pp 1–8 | Cite as

Friction of two-dimensional colloidal particles with magnetic dipole and Lennard–Jones interactions: A numerical study

  • Zhongying Zhang
  • Cange Wu
  • Qi Zhang
  • Yigang CaoEmail author
Open Access
Research Article


We use Langevin simulations to study the sliding friction of two-dimensional colloidal particles on a substrate with randomly distributed point-like pinning centers. The colloidal particles are modeled to interact with each other through repulsive magnetic dipole and attractive Lennard–Jones potentials. The subsequent occurrence of superlubricity, wherein the average friction force equals to zero, is accompanied by the appearance of islands with clear boundaries in the microscopic colloidal structures for weak pinning substrates. Friction arises for strong pinning substrates, and the average friction force increases with the substrate pinning intensity, and further, the islands disperse into disordered plastic structures. Moreover, the average friction force decreases with the repulsion intensity between the colloidal particles, and superlubricity finally results when the repulsion becomes sufficiently strong. Superlubricity also occurs for sufficiently weak attraction between colloidal particles, with an increase in the attraction intensity between colloidal particles leading to a nonlinear increase in the average friction force. With increasing temperature, the average friction force firstly increases and subsequently decreases rapidly. The above results can provide a theoretical framework for biological self-organization via utilization of the friction properties of microscopic or mesoscopic colloidal systems.


friction sliding friction superlubricity self-assembly 



This work was supported by the Postgraduate Education Reform Project of Henan Province under Grant No. 2017SJGLX011Y and Postgraduate Education Research Project of Zhengzhou University under Grant No. YJSJY201758 as well as University Students’ Innovative Entrepreneurial Project under Grant No. 2017cxcy20.


