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  • Letter
  • Open Access

Absorbing states govern the charging of vibrated grains

Michael R. Swift and Mike I. Smith*

  • *Contact author: mike.i.smith@nottingham.ac.uk
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Phys. Rev. E 114, L033402 – Published 29 September, 2026

DOI: https://doi.org/10.1103/37yf-n6f7

Abstract

The electrostatic charging of insulators is notoriously irreproducible. Using experiments and simulations we study the charging of a single bouncing ball on a vibrating surface. We show that a ball's final charge results from a coupling between its chaotic dynamics and its evolving charge distribution. This results in a permanent charge dipole which traps the particle in an “orientational absorbing state” preventing further charging. The variability of each particle's final charge is a direct consequence of this dynamical coupling.

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References (38)

  1. V. Lee, S. Waitukaitis, M. Miskin, and H. Jaeger, Direct observation of particle interactions and clustering in charged granular streams, Nat. Phys. 11, 733 (2015).
  2. T. Steinpilz, K. Joeris, F. Jungmann, D. Wolf, L. Brendel, J. Teiser, T. Shinbrot, and G. Wurm, Electrical charging overcomes the bouncing barrier in planet formation, Nat. Phys. 16, 225 (2020).
  3. T. Burgo, T. Ducati, K. Francisco, K. Clinckspoor, F. Galembeck, and S. Galembeck, Triboelectricity: Macroscopic charge patterns formed by self-arraying ions on polymer surfaces, Langmuir 28, 7407 (2012).
  4. K. Sayfidinov, S. Cezan, B. Baytekin, and H. Baytekin, Minimizing friction, wear and energy losses by eliminating contact charging, Sci. Adv. 4, eaau3808 (2018).
  5. F. Jungmann, T. Steinpilz, J. Teiser, and G. Wurm, Sticking and restitution in collisions of charged sub-mm dielectric grains, J. Phys. Commun. 2, 095009 (2018).
  6. T. Pähtz, H. Hermann, and T. Shinbrot, Why do particle clouds generate electric charges? Nat. Phys. 6, 364 (2010).
  7. J. S. M. Harper, G. McDonald, J. Dufek, M. Malaska, D. Burr, A. Hayes, J. McAdams, and J. Wray, Electrification of sand on titan and its influence on sediment transport, Nat. Geosci. 10, 260 (2017).
  8. Y. Pu, M. Mazumder, and C. Cooney, Effects of electrostatic charging on pharmaceutical powder blending homogeneity, J. Pharm. Sci. 98, 2412 (2009).
  9. A. Mehrotra, F. J. Muzzo, and T. Shinbrot, Spontaneous separation of charged grains, Phys. Rev. Lett. 99, 058001 (2007).
  10. M. Maammar, T. Zeghoul, W. Aksa, S. Touhami, I. Achouri, and L. Dascalescu, Factors that influence the trajectories of charged insulating particles in roll-type electrostatic separators, J. Electrost. 115, 103672 (2022).
  11. H. Baytekin, B. Baytekin, J. Incorvati, and B. Gryzbowski, Material transfer and polarity reversal in contact charging, Angew. Chem. 124, 4927 (2012).
  12. S. R. Waitukaitis, V. Lee, J. M. Pierson, S. L. Forman, and H. M. Jaeger, Size-dependent same-material tribocharging in insulating grains, Phys. Rev. Lett. 112, 218001 (2014).
  13. D. Liu, L. Zhou, S. Cui, Y. Gao, S. Li, Z. Zhao, Z. Yi, H. Zou, Y. Fan, J. Wang, and Z. Wang, Standardized measurement of dielectric materials' intrinsic triboelectric charge density through the suppression of air breakdown, Nat. Commun. 13, 6019 (2022).
  14. D. Lacks and T. Shinbrot, Long-standing and unresolved issues in triboelectric charging, Nat. Rev. Chem. 3, 465 (2019).
  15. F. Paschen, Über die zum funkenübergang in luft, wasserstoff und kohlensäure bei verschiedenen drucken erforderliche potentialdifferenz, Ann. Phys. 273, 69 (1889).
  16. F. W. Peek, The law of corona and the dielectric strength of air, in Proceedings of the American Institute of Electrical Engineers (IEEE, New York, 1911), Vol. 30, pp. 1485–1561.
  17. R. Arora and W. Mosch, High Voltage and Electrical Insulation Engineering (Wiley & Sons, New York, 2011).
  18. M. Matsuyama and H. Yamamoto, Charge relaxation process dominates contact charging of a particle in atmospheric conditions, J. Phys. D: Appl. Phys. 28, 2418 (1995).
  19. M. Apodaca, P. Wesson, K. Bishop, M. Ratner, and B. Grzybowski, Contact electrification between identical materials, Angew. Chem. Int. Ed. 49, 946 (2010).
  20. R. Cruise, S. Starr, K. Hadler, and J. Cilliers, Triboelectric charge saturation on single and multiple insulating particles in air and vacuum, Sci. Rep. 13, 15178 (2023).
  21. Y. Sobolev, W. Adamkiewicz, M. Siek, and B. Grzybowski, Charge mosaics on contact-electrified dielectrics result from polarity-inverting discharges, Nat. Phys. 18, 1347 (2022).
  22. F. Chowdhury, M. Ray, A. Sowinski, P. Mehrani, and A. Passalacqua, Charge relaxation process dominates contact charging of a particle in atmospheric conditions, Powder Technol. 389, 104 (2021).
  23. T. Matsuyama, M. Ogu, H. Yamamoto, J. Marijnessen, and B. Scarlett, Impact charging experiments with single particles of hundred micrometer size, Powder Technol. 135–136, 14 (2003).
  24. H. Grosshans and M. Papalexandris, A model for non-uniform contact charging of particles, Powder Technol. 305, 518 (2017).
  25. D. Hays, Toner adhesion, J. Adhesion 51, 41 (1995).
  26. M. Swift and M. Smith, Torque about electrostatically charged particles makes them more attractive, Soft Matter 20, 7038 (2024).
  27. R. Yoshimatsu, N