Skip to main content
SpringerLink
Log in

Polyelectrolyte Theory

  • Chapter
Polyelectrolytes with Defined Molecular Architecture II

Part of the book series: Advances in Polymer Science ((POLYMER,volume 166))

Abstract.

In this chapter we review recent advances which have been achieved in the theoretical description and understanding of polyelectrolyte solutions. We will discuss an improved density functional approach to go beyond mean-field theory for the cell model and an integral equation approach to describe stiff and flexible polyelectrolytes in good solvents and compare some of the results to computer simulations. Then we review some recent theoretical and numerical advances in the theory of poor solvent polyelectrolytes. At the end we show how to describe annealed polyelectrolytes in the bulk and discuss their adsorption properties.

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

DH:

Debye-Hückel

PB:

Poisson-Boltzmann

OCP:

One-Component-Plasma

PRISM:

Polymer-Reference-Interaction-Site model

RLWC:

Reference-Laria-Wu-Chandler closure

Z c :

counterion valence

Z m :

monomer valence

N :

polymer chain length, number of repeat units

h(r):

total correlation function

g(r):

pair correlation function

β=:

(k B T)−1

\(v^{{HC}}_{{ij}} {\left( r \right)}\) :

hard core potential

l :

bond length

l p :

persistence length

b :

monomer size

l B :

Bjerrum length

λ D :

Debye (screening) length

κ :

inverse (Debye length)

ρ :

monomer density

ρ c :

counterion density

R E :

ent-to-end distance

R G :

radius of gyration

f :

fraction of charged monomers

S(q):

total structure factor

S IC :

inter-chain structure factor

S 1 :

spherically averaged chain form factor

ξ :

correlation length

q * :

peak in the structure factor S IC (q)

q m :

peak in the total structure factor S(q)

µ :

chemical potential (of charges)

ξ el :

electrostatic blob size

v :

virial coefficient

τ :

reduced temperature

References

  1. deGennes PG (1985) Scaling concepts in polymer physics, 2nd edn. Cornell University Press, Ithaca

    Google Scholar 

  2. Gouy GL (1910) Journal de Phys 9:457; Chapman DL (1913) London and Edinburg Phil Mag and J of Sci 25:475

    Google Scholar 

  3. Alfrey T, Berg PW, Morawetz HJ (1951) J Polym Sci 7:543

    Google Scholar 

  4. Katchalsky A (1971) Pure Appl Chem 26:327

    Google Scholar 

  5. Manning G (1969) J Chem Phys 51:924

    Google Scholar 

  6. Oosawa F (1971) Polyelectrolytes. Marcel Dekker, New York

    Google Scholar 

  7. LeBret M, Zimm B (1984) Biopolymers 23:271; ibd. 23:287

    Google Scholar 

  8. Belloni L, Drifford M, Turq P (1984) Chem Phys 83:147

    Google Scholar 

  9. Deserno M, Holm C, May S (2000) Macromolecules 33:199

    Google Scholar 

  10. Deserno M, Holm C, Kremer K (2001) In: Radeva T (ed) Physical Chemistry of Polyelectrolytes, vol 99, chap 2. Marcel Decker, New York, p 59

    Google Scholar 

  11. Deserno M, Holm C (2002) Molecular Physics 100:2941

    Google Scholar 

  12. Deserno M, Arnold A, Holm C (2003) Macromolecules 36:249

    Google Scholar 

  13. Holm C, Kékicheff P, Podgornik R (2001) Electrostatic Effects in Soft Matter and Biophysics. NATO Science Series II- Mathematics, vol 46. Physics and Chemistry, Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  14. Nordholm S (1984) Chem Phys Lett 105:302

