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Theoretical Approaches to Neutral and Charged Polymer Brushes

  • Ali Naji
  • Christian Seidel
  • Roland R. NetzEmail author
Chapter
Part of the Advances in Polymer Science book series (POLYMER, volume 198)

Abstract

Neutral or charged polymers that are densely end-grafted to surfaces form brush-like structures and are highly stretched under good-solvent conditions. We discuss and compare relevant results from scaling models, self-consistent field methods and MD simulations and concentrate on the conceptual simple case of planar substrates. For neutral polymers the main quantity of interest is the brush height and the polymer density profile, which can be well predicted from self-consistent calculations and simulations. Charged polymers (polyelectrolytes) are of practical importance since they are soluble in water. Counterion degrees of freedom determine the brush behavior in a decisive way and lead to a strong and nonlinear swelling of the brush.

Brushes Polyelectrolytes Scaling theory Self-consistent field theory Simulation techniques 

Abbreviations

a

Kuhn length or effective monomer size

d

height of counterion layer

f

fractional charge of the chain 0 < f < 1

F

free energy in units of k B T (per chain or unit area)

h

height of brush

kBT

thermal energy

L

contour length of a chain

B=e2/(4 πε kBT)

Bjerrum length

N

polymerization index

R

end-to-end polymer chain radius

R0

end-to-end radius of an ideal polymer

RF

Flory radius of a self-avoiding chain

v2

2nd virial coefficient of monomers in solution

κ−1

Debye–Hückel screening length

ν

Flory exponent for the polymer size

Π

osmotic pressure, rescaled by k B T

ρa

grafting density of a polymer brush

ρ(z)

