Lett 81:1011

    Article  CAS  Google Scholar 

  45. Podgornik R, Parsegian VA (1998) Phys Rev Lett 80:1560

    Article  CAS  Google Scholar 

  46. Shklovskii BI (1999) Phys Rev Lett 82:3268

    Article  CAS  Google Scholar 

  47. Solis FJ, Olverade la Cruz M (1999) Phys Rev E 60:4496

    Article  CAS  Google Scholar 

  48. Deserno M, Arnold A, Holm C (2003) Macromolecules 2003:249

    Article  CAS  Google Scholar 

  49. Stevens MJ (1999) Phys Rev Lett 82:101

    Article  CAS  Google Scholar 

  50. Stevens MJ, Kremer K (1995) J Chem Phys 103:1669

    Article  CAS  Google Scholar 

  51. Winkler RG, Gold M, Reineker P (1998) Phys Rev Lett 80:3731

    Article  CAS  Google Scholar 

  52. Khan MO, Jönsson B (1999) Biopolymers 49:121

    Article  CAS  Google Scholar 

  53. Pais AACC, Miguel MG, Linse P, Lindman B (2002) J Chem Phys 117:1385

    Article  CAS  Google Scholar 

  54. Orkoulas G, Kumar SK, Panagiotopoulos AZ (2003) Phys Rev Lett 90:048303

    Article  CAS  Google Scholar 

  55. Stevens MJ (2001) Biophys J 80:130

    CAS  Google Scholar 

  56. Yan Q, de Pablo JJ (2003) Phys Rev Lett 67:061803

    Google Scholar 

  57. Schneider S, Linse P (2004) Macromolecules 37:3850

    Article  CAS  Google Scholar 

  58. Linse P (1990) J Chem Phys 93:1376

    Article  CAS  Google Scholar 

  59. Ewald P (1921) Ann Phys 64:253

    Google Scholar 

  60. Gordon HL, Valleau JP (1995) Mol Simul 14:361

    CAS  Google Scholar 

  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. McMillan WG, Mayer JE (1945) J Chem Phys 13:276

    Article  CAS  Google Scholar 

  63. Hill TL (1960 and 1986) An Introduction to Statistical Thermodynamics. Dover, New York

    Google Scholar 

  64. Allen MP, Tildelsley DJ (1987) Computer simulation of liquids. Oxford, New York

    Google Scholar 

  65. Frenkel D, Smit B (1996) Understanding Molecular Simulation: From Algorithms to Applications. Academic, San Diego

    Google Scholar 

  66. Sokal AD (1996) Lectures at the Cargèse Summer School on “Functional Integration: Basis and Applications”

    Google Scholar 

  67. Mille M (1977) J Colloid Interface Sci 59:211

    Article  CAS  Google Scholar 

  68. Frahm J, Diekmann S (1979) J Colloid Interface Sci 70:440

    Article  CAS  Google Scholar 

  69. Bentz J (1981) J Colloid Interface Sci 80:179

    Article  CAS  Google Scholar 

  70. Linse P, Gunnarsson G, Jönsson B (1982) J Phys Chem 86:413

    Article  CAS  Google Scholar 

  71. Lampert MA, Martinelli RU (1985) Chem Phys Lett 121:121

    Article  CAS  Google Scholar 

  72. Amaro ML, Bhuiyan LB, Outhwaite CW (1995) Mol Phys 86:725

    Article  CAS  Google Scholar 

  73. Degreve L, Lozada-Cassou M (1995) Mol Phys 86:758

    Google Scholar 

  74. Rebolj N, Kristl J, Kalyuzhnyi YV, Vlachy V (1997) Langmuir 13:3646

    Article  CAS  Google Scholar 

  75. Bell GM (1964) J Trans Faraday Soc 60:1752

    Article  CAS  Google Scholar 

  76. Bell GM, Dunning AJ (1970) J Trans Faraday Soc 66:500

    Article  CAS  Google Scholar 

  77. Bratko D, Lindman B (1985) J Phys Chem 89:1437

    Article  CAS  Google Scholar 

  78. Jönsson B, Wennerström H, Nilsson PG, Linse P (1986) Colloid Polym Sci 264:77

    Article  Google Scholar 

  79. Gunnarsson G, Jönsson B, Wennerström H (1980) J Phys Chem 84:3114

    Article  CAS  Google Scholar 

  80. Jönsson B, Wennerström H (1981) J Colloid Interface Sci 80:482

    Article  Google Scholar 

  81. Wennerström H, Jönsson B, Linse P (1982) J Chem Phys 76:4665

    Article  Google Scholar 

  82. Marcus RA (1955) J Chem Phys 23:1057

    Article  CAS  Google Scholar 

  83. da Silva FLB, Bogren D, Söderman O, Åkesson T, Jönsson B (2002) J Phys Chem B 106:3515

