Skip to main content

Structure of polyelectrolyte brushes studied by coarse grain simulations

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.

References

  1. [1]

    Washizu H, Ohmori T. Molecular dynamics simulations of elastohydrodynamic lubrication oil film. Lubr Sci22(8): 323–340 (2010)

    Article  Google 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)

    Article  Google 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)

    Article  Google Scholar 

  4. [4]

    Kajita S, Washizu H, Ohmori T. Deep bulk atoms in a solid cause friction. Europhys Lett87(6): 66002 (2009)

    Article  Google 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)

    Article  Google 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)

    Article  Google 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)

    Article  Google 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)

    Article  Google Scholar 

  10. [10]

    Kobayashi M, Terada M, Takahara A. Polyelectrolyte brushes: A novel stable lubrication system in aqueous conditions. Faraday Discuss156: 403–412 (2012)

    Article  Google Scholar 

  11. [11]

    Washizu H, Kikuchi K. Electric polarizability of DNA in aqueous salt solution. J Phys Chem B110(6): 2855–2861 (2006)

    Article  Google 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)

    Article  Google 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)

    Article  Google 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)

    Article  Google 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)

    Article  Google 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)

    Article  Google Scholar 

  17. [17]

    Manning G S. Limiting laws and counterion condensation in polyelectrolyte solutions I. colligative properties. J Chem Phys51: 924–933 (1969)

    Article  Google 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)

    Article  Google Scholar 

  19. [19]

    Pincus P. Colloid stabilization with grafted polyelectrolytes. Macromolecules24: 2912–2919 (1991)

    Article  Google Scholar 

  20. [20]

    Tran Y, Auroy P, Lee L-T. Determination of the structure of polyelectrolyte brushes. Macromolecules32: 8952–8964 (1999)

    Article  Google 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)

    Article  Google 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)

    Article  Google 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)

    Article  Google Scholar 

  27. [27]

    Washizu H, Kikuchi K. Electrical polarizability of polyelectrolytes in salt-free aqueous solution. J Phys Chem B106(43): 11329–11342 (2002)

    Article  Google 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)

    Article  Google Scholar 

  29. [29]

    Klein J. Hydration lubrication. Friction1(1): 1–23 (2013)

    Article  Google Scholar 

  30. [30]

    Kinjo T, Yoshida H, Washizu H. Coarse-grained particle model for polar solvent. J Phys Soc Jpn Suppl, in press.

  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 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Hitoshi Washizu.

Additional information

This article is published with open access at Springerlink.com

A preliminary version of this work was presented at the 3rd International Symposium on Tribology of IFToMM, Luleå, Sweden, 2013.

Hitoshi WASHIZU. He received his M.A. and Ph. D degrees in Physical Chemistry from the University of Tokyo, Japan, in 1998 and 2001 respectively. He joined Toyota Central R&D Labs., Inc., from 2001. His current position is a leader of Washizu Research Group, Forintier Research Center of the TCRD. He is also a delegate of his research group in the Elements Strategy Initiative for Catalysts and Batteries, Kyoto University. His research areas cover computational chemistry of surfaces in tribology, polymer science, and electrochemistry.

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

Reprints and Permissions

About this article

Cite this article

Washizu, H., Kinjo, T. & Yoshida, H. Structure of polyelectrolyte brushes studied by coarse grain simulations. Friction 2, 73–81 (2014). https://doi.org/10.1007/s40544-014-0041-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40544-014-0041-7

Keywords

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