monomer density at distance z from grafting surface

σ

Lennard-Jones diameter in simulation

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References

  1. 1.
    Yamakawa H (1971) Modern Theory of Polymer Solutions. Harper & Row, New York Google Scholar
  2. 2.
    de Gennes PG (1979) Scaling Concepts in Polymer Physics. Cornell University, Ithaca Google Scholar
  3. 3.
    Grosberg AY, Khokhlov AR (1994) Statistical Physics of Macromolecules. AIP Press, New York Google Scholar
  4. 4.
    Rubinstein M (2003) Polymer Physics. Oxford University Press, Oxford Google Scholar
  5. 5.
    Netz RR, Andelman D (2003) Physics Reports 380:1 CrossRefGoogle Scholar
  6. 6.
    Halperin A, Tirell M, Lodge TP (1992) Adv Pol Sci 100:31 CrossRefGoogle Scholar
  7. 7.
    Szleifer I, Carignano MA (1996) Adv Chem Phys XCIV:165 Google Scholar
  8. 8.
    Taunton HJ, Toprakcioglu C, Fetters LJ, Klein J (1988) Nature 332:712; (1990) Macromolecules 23:571 Google Scholar
  9. 9.
    Auroy P, Auvray L, Leger L (1991) Phys Rev Lett 66:719; (1991) Macromolecules 24:2523; (1991) Macromolecules 24:5158 Google Scholar
  10. 10.
    Marques CM, Joanny JF, Leibler L (1988) Macromolecules 21:1051; Marques CM, Joanny JF (1989) Macromolecules 22:1454 Google Scholar
  11. 11.
    Field JB, Toprakcioglu C, Dai L, Hadziioannou G, Smith G, Hamilton W (1992) J Phys II France 2:2221 CrossRefGoogle Scholar
  12. 12.
    Kent MS, Lee LT, Factor BJ, Rondelez F, Smith GS (1995) J Chem Phys 103:2320 CrossRefGoogle Scholar
  13. 13.
    Bijsterbosch HD, de Haan VO, de Graaf AW, Mellema M, Leermakers FAM, Cohen Stuart MA, van Well AA (1995) Langmuir 11:4467 CrossRefGoogle Scholar
  14. 14.
    Teppner R, Motschmann H (1998) Macromolecules 31:7467 CrossRefGoogle Scholar
  15. 15.
    Oosawa F (1971) Polyelectrolytes. Dekker, New York Google Scholar
  16. 16.
    Förster S, Schmidt M (1995) Adv Polym Sci 120:50 Google Scholar
  17. 17.
    Barrat JL, Joanny JF (1996) Adv Chem Phys 94:1 CrossRefGoogle Scholar
  18. 18.
    Holm H, Joanny JF, Kremer K, Netz RR, Reineker P, Seidel C, Vilgis TA, Winkler RG (2004) Adv Polym Science 166:67 Google Scholar
  19. 19.
    Rühe J, Ballauff M, Biesalski M, Dziezok P, Gröhn F, Johannsmann D, Houbenov N, Hugenberg N, Konradi R, Minko S, Motornov M, Netz RR, Schmidt M, Seidel C, Stamm M, Stephan T, Usov D, Zhang H (2004) Adv Polym Science 165:79 Google Scholar
  20. 20.
    Dolan AK, Edwards SF (1974) Proc R Soc Lond A 337:509; 343:427 CrossRefGoogle Scholar
  21. 21.
    Alexander S (1977) J Phys (France) 38:983 Google Scholar
  22. 22.
    de Gennes PG (1980) Macromolecules 13:1069 CrossRefGoogle Scholar
  23. 23.
    Semenov AN (1985) Sov Phys JETP 61:733 Google Scholar
  24. 24.
    Daoud M, Cotton JP (1982) J Phys France 43:531 CrossRefGoogle Scholar
  25. 25.
    Karim A, Satija SK, Douglas JF, Ankner JF, Fetters LJ (1994) Phys Rev Lett 73:3407 CrossRefGoogle Scholar
  26. 26.
    Baltes H, Schwendler M, Helm CA, Heger R, Goedel WA (1997) Macromolecules 30:6633 CrossRefGoogle Scholar
  27. 27.
    Netz RR (2003) J Phys Condens Mat 15:S239 Google Scholar
  28. 28.
    Friedsam C, Gaub HE, Netz RR (2005) Europhys Lett 72:844 CrossRefGoogle Scholar
  29. 29.
    Burak Y, Netz RR (2004) J Chem Phys B 108:4840 Google Scholar
  30. 30.
    Odijk T (1977) J Polym Sci Polym Phys Ed 15:477; (1978) Polymer 19:989 Google Scholar
  31. 31.
    Skolnick J, Fixman M (1977) Macromolecules 10:944 CrossRefGoogle Scholar
  32. 32.
    Barrat JL, Joanny JF (1993) Europhys Lett 24:333 CrossRefGoogle Scholar
  33. 33.
    Netz RR, Orland H (1999) Eur Phys J B 8:81 CrossRefGoogle Scholar
  34. 34.
    Manghi M, Netz RR (2004) Eur Phys J E 14:67 CrossRefGoogle Scholar
  35. 35.
    Ullner M, Woodward CE (2002) Macromolecules 35:1437 CrossRefGoogle Scholar
  36. 36.
