Friction

, Volume 2, Issue 1, pp 73–81 | Cite as

Structure of polyelectrolyte brushes studied by coarse grain simulations

Open Access
Research Article

Abstract

As an example of a very low friction system, Monte Carlo Brownian dynamics simulations have been used to calculate equilibrium structures of a polyelectrolyte brush grafted onto planes. The polymers were calculated in a semi-flexible coarse-grain model that is appropriate to treat the charge density of the polyion. The effect of linear charge density on the polyion ξ, the surface negative charge, and added salts were studied. In salt-free solution, scaling theories predicted the structure well in the low — region. In the high ξ region, additional shrinkage was found from the theories due to counterion condensation. The effect of surface charge showed not only the repulsion of the polyion from the surface but also the shrinkage in the high ξ region due to the additional counterions required for electrical neutrality. The addition of salts led to the shrinkage of the brush heights, and in the high ξ region, additional extension was found. The computational strategy for calculating the friction dynamics of the system is also discussed.

Keywords

polyelectrolyte brush friction Monte Carlo Brownian dynamics simulation soft materials automotive tribology 

References

  1. [1]
    Washizu H, Ohmori T. Molecular dynamics simulations of elastohydrodynamic lubrication oil film. Lubr Sci22(8): 323–340 (2010)CrossRefGoogle Scholar
  2. [2]
    Washizu H, Sanda S, Hyodo S, Ohmori T, Nishino N, Suzuki A. Molecular dynamics simulations of elasto-hydrodynamic lubrication and boundary lubrication for automotive tribology. J Phys Conf Ser89: 12009 (2007)CrossRefGoogle Scholar
  3. [3]
    Washizu H, Kajita S, Tohyama M, Ohmori T, Nishino N, Teranishi H, Suzuki A. Mechanism of ultra low friction of multilayer graphene studied by coarse-grained molecular simulation. Faraday Discuss156: 279–291 (2012)CrossRefGoogle Scholar
  4. [4]
    Kajita S, Washizu H, Ohmori T. Deep bulk atoms in a solid cause friction. Europhys Lett87(6): 66002 (2009)CrossRefGoogle Scholar
  5. [5]
    Kajita S, Washizu H, Ohmori T. Approach of semi-infinite dynamic lattice Green’s function and energy dissipation due to phonons in solid friction between commensurate surfaces. Phys Rev B82(11): 115424 (2010)CrossRefGoogle Scholar
  6. [6]
    Kajita S, Washizu H, Ohmori T. Simulation of solid-friction dependence on number of surface atoms and theoretical approach for infinite number of atoms. Phys Rev B86(7): 075453 (2012)CrossRefGoogle Scholar
  7. [7]
    Israelachvili J. Intermolecular and Surface Forces, 3d Ed. London: Academic Press, 2011.Google Scholar
  8. [8]
    Raviv U, Giasson S, Kampf N, Gohy J F, Jerome R, Klein J. Lubrication by charged polymers. Nature425(6954): 163–165 (2003)CrossRefGoogle Scholar
  9. [9]
    Gaisinskaya A, Ma L, Silbert G, Sorkin R, Tairy O, Goldberg R, Kampf N, Klein J. Hydration lubrication: Exploring a new paradigm. Faraday Discuss156: 217–233 (2012)CrossRefGoogle Scholar
  10. [10]
    Kobayashi M, Terada M, Takahara A. Polyelectrolyte brushes: A novel stable lubrication system in aqueous conditions. Faraday Discuss156: 403–412 (2012)CrossRefGoogle Scholar
  11. [11]
    Washizu H, Kikuchi K. Electric polarizability of DNA in aqueous salt solution. J Phys Chem B110(6): 2855–2861 (2006)CrossRefGoogle Scholar
  12. [12]
    Carrillo J-M Y, Brown W M, Dobrynin A V. Explicit solvent simulations of friction between brush layers of charged and neutral bottle-brush macromolecules. Macromolecules45(21): 8880–8891 (2012)CrossRefGoogle Scholar
  13. [13]
