Skip to main content
SpringerLink
Log in

Analytical solutions of nonlinear Poisson–Boltzmann equation for colloidal particles immersed in a general electrolyte solution by homotopy perturbation technique

  • Original Contribution
  • Published:
Colloid and Polymer Science Aims and scope Submit manuscript

Abstract

We present the first application of the homotopy perturbation technique to analytically solve the nonlinear PB equation describing spherical and planar colloidal particles immersed in an arbitrary valence and mixed electrolyte solution. Analytical expressions for electrical potential distribution and surface charge density/surface potential relationship are acquired. Our analytical solutions contrast sharply with previous ones by two striking features: (1) the present ones apply irrespective of the types of electrolyte considered or whether single electrolyte or mixed electrolytes are being considered, and (2) the valid application scopes of present solutions are in small κa domain and thus are complementary with those of previous ones. Our expressions are considered to provide the constituents whose combinations with previous solutions may end up global valid expressions.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Kanduc M, Naji A, Podgornik R (2010) J Chem Phys 132:224703

    Article  Google Scholar 

  2. Wernersson E, Kjellander R (2008) J Chem Phys 129:144701

    Article  Google Scholar 

  3. Netz RR, Orland H (2000) Eur Phys J E 1:203

    Article  CAS  Google Scholar 

  4. Quesada-Perez M, Hidalgo-Alvarez R, Martin-Molina A (2010) Colloid Polym Sci 288:151

    Article  CAS  Google Scholar 

  5. Paillusson F, Trizac E (2011) Phys Rev E 84:011407

    Article  Google Scholar 

  6. Wolansky G, Taflia A (2010) J Chem Phys 133:234113

    Article  CAS  Google Scholar 

  7. Duval JFL, Merlin J, Narayana PAL (2011) Phys Chem Chem Phys 13:1037

    Article  CAS  Google Scholar 

  8. Koehl P, Orland H, Delarue M (2011) J Chem Phys 135:055104

    Article  Google Scholar 

  9. Paillusson F, Dahirel V, Jardat M, Victor JM, Barbi M (2011) Phys Chem Chem Phys 13:12603

    Article  CAS  Google Scholar 

  10. Watanabe H, Okiyama Y, Nakano T, Tanaka S (2010) Chem Phys Lett 500:116

    Article  CAS  Google Scholar 

  11. Ohshima H (1999) Colloid Polym Sci 277:563

    Article  CAS  Google Scholar 

  12. Arkhipov YV, Baimbetov FB, Davletov AE (2011) Phys Rev E 83:016405

    Article  Google Scholar 

  13. Manzanilla-Granados HM, Jimenez-Angeles F, Lozada-Cassou M (2011) Colloids Surf A Physicochem Eng Asp 376:59

    Article  CAS  Google Scholar 

  14. Companys E, Garces JL, Salvador J, Galceran J, Puy J, Mas F (2007) Colloids Surf A Physicochem Eng Asp 306:2

    Article  CAS  Google Scholar 

  15. Gorham RD, Kieslich CA, Nichols A, Sausman NU, Foronda M, Morikis D (2011) Biopolymers 95:746

    CAS  Google Scholar 

  16. Fenley MO, Russo C, Manning GS (2011) J Phys Chem B 115:9864

    Article  CAS  Google Scholar 

  17. Ohshima H, Kondo T (1988) Biophys Chem 32:161

    Article  CAS  Google Scholar 

  18. Chen Z, Baker NA, Wei GW (2011) J Math Biol 63:1139

    Article  Google Scholar 

  19. Okubo T, Suzuki D, Yamagata T, Horigome K, Shibata K, Tsuchida A (2011) Colloid Polym Sci 289:1273

    Article  CAS  Google Scholar 