    Everaers R, Milchev A, Yamakov V (2002) Eur Phys J E 8:3 CrossRefGoogle Scholar
  37. 37.
    Netz RR, Joanny JF (1999) Macromolecules 32:9013; Netz RR, Joanny JF (1999) Macromolecules 32:9026 Google Scholar
  38. 38.
    Manning GS (1969) J Chem Phys 51:924 CrossRefGoogle Scholar
  39. 39.
    Manning GS (1969) J Chem Phys 51:934 CrossRefGoogle Scholar
  40. 40.
    Manning GS, Ray J (1998) J Biomol Struct Dyn 16:461 Google Scholar
  41. 41.
    Naji A, Netz RR (2005) Phys Rev Lett 95:185703 CrossRefGoogle Scholar
  42. 42.
    Fixman M (1982) J Chem Phys 76:6346 CrossRefGoogle Scholar
  43. 43.
    Le Bret M (1982) J Chem Phys 76:6243 CrossRefGoogle Scholar
  44. 44.
    Manning GS, Mohanty U (1997) Physica A 247:196 CrossRefGoogle Scholar
  45. 45.
    Manning GS (1988) J Chem Phys 89:3772 CrossRefGoogle Scholar
  46. 46.
    Wandrey C, Hunkeler D, Wendler U, Jaeger W (2000) Macromolecules 33:7136 CrossRefGoogle Scholar
  47. 47.
    Blaul J, Wittemann M, Ballauff M, Rehahn M (2000) J Phys Chem B 104:7077 CrossRefGoogle Scholar
  48. 48.
    Cosgrove T, Heath T, van Lent B, Leermakers FAM, Scheutjens J (1987) Macromolecules 20:1692 CrossRefGoogle Scholar
  49. 49.
    Murat M, Grest GS (1989) Macromolecules 22:4054; Chakrabarti A, Toral R (1990) Macromolecules 23:2016; Lai PY, Binder K (1991) J Chem Phys 95:9288 CrossRefGoogle Scholar
  50. 50.
    Milner ST, Witten TA, Cates ME (1988) Europhys Lett 5:413; (1988) Macromolecules 21:610 Google Scholar
  51. 51.
    Skvortsov AM, Pavlushkov IV, Gorbunov AA, Zhulina YB, Borisov OV, Pryamitsyn VA (1988) Polymer Science 30:1706 Google Scholar
  52. 52.
    Netz RR, Schick M (1997) Europhys Lett 38:37; (1998) Macromolecules 31:5105 Google Scholar
  53. 53.
    Carignano MA, Szleifer I (1995) J Chem Phys 102:8662 CrossRefGoogle Scholar
  54. 54.
    Martin JI, Wang ZG (1995) J Chem Phys 99:2833 CrossRefGoogle Scholar
  55. 55.
    Baranowski R, Whitmore MD (1995) J Chem Phys 103:2343 CrossRefGoogle Scholar
  56. 56.
    Currie EPK, Leermakers FAM, Cohen Stuart MA, Fleer GJ (1999) Macromolecules 32:487 CrossRefGoogle Scholar
  57. 57.
    Grest GS (1994) Macromolecules 27:418 CrossRefGoogle Scholar
  58. 58.
    Seidel C, Netz RR (2000) Macromolecules 33:634 CrossRefGoogle Scholar
  59. 59.
    Witten TA, Pincus PA (1986) Macromolecules 19:2509; Zhulina EB, Borisov OV, Priamitsyn VA (1990) J Coll Surf Sci 137:495 CrossRefGoogle Scholar
  60. 60.
    Milner ST (1988) Europhys Lett 7:695 CrossRefGoogle Scholar
  61. 61.
    Milner ST, Witten TA, Cates ME (1989) Macromolecules 22:853 CrossRefGoogle Scholar
  62. 62.
    Halperin A (1988) J Phys France 49:547; Zhulina EB, Borisov OV, Pryamitsyn VA, Birshtein TM (1991) Macromolecules 24:140; Williams DRM (1993) J Phys II France 3:1313 Google Scholar
  63. 63.
    Auroy P, Auvray L (1992) Macromolecules 25:4134 CrossRefGoogle Scholar
  64. 64.
    Marko JF (1993) Macromolecules 26:313 CrossRefGoogle Scholar
  65. 65.
    Lai PY, Binder K (1992) J Chem Phys 97:586; Grest GS, Murat M (1993) Macromolecules 26:3108 Google Scholar
  66. 66.
    Ball RC, Marko JF, Milner ST, Witten TA (1991) Macromolecules 24:693; Li H, Witten TA (1994) Macromolecules 27:449; Manghi M, Aubouy M, Gay C, Ligoure C (2001) Eur Phys J E 5:519 Google Scholar
  67. 67.
    Dan N, Tirrell M (1992) Macromolecules 25:2890 CrossRefGoogle Scholar
  68. 68.
    Murat M, Grest GS (1991) Macromolecules 24:704 CrossRefGoogle Scholar
  69. 69.
    Milner ST, Witten TA (1988) J Phys France 49:1951 CrossRefGoogle Scholar
  70. 70.
    Aubouy M, Fredrickson GH, Pincus P, Raphael E (1995) Macromolecules 28:2979 CrossRefGoogle Scholar
  71. 71.
    Gast AP, Leibler L (1986) Macromolecules 19:686 CrossRefGoogle Scholar
  72. 72.
    Borukhov I, Leibler L (2000) Phys Rev E 62:R41 CrossRefGoogle Scholar