    Goujon F, Ghoufi A, Malfreyt P, Tildesley D J. Frictional forces in polyelectrolyte brushes: Effects of sliding velocity, solvent quality and salt. Soft Matter8(17): 4635–4644 (2012)CrossRefGoogle Scholar
  14. [14]
    Carrillo J-M Y, Russano D, Dobrynin A V. Friction between brush layers of charged and neutral bottle-brush macromolecules. Molecular dynamics simulations. Langmuir27(23): 14599–14608 (2011)CrossRefGoogle Scholar
  15. [15]
    Kikuchi K, Yoshida M, Maekawa T, Watanabe H. Metropolis monte carlo method as a numerical technique to solve the fokker-planck equation. Chem Phys Lett185: 335–338 (1991)CrossRefGoogle Scholar
  16. [16]
    Seror J, Merkher Y, Kampf N, Collinson L, Day A J, Maroudas A, Klein J. Normal and shear interactions between hyaluronan aggrecan complexes mimicking possible boundary lubricants in articular cartilage in synovial joints. Biomacromolecules13(11): 3823–3832 (2012)CrossRefGoogle Scholar
  17. [17]
    Manning G S. Limiting laws and counterion condensation in polyelectrolyte solutions I. colligative properties. J Chem Phys51: 924–933 (1969)CrossRefGoogle Scholar
  18. [18]
    Saito M. Molecular dynamics simulations of proteins in water without the truncation of long-range coulomb interactions. Mol Simulation8: 321–333 (1992)CrossRefGoogle Scholar
  19. [19]
    Pincus P. Colloid stabilization with grafted polyelectrolytes. Macromolecules24: 2912–2919 (1991)CrossRefGoogle Scholar
  20. [20]
    Tran Y, Auroy P, Lee L-T. Determination of the structure of polyelectrolyte brushes. Macromolecules32: 8952–8964 (1999)CrossRefGoogle Scholar
  21. [21]
    Hidetsugu Seki, Suzuki Y Y, Orland H. Self-consistent field study of polyelectrolyte brushes. J Phys Soc Jpn76: 10461 (2007)Google Scholar
  22. [22]
    Zhulina E B, Borisov O V, Birshtein T M. Structure of grafted polyelectrolyte layer. J Phys II France2: 63–74 (1992)CrossRefGoogle Scholar
  23. [23]
    Ho Y-F, Shendruk T N, Slater G W, Hsiao P-Yi. Structure of polyelectrolyte brushes subject to normal electric fields. Langmuir29: 2359–2370 (2013)CrossRefGoogle Scholar
  24. [24]
    Oosawa F. Polyelectrolytes, Chapter 5. New York: CPC Press, 1971.Google Scholar
  25. [25]
    Güven N. The crystal structures of 2M1 phengite and 2M1 muscovite. Z Kristallogr134: 196–212 (1971)Google Scholar
  26. [26]
    Wang X, Liu G, Zhang G. Conformational behavior of grafted weak polyelectrolyte chains: Effects of counterion condensation and nonelectrostatic anion adsorption. Langmuir27(16): 9895–9901 (2011)CrossRefGoogle Scholar
  27. [27]
    Washizu H, Kikuchi K. Electrical polarizability of polyelectrolytes in salt-free aqueous solution. J Phys Chem B106(43): 11329–11342 (2002)CrossRefGoogle Scholar
  28. [28]
    Guo L-Y, Zhao Y-P. Effect of chain length of self-assembled monolayers on adhesion force measurement by AFM. J Adhes Sci Technol20: 1281–1293 (2006)CrossRefGoogle Scholar
  29. [29]
    Klein J. Hydration lubrication. Friction1(1): 1–23 (2013)CrossRefGoogle Scholar
  30. [30]
    Kinjo T, Yoshida H, Washizu H. Coarse-grained particle model for polar solvent. J Phys Soc Jpn Suppl, in press.Google Scholar
  31. [31]
    Yoshida H, Kinjo T, Washizu H. Coupled lattice Boltzmann method for simulating electrokinetic flows in microchannels. In Proceedings of the 3rd European Conference on Microfluidics, 2012.Google Scholar

Copyright information

© The author(s) 2014

This article is published under license to BioMed Central Ltd. Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited

Authors and Affiliations

  • Hitoshi Washizu
    • 1
    • 2
  • Tomoyuki Kinjo
    • 1
    • 2
  • Hiroaki Yoshida
    • 1
    • 2
  1. 1.Toyota Central R&D Labs., Inc.AichiJapan
  2. 2.Elements Strategy Initiative for Catalysts and BatteriesKyoto UniversityKatsura, KyotoJapan

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