    Article  CAS  Google Scholar 

  84. Messina R, Holm C, Kremer K (2001) Eur Phys J D 4:363

    CAS  Google Scholar 

  85. Messina R (2002) Physica A 308:57

    Article  Google Scholar 

  86. Linse S, Jönsson B, Chazin WJ (1995) Proc Natl Acad Sci USA 92:4748

    Article  CAS  Google Scholar 

  87. Linse P (1986) J Phys Chem 90:6821

    Article  CAS  Google Scholar 

  88. Messina R (2002) J Chem Phys 117:11062

    Article  CAS  Google Scholar 

  89. von Grünberg HH, Belloni L (2000) Phys Rev E 62:2493

    Article  Google Scholar 

  90. Wallin T, Linse P (1996) J Phys Chem 100:17873

    Article  CAS  Google Scholar 

  91. Wallin T, Linse P (1996) Langmuir 12:305

    Article  CAS  Google Scholar 

  92. Wallin T, Linse P (1997) J Phys Chem B 101:5506

    Article  CAS  Google Scholar 

  93. Mateescu EM, Jeppesen C, Pincus P (1999) Europhys Lett 46:493

    Article  CAS  Google Scholar 

  94. Nguyen TT, Shklovskii BI (2001) Physica A 293:324

    Article  CAS  Google Scholar 

  95. Akinchina A, Linse P (2002) Macromolecules 35:5183

    Article  CAS  Google Scholar 

  96. Akinchina A, Linse P (2003) Macromolecules 107:8011

    CAS  Google Scholar 

  97. Woodward C, Jönsson B, Åkesson T (1988) J Chem Phys 89:5145

    Article  CAS  Google Scholar 

  98. Granfeldt MK, Jönsson B, Woodward CE (1991) J Phys Chem 95:4819

    Article  CAS  Google Scholar 

  99. Striolo A, Bratko D, Wu JZ, Elvassore N, Blanch HW, Prausnitz JM (2002) J Chem Phys 116:7733

    Article  CAS  Google Scholar 

  100. Allahyarov E, Löwen H, Louis AA, Hansen JP (2002) Europhys Lett 57:731

    Article  CAS  Google Scholar 

  101. Allahyarov E, Löwen H, Hansen JP, Louis AA (2003) Phys Rev E 67:051404

    Article  CAS  Google Scholar 

  102. Lund M, Jönsson B (2003) Biophys J 85:2940

    Article  CAS  Google Scholar 

  103. Linse P, Jönsson B (1983) J Chem Phys 78:3167

    Article  CAS  Google Scholar 

  104. Vlachy V, Marshall CH, Haymet ADJ (1989) J Am Chem Soc 111:4160

    Article  CAS  Google Scholar 

  105. Hribar B, Kalyuzhnyi YV, Vlachy V (1996) Mol Phys 87:1317

    CAS  Google Scholar 

  106. Hribar B, Vlachy V (1997) J Phys Chem B 101:3457

    Article  CAS  Google Scholar 

  107. Hribar B, Krienke H, Kalyuzhnyi YV, Vlachy V (1997) J Mol Liq 73–74:277

    Article  Google Scholar 

  108. Lobaskin V, Linse P (1998) J Chem Phys 109:3530

    Article  CAS  Google Scholar 

  109. Lobaskin V, Linse P (1999) J Chem Phys 111:4300

    Article  CAS  Google Scholar 

  110. Neu JC (1999) Phys Rev E 82:1072

    CAS  Google Scholar 

  111. Sader JE, Chan DYC (1999) J Colloid Interface Sci 203:268

    Article  Google Scholar 

  112. Rescic J, Linse P (2000) J Phys Chem B 104:7852

    Article  CAS  Google Scholar 

  113. Skepö M, Linse P (2002) J Phys Chem B 36:508

    Google Scholar 

  114. Carlsson F, Malmsten M, Linse P (2003) J Am Chem Soc 125:3140

    Article  CAS  Google Scholar 

  115. Jardat M, Cartailler T, Turq P (2001) J Chem Phys 115:1066

    Article  CAS  Google Scholar 

  116. Landau LD, Lifshitz EM (1960) Electrodynamics of continuous media. Pergamon, Bristol

    Google Scholar 

  117. Russel WB, Saville DA, Schowalter WR (1989) Colloidal dispersions. Cambridge University Press, New York

    Google Scholar 

  118. Adams DJ (1979) Chem Phys Lett 62:329

    Article  CAS  Google Scholar 

  119. Ceperly D (1980) NRCC Proc no 9. National Technical Information Service, Springfield, VA

    Google Scholar 

  120. de Leeuw SW, Perram JW, Smith ER (1980) Proc R Soc Lond A 373:27

    Google Scholar 

  121. Romero-Enrique JM, Orkoulas G, Panagiotopoulos AZ, Fisher ME (2000) Phys Rev Lett 85:4558

    Article  CAS  Google Scholar 

  122. de Leeuw SW, Perram JW, Smith ER (1980) Proc R Soc Lond A 373:57

    Article  Google Scholar 

  123. Perram JW, Petersen HG, de Leeuw SW (1988) Mol Phys 65:875

    Article  CAS  Google Scholar 

  124. Darden T, York D, Pedersen L (1993) J Chem Phys 98:10089

    Article  CAS  Google Scholar 

  125. Essmann U, Perera L, Berkowitz ML, Darden T, Lee H, Pedersen LG (1995) J Chem Phys 103:8577

    Article  CAS  Google Scholar 

  126. Petersen HG (1995) J Chem Phys 103:3668

    Article  CAS  Google Scholar 

  127. Deserno M, Holm C (1998) J Chem Phys 109:7678

    Article  CAS  Google Scholar 

  128. Kolafa J, Perram JW (1992) Molec Sim 9:351

    CAS  Google Scholar 

  129. Linse P (1999) J Chem Phys 110:3493

    Article  CAS  Google Scholar 

  130. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) J Chem Phys 21:1087

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, S-221 00, Lund, Sweden

    Per Linse

Authors
  1. Per Linse
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Per Linse .

Editor information

Christian Holm Kurt Kremer

Rights and permissions

Reprints and permissions

About this chapter

Cite this chapter

Linse, P. Simulation of Charged Colloids in Solution . In: Holm, C., Kremer, K. (eds) Advanced Computer Simulation Approaches for Soft Matter Sciences II. Advances in Polymer Science, vol 185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b136795

Download citation

Publish with us

Policies and ethics

Search

Navigation