  73. 73.
    Marko JF, Witten TA (1991) Phys Rev Lett 66:1541 CrossRefGoogle Scholar
  74. 74.
    Brown G, Chakrabarti A, Marko JF (1995) Macromolecules 28:7817; Zhulina EB, Singhm C, Balazs AC (1996) Macromolecules 29:8254 CrossRefGoogle Scholar
  75. 75.
    Halperin A, Alexander S (1988) Europhys Lett 6:329; Johner A, Joanny JF (1990) Macromolecules 23:5299; Ligoure C, Leibler L (1990) J Phys France 51:1313; Milner ST (1992) Macromolecules 25:5487; Johner A, Joanny JF (1993) J Chem Phys 98:1647 Google Scholar
  76. 76.
    Miklavic SJ, Marcelja S (1988) J Phys Chem 92:6718 CrossRefGoogle Scholar
  77. 77.
    Misra S, Varanasi S, Varanasi PP (1989) Macromolecules 22:5173 CrossRefGoogle Scholar
  78. 78.
    Pincus P (1991) Macromolecules 24:2912 CrossRefGoogle Scholar
  79. 79.
    Borisov OV, Birstein TM, Zhulina EB (1991) J Phys II (France) 1:521 CrossRefGoogle Scholar
  80. 80.
    Ross RS, Pincus P (1992) Macromolecules 25:2177; Zhulina EB, Birstein TM, Borisov OV (1992) J Phys II (France) 2:63 CrossRefGoogle Scholar
  81. 81.
    Wittmer J, Joanny JF (1993) Macromolecules 26:2691 CrossRefGoogle Scholar
  82. 82.
    Israels R, Leermakers FAM, Fleer GJ, Zhulina EB (1994) Macromolecules 27:3249 CrossRefGoogle Scholar
  83. 83.
    Borisov OV, Zhulina EB, Birstein TM (1994) Macromolecules 27:4795 CrossRefGoogle Scholar
  84. 84.
    Zhulina EB, Borisov OV (1997) J Chem Phys 107:5952 CrossRefGoogle Scholar
  85. 85.
    Mir Y, Auvroy P, Auvray L (1995) Phys Rev Lett 75:2863 CrossRefGoogle Scholar
  86. 86.
    Guenoun P, Schlachli A, Sentenac D, Mays JM, Benattar JJ (1995) Phys Rev Lett 74:3628 CrossRefGoogle Scholar
  87. 87.
    Ahrens H, Förster S, Helm CA (1997) Macromolecules 30:8447; (1998) Phys Rev Lett 81:4172 CrossRefGoogle Scholar
  88. 88.
    Ballauff M, Guo X (2001) Phys Rev E 64:051406 CrossRefGoogle Scholar
  89. 89.
    Balastre M, Li F, Schorr P, Yang J, Mays JW, Tirrell MV (2002) Macromolecules 35:9480 CrossRefGoogle Scholar
  90. 90.
    Csajka FS, Netz RR, Seidel C, Joanny JF (2001) Eur Phys J E 4:505 CrossRefGoogle Scholar
  91. 91.
    Santangelo CD, Lau AWC (2004) Eur Phys J E 13:335 CrossRefGoogle Scholar
  92. 92.
    Naji A, Netz RR, Seidel C (2003) Eur Phys J E 12:223 CrossRefGoogle Scholar
  93. 93.
    Hugel T, Rief M, Seitz M, Gaub HE, Netz RR (2005) Phys Rev Lett 94:048301 CrossRefGoogle Scholar
  94. 94.
    Moreira AG, Netz RR (2001) Phys Rev Lett 87:078301; (2002) Eur Phys J E 8:33 CrossRefGoogle Scholar
  95. 95.
    Csajka F, Seidel C (2000) Macromolecules 33:2728 CrossRefGoogle Scholar
  96. 96.
    Seidel C (2003) Macromolecules 36:2536 CrossRefGoogle Scholar
  97. 97.
    Romet-Lemonne, Daillant J, Guenoun P, Yang J, Mays JW (2004) Phys Rev Lett 93:148301 CrossRefGoogle Scholar
  98. 98.
    Ahrens H, Förster S, Helm CA, Kumar NA, Naji A, Netz RR, Seidel C (2004) J Chem Phys B 108:16870–16876 Google Scholar
  99. 99.
    Shen H, Zhang L, Eisenberg A (1999) J Am Chem Soc 121:2728 CrossRefGoogle Scholar
  100. 100.
    Netz RR (1999) Europhys Lett 47:391 CrossRefGoogle Scholar
  101. 101.
    Guenoun P, Muller F, Delsanti M, Auvray L, Chen YJ, Mays JW, Tirrell M (1998) Phys Rev Lett 81:3872; Guenoun P, Delsanti M, Gazeau D, Mays JW, Cook DC, Tirrell M, Auvray L (1998) Eur Phys J B 1:77 CrossRefGoogle Scholar
  102. 102.
    Förster S, Hermsdorf N, Leube W, Schnablegger H, Regenbrecht M, Akarai S, Lindner P, Böttcher C (1999) J Phys Chem B 103:6657 CrossRefGoogle Scholar
  103. 103.
    Boroudjerdi H, Kim YW, Naji A, Netz RR, Schlagberger X, Serr A (2005) Phys Rep 416:129 CrossRefGoogle Scholar

Authors and Affiliations

  1. 1.Dept. of PhysicsTechnical University of MunichGarchingGermany
  2. 2.Max-Planck-Institute of Colloids and InterfacesPotsdamGermany

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