    Google Scholar 

  15. Baus M, Hansen JP (1980) Phys Rep 59:1

    Google Scholar 

  16. Penfold R, Nordholm S, Jönsson B, Woodward CE (1990) J Chem Phys 92:1915

    Google Scholar 

  17. Groot RD (1991) J Chem Phys 95:9191

    Google Scholar 

  18. Barbosa MC, Deserno M, Holm C (2000) Europhys Lett 52:80

    Google Scholar 

  19. Deserno M (2000) Physica A 278:405

    Google Scholar 

  20. Hansen JP, McDonald IR (1986) Theory of simple liquids. Academic Press, London

    Google Scholar 

  21. Curro JO, Schweizer KS (1987) Macromolecules 20:1928

    Google Scholar 

  22. Curro 10, Schweizer KS (1987) J Chem Phys 87:1842

    Google Scholar 

  23. Shew CY. Yethiraj A (1997) J Chem Phys 106:5706

    Google Scholar 

  24. Hofmann T, Winkler RG, Reineker P (2001) J Chem Phys 114:10181

    Google Scholar 

  25. Laria D, Wu D, Chandler D (1991) J Chem Phys 95:4444

    Google Scholar 

  26. Yethiraj A, Shew CY (1996) Phys Rev Lett 77:3937

    Google Scholar 

  27. Shew CY, Yethiraj A (1999) J Chem Phys 110:5437

    Google Scholar 

  28. Hofmann T (2002) Ph D thesis, University of Ulm, Ulm

    Google Scholar 

  29. Muthukumar M (1996) J Chem Phys 105:5183

    Google Scholar 

  30. Grønbech-Jensen N, Mashl RJ, Bruinsma RE, Gelbert WM (1997) Phys Rev Lett 78:2477

    Google Scholar 

  31. Ha BY, Liu AJ (1997) Phys Rev Lett 79:1289

    Google Scholar 

  32. Hofmann T, Winkler RG, Reineker P, in preparation

    Google Scholar 

  33. Winkler RG, Harnau L, Reineker P (1994) J Chem Phys 101:8119

    Google Scholar 

  34. Muthukumar M (1987) J Chem Phys 86:7230

    Google Scholar 

  35. Yethiraj A(1998) J Chem Phys 108:1184

    Google Scholar 

  36. Ha BY, Thirumalai D (1999) J Chem Phys 110:7533

    Google Scholar 

  37. Netz RR, Orland H (1999) Eur Phys JB 8:81

    Google Scholar 

  38. Ghosh K, Carri GA, Muthukumar M (2001)J Chem Phys 115:4367

    Google Scholar 

  39. Edwards SF, Singh P (1979)J Chem Soc Faraday Trans 275:1001

    Google Scholar 

  40. Barrat JL, Joanny JF (1996) Adv Chem Phys XCIV:1

    Google Scholar 

  41. Higgs PG, Orland H (1991) J Chem Phys 95:4506

    Google Scholar 

  42. Odijk T (1977) J Polym Sci 15:477

    Google Scholar 

  43. Skolnick J, Fixman M (1977) Macromolecules 10:944

    Google Scholar 

  44. Everaers R, Milchev A, Yamakov V (2002) Eur Phys 3 B 8:3

    Google Scholar 

  45. Ullner M, Jönsson S (1997)J Chem Phys 107:1279

    Google Scholar 

  46. Ullner M, Woodward CE (2002) Macromolecules 35:1437

    Google Scholar 

  47. Grayce CJ, Yethiraj A, Schweizer KS (1994) J Chem Phys 100:6857

    Google Scholar 

  48. Dymitrowska M, Belloni L (1999) J Chem Phys 111:6633

    Google Scholar 

  49. Stevens M, Kremer K (1995) J Chem Phys 103:1669

    Google Scholar 

  50. Winkler RG, Gold M, Reineker P (1998) Phys Rev Lett 80:373 1

    Google Scholar 

  51. deGennes PC, Pincus P, Velasco R, Brochard F(1976) J Phys (Paris) 37:1461

    Google Scholar 

  52. Förster CF, Schmidt M (1995) Adv Polym Sci 120:50

    Google Scholar 

  53. Hagenbuchle M, Weyerich B, Deggelmann M, Graf C, Krause R, Maier EE, Schulz SF, Klein R, Weber R (1990) Physica A 169:29

    Google Scholar 

  54. Nishida K, Kaji K, Kanaya T (1995) Macromolecules 28:2472

    Google Scholar 

  55. Essafi W, Lafuma F, Williams CE (1995) J Phys II (France) 5:1269

    Google Scholar 

  56. Stevens M, Kremer K (1993) Phys Rev Lett 71:2228; Macromolecules 26:4717

    Google Scholar 

  57. Stevens M, Kremer K (1996) J Phys 2 (France) 6:1607

    Google Scholar 

  58. Holm C, Kremer K (1999) Polyelectrolytes in Solution—Recent Computer Simulations. In: Noda I, Kokufuta E (eds) Proc Yamada Conf Polyelectrolytes 1998. Yamada Science Foundation, Osaka, Japan, p 27