  20. Yoshida E (2010) Colloid Polym Sci 288:1321

    Article  CAS  Google Scholar 

  21. Hua CK, Lee DW, Kang IS (2010) Colloids Surf A Physicochem Eng Asp 372:86

    Article  CAS  Google Scholar 

  22. Bardhan JP (2011) J Chem Phys 135:104113

    Article  Google Scholar 

  23. Elter P, Lange R, Beck U (2011) Langmuir 27:8767

    Article  CAS  Google Scholar 

  24. Okubo T, Suzuki D, Yamagata T, Katsuno A, Sakurai M, Kimura H, Tsuchida A (2011) Colloid Polym Sci 289:291

    Article  CAS  Google Scholar 

  25. Miller MA, Engstrom JD, Ludher BS, Johnston KP (2010) Langmuir 26:1067

    Article  CAS  Google Scholar 

  26. Verwey EJW, Overbeek JTG (1948) Theory of the Stability of Lyophobic Colloids. Elsevier, Amsterdam

    Google Scholar 

  27. Crocker JC, Grier DG (1996) Phys Rev Lett 77:1897

    Article  CAS  Google Scholar 

  28. Maffeo C, Schoepflin R, Brutzer H, Stehr R, Aksimentiev A, Wedemann G, Seidel R (2010) Phys Rev Lett 105:158101

    Article  Google Scholar 

  29. Liu L, Moreno L, Neretnieks I (2009) Langmuir 25:688

    Article  Google Scholar 

  30. Bhardwaj R, Fang XH, Somasundaran P, Attinger D (2010) Langmuir 26:7833

    Article  CAS  Google Scholar 

  31. Sharp KA, Honig B (1990) J Phys Chem 94:7684

    Article  CAS  Google Scholar 

  32. van Aken GA, Lekkerkerker HNW, Overbeek JTG, de Bruyn PL (1990) J Phys Chem 94:8468

    Article  Google Scholar 

  33. Stigter D, Dill KA (1996) Biophys J 71:2064

    Article  CAS  Google Scholar 

  34. Rouzina I, Bloomfield VA (1996) J Phys Chem 100:4292

    Article  CAS  Google Scholar 

  35. Record MT, Zhang W Jr, Anderson CF (1998) Adv Protein Chem 51:281

    Article  CAS  Google Scholar 

  36. Ohshima H (1995) J Colloid Interface Sci 171:525

    Article  CAS  Google Scholar 

  37. Zhou S (1998) J Colloid Interface Sci 208:347

    Article  CAS  Google Scholar 

  38. Teso A, Filho ED, Neto AA (1997) J Math Biol 35:814

    Article  Google Scholar 

  39. Tuinier R (2003) J Colloid Interface Sci 258:45

    Article  CAS  Google Scholar 

  40. Tseng S, Wong N-B, Liu P-C, Hsu J-P (2007) Langmuir 23:10448

    Article  CAS  Google Scholar 

  41. Hsu JP, Huang CH, Tseng S (2011) J Colloid Interface Sci 356:550

    Article  CAS  Google Scholar 

  42. Liao SJ (1995) Int J Non-Linear Mech 30:371

    Article  Google Scholar 

  43. He J-H (1999) Comput Methods Appl Mech Eng 178:257

    Article  Google Scholar 

  44. Zhou S, Zhang G (2011) Colloids Surf A Physicochem Eng Asp 385:28

    Article  CAS  Google Scholar 

Download references

Acknowledgment

This project is supported by the National Natural Science Foundation of China (nos. 20973202 and 21173271).

Author information

Authors and Affiliations

  1. School of Physics and Electronics, Central South University, Changsha, Hunan, 410083, China

    S. Zhou & H. Wu

Authors
  1. S. Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Zhou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, S., Wu, H. Analytical solutions of nonlinear Poisson–Boltzmann equation for colloidal particles immersed in a general electrolyte solution by homotopy perturbation technique. Colloid Polym Sci 290, 1165–1180 (2012). https://doi.org/10.1007/s00396-012-2622-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00396-012-2622-1

Keywords

Search

Navigation