  1. [1]
    Vanossi A, Manini N, Urbakh M, Zapperi S, Tosatti E. Colloquium: Modeling friction: From nanoscale to mesoscale. Rev Mod Phys 85(2): 529–548 (2013)CrossRefGoogle Scholar
  2. [2]
    Persson B N J. Sliding Friction, Physical Principles and Applications. Berlin: Springer, 2000CrossRefzbMATHGoogle Scholar
  3. [3]
    Urbakh M, Meyer E. The renaissance of friction. Nat Mater 9(1): 8–10 (2010)CrossRefGoogle Scholar
  4. [4]
    Löwen H. Colloidal soft matter under external control. J Phys: Condens Matter 13(24): R415–R432 (2001)Google Scholar
  5. [5]
    Löwen H, Messina R, Hoffmann N, Likos C N, Eisenmann C, Keim P, Gasser U, Maret G, Goldberg R, Palberg T. Colloidal layers in magnetic fields and under shear flow. J Phys: Condens Matter 17(45): S3379 (2005)Google Scholar
  6. [6]
    Köppl M, Henseler P, Erbe A, Nielaba P, Leiderer P. Layer reduction in driven 2D-colloidal systems through microchannels. Phys Rev Lett 97(20): 208302 (2006)CrossRefGoogle Scholar
  7. [7]
    Ebert F, Keim P, Maret G. Local crystalline order in a 2D colloidal glass former. Eur Phys J E 26(1–2): 161–168 (2008)CrossRefGoogle Scholar
  8. [8]
    Ebert F, Maret G, Keim P. Partial clustering prevents global crystallization in a binary 2D colloidal glass former. Eur Phys J E 29(3): 311–318 (2009)CrossRefGoogle Scholar
  9. [9]
    Ebert F, Dillmann P, Maret G, Keim P. The experimental realization of a two-dimensional colloidal model system. Rev Sci Instrum 80(8): 083902 (2009)CrossRefGoogle Scholar
  10. [10]
    Löwen H. Colloidal dispersions in external fields: recent developments. J Phys: Condens Matter 20(40): 404201 (2008)Google Scholar
  11. [11]
    Cao Y G, Li Q X. Dynamics of magnetized colloids on a disordered substrate. Physica A 387(19–20): 4755–4759 (2008)CrossRefGoogle Scholar
  12. [12]
    Cao Y G, Li Q X, Fu G Y, Liu J, Hu X, Li X J. Depinning dynamics of two-dimensional magnetized colloids on a random substrate. J Phys: Condens Matter 22(15): 155101 (2010)Google Scholar
  13. [13]
    Cao Y G, Zhang Z F, Zhao M F, Fu G Y, Ouyang D X. Depinning dynamics of two-dimensional magnetized colloids on a substrate with periodic pinning centers. Physica A 391(10): 2940–2947 (2012)CrossRefGoogle Scholar
  14. [14]
    Ramaswamy S. The mechanics and statistics of active matter. Annu Rev Condens Matter Phys 1(15):323–345 (2010)CrossRefGoogle Scholar
  15. [15]
    Zhao H J, Misko V R, Peeters F M. Dynamics of self-organized driven particles with competing range interaction. Phys Rev E 88(2): 022914 (2013)CrossRefGoogle Scholar
  16. [16]
    Palacci J, Sacanna S, Steinberg A P, Pine D J, Chaikin P M. Living crystals of light-activated colloidal surfers. Science 339(6122): 936–940 (2013)CrossRefGoogle Scholar
  17. [17]
    Zhang T H, Kuipers B W M, Tian W D, Groenewold J, Kegel W K. Polydispersity and gelation in concentrated colloids with competing interactions. Soft Matter 11(2): 297–302 (2015)CrossRefGoogle Scholar
  18. [18]
    Bechinger C, Leonardo R D, Löwen H, Reichhardt C, Volpe G. Active particles in complex and crowded environments. Rev Mod Phys 88(4):045006 (2016)MathSciNetCrossRefGoogle Scholar
  19. [19]
    Reichhardt C, Reichhardt C J O. Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review. Rep Prog Phys 80(2): 026501 (2017)CrossRefGoogle Scholar
  20. [20]
    Cao T T, Li Z, Lv W L, Cao Y G. Living islands of driven two-dimensional magnetic colloids on the disordered substrate. J Phys Commun 1(4): 045008 (2017)CrossRefGoogle Scholar
  21. [21]
    Li F, Josephson D P, Stein A. Colloidal assembly: The road from particles to colloidal molecules and crystals. Angew Chem Int Ed 50(2): 360–388 (2011)CrossRefGoogle Scholar
  22. [22]
    Charbonneau P, Reichman D R. Phase behavior and far-from-equilibrium gelation in charged attractive colloids. Phys Rev E 75(5): 050401 (2007)CrossRefGoogle Scholar
  23. [23]
    Theurkauff I, Cottin-Bizonne C, Palacci J, Ybert C, Bocquet L. Dynamic clustering in active colloidal suspensions with chemical signaling. Phys Rev Lett 108(26): 268303 (2012)CrossRefGoogle Scholar
  24. [24]
    Mognetti B M, Saric A, Angioletti-Uberti S, Cacciuto A, Valeriani C, Frenkel D. Living clusters and crystals from low-density suspensions of active colloids. Phys Rev Lett 111(24): 245702 (2013)CrossRefGoogle Scholar
  25. [25]
    Redner G S, Baskaran A, Hagan M F. Reentrant phase behavior in active colloids with attraction. Phys Rev E 88(1): 012305 (2013)CrossRefGoogle Scholar
  26. [26]
    Benassi A, Vanossi A, Santoro G E, Tosatti E. Sliding over a phase transition. Phys Rev Lett 106(25): 256102 (2011)CrossRefGoogle Scholar
  27. [27]
    Steiner P, Roth R, Gnecco E, Baratoff A, Maier S, Glatzel T, Meyer E. Two-dimensional simulation of superlubricity on NaCl and highly oriented pyrolytic graphite. Phys Rev B 79(4): 045414 (2009)CrossRefGoogle Scholar
  28. [28]
    Li X D, Wu C G, Cao T T, Cao Y G. Directional mode-locking of driven two-dimensional active magnetized colloids with periodic pinning centers. Physica A 515(2): 279–287 (2019)MathSciNetCrossRefGoogle Scholar
  29. [29]
    Song K N, Wang H L, Ren J, Cao Y G. Interference mode-locking of 2D magnetized colloids driven by dc and ac forces in periodic pinning arrays. Physica A 417(1): 102–109 (2015)CrossRefGoogle Scholar
  30. [30]
    Fisher D S. Flux-lattice melting in thin-film superconductors. Phys Rev B 22(3): 1190–1199 (1980)CrossRefGoogle Scholar

Copyright information

© The author(s) 2019

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

Authors and Affiliations

  • Zhongying Zhang
    • 1
  • Cange Wu
    • 1
  • Qi Zhang
    • 1
  • Yigang Cao
    • 1
    Email author
  1. 1.School of Physics and EngineeringZhengzhou UniversityZhengzhouChina

Personalised recommendations