    Google Scholar 

  59. Micka U, Kremer K (1996) Phys Rev B 54:2653

    Google Scholar 

  60. Micka U, Kremer K (1997) Europhys Lett 38:279

    Google Scholar 

  61. Khokhlov AR, Khachaturian KA (1982) Polymer 23:1742

    Google Scholar 

  62. Halperin A, Zhulina EB (1991) Europhys Lett 15:417

    Google Scholar 

  63. Khokhlov AR (1980) J Phys A (Math Gen) 13:979

    Google Scholar 

  64. Dobrynin AV, Rubinstein M, Obukhov SP (1996) Macromolecules 29:2974

    Google Scholar 

  65. Lord Rayleigh (1882) Philos Mag 14:184

    Google Scholar 

  66. Kantor Y, Kardar M (1994) Europhys Lett 27:643

    Google Scholar 

  67. Haronska P, Wilder J, Vilgis TA (1997) J Phys II (France) 7:1273

    Google Scholar 

  68. Wilder J, Vilgis TA (1998) Phys Rev B 57:6865

    Google Scholar 

  69. Vilgis TA, Johner A, Joanny JF (2000) Eur Phys J E 2:289

    Google Scholar 

  70. Migliorini G, Rostaishvili VG, Vilgis TA (2001) Eur Phys J E 4:475

    Google Scholar 

  71. Migliorini G, Lee N, Rostiashvili VG, Vilgis TA (2001) Eur Phys J E 6:259

    Google Scholar 

  72. Lee N, Vilgis TA (2002) Europhys Lett 57:817

    Google Scholar 

  73. Lee N, Vilgis TA (2002) Eur Phys J (in press)

    Google Scholar 

  74. Kantor Y, Kardar M (1995) Phys Rev B 51:1299

    Google Scholar 

  75. Lyulin AV, Dünweg B, Borisov OV, Darinskii AA (1999) Macromolecules 32:3264; Chodanowski P, Stoll S (1999) JChemPhys 111:6069

    Google Scholar 

  76. Micka U, Holm C, Kremer K (1999) Langmuir 15:4033; Micka U, Kremer K (2000) Europhys Lett 49:189

    Google Scholar 

  77. Limbach HJ, Holm C (2002) Computer Physics Communications 147:321; Limbach HJ, Holm C, Kremer K (2002) Europhys Lett 60:566; Holm C, Limbach HJ, Kremer K; J Phys: Condens Matter 15:205

    Google Scholar 

  78. Limbach HJ, Holm C (2002) J Phys Chem B, in press

    Google Scholar 

  79. Schiessel H, Pincus P (1998) Macromolecules 31:7953

    Google Scholar 

  80. Dobrynia AV, Rubinstein M (1999) Macromolecules 32:915

    Google Scholar 

  81. Deserno M (2001) Eur Phys J E 6:163

    Google Scholar 

  82. Nierlich M et al. (1979) J Physique 40:701; Drifford M, Dalbiez JP (1984) J Phys Chem 88:5368; Kaji K, Urakawa H, Kanaya T, Kitamaru R (1988) 1 Physique 49:993; Wang L, Bloomfield V (1991) Macromolecules 24:5791

    Google Scholar 

  83. Joanny JF (2001) Scaling description of charged polymers. In: Ref. [13]

    Google Scholar 

  84. Limbach HJ (2001) Ph D thesis, Johannes Gutenberg Universität, Mainz, Germany

    Google Scholar 

  85. Essafi W, Lafuma F, Williams CE (1995) J Phys 115:1269; Heitz C, Rawiso M, François J, Polymer (1999) 40:1637; Waigh TA, Ober R, Williams CE, Galin JC (2001) Macromolecules 34:1973

    Google Scholar 

  86. Baigl D, Ober R, Qu D, Fery A, Williams CE (2002) Europhys Lett 63:588

    Google Scholar 

  87. Hugel T et al. (2001) Macromolecules 4:1039

    Google Scholar 

  88. Tamashiro MN, Schiessel H (2000) Macromolecules 33:5263

    Google Scholar 

  89. Pickett GT, Balazs AC (2001) Langmuir 17:5111

    Google Scholar 

  90. Raphael E, Joanny JF (1990) Europhys Lett 13:623

    Google Scholar 

  91. van der Schoot P (1997) Langmuir 13:4926

    Google Scholar 

  92. Fleer GJ, Cohen Stuart MA, Scheutjens JMHM, Cosgrove T, Vincent B (1993) Polymers at Interfaces. Chapman & Hall, London

    Google Scholar 

  93. Israels R, Leermakers AM, Fleer GJ (1994) Macromolecules 27:3087

    Google Scholar 

  94. Zhulina EB, Birshtein TM, Borisov OV (1995) Macromolecules 28:1491

    Google Scholar 

  95. Mandel M (1988) Polyelectrolytes. In: Mark HF, Bikales NM, Overberger CG, Menges C, Kroschwitz JI (eds) Encyclopedia of Polymers and Engineering. Wiley, New York, vol 11, p 739

    Google Scholar 

  96. Kötz J, Philipp B, Pfannmüller B (1990) Makromol Chem 191:1219

    Google Scholar 

  97. Tirtaatmadja V, Tam KC, Jenkins RD (1997) Macromolecules 30:3271

    Google Scholar 

  98. Jönsson B, Ullner M, Peterson C, Somelius O, Söderberg B (1996) J Phys Chem 100:407

    Google Scholar 

  99. Berghold G, van der Schoot P, Seidel C (1997) J Chem Phys 107:8083

    Google Scholar 

  100. Borukhov I, Andelman D, Borrega R, Cloitre M, Leibler L, Orland H (2000) J Phys Chem B 104:11027

    Google Scholar 

  101. Castelnovo M, Sens P, Joanny JF (2000) Eur Phys JE 1:115

    Google Scholar 

  102. Reed CE, Reed WF (1992) J Chem Phys 96:1609

    Google Scholar 

  103. Sassi AP, Beltrán S, Hooper HH, Blanch HW, Prausnitz JM, Siegel RA (1992) J Chem Phys 97:8767

    Google Scholar 

  104. Ullner M, Jönsson B, Söderberg B, Peterson C (1996) J Chem Phys 104:3048

    Google Scholar 

  105. Ullner M, Jönsson B (1996) Macromolecules 29:6645

    Google Scholar 

  106. Zito T, Seidel C (2002) Eur Phys J E 8:339

    Google Scholar 

  107. Limbach HJ, Holm C (2001) J Chem Phys 114:9674

    Google Scholar 

  108. Abramowitz M, Stegun IA (1965) Handbook of Mathematical Functions. Dover Publications, New York

    Google Scholar 

  109. Deserno M, Holm C (1998) J Chem Phys 109:7678; ibd 109:7694

    Google Scholar 

  110. Ahrens H, Förster S, Helm CA (1997) Macromolecules 30:8447

    Google Scholar 

  111. Klitzing R, Espert A, Asnacios A, Hellweg T, Colin A, Langevin D (1999) Coll Surf A 149:131

    Google Scholar 

  112. Theodoly O, Ober R, Williams CE (2001) Eur Phys J E 5:51

    Google Scholar 

  113. Yim H, Kent M, Matheson A, Stevens M, Ivkov R, Satija S, Majewski J, Smith GS (to be published)

    Google Scholar 

  114. Netz RR (1999) Phys Rev E 60:3174

    Google Scholar 

  115. Harris FE, Rice SA (1954) J Phys Chem 58:725 and 733

    Google Scholar 

  116. Marcus RA (1954) J Phys Chem 58:621

    Google Scholar 

  117. Lifson S (1957) J Chem Phys 26:727

    Google Scholar 

  118. Helm CA, Laxhuber L, Lösche M, Möhwald H (1986) Coll Pol Sci 264:46

    Google Scholar 

  119. Müller H, Leube W, Tauer K, Förster S, Antonietti M (1997) Macromolecules 30:2288

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Polymerforschung, Ackermannweg 10, 55128, Mainz, Germany

    C. Holm, K. Kremer & T. A. Vilgis

  2. Institut Curie Section Recherche, Physicochimie Curie, 26 rue d’Ulm, 75248 Paris Cedex 05, Paris, France

    J. F. Joanny

  3. Max-Planck-Institut für Kolloid- und Grenzflächenforschung, Am Mühlenberg, 14476 , Golm, Germany

    C. Seidel

  4. Abteilung Theoretische Physik, Universität Ulm, 89069 , Ulm, Germany

    P. Reineker

  5. Institut für Festkörperforschung, Forschungszentrum Jülich, 52425 , Jülich, Germany

    R. G. Winkler

  6. Sektion Physik, LMU Munich, Theresienstrasse 37, 80333 , Munich, Germany

    R. R. Netz

Authors
  1. C. Holm
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. F. Joanny
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Kremer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. R. Netz
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. P. Reineker
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. C. Seidel
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. T. A. Vilgis
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. R. G. Winkler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Holm .

Editor information

Manfred Schmidt

Rights and permissions

Reprints and permissions

About this chapter

Cite this chapter

Holm, C. et al. Polyelectrolyte Theory. In: Schmidt, M. (eds) Polyelectrolytes with Defined Molecular Architecture II. Advances in Polymer Science, vol 166. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b11349

Download citation

  • DOI: https://doi.org/10.1007/b11349

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00556-8

  • Online ISBN: 978-3-540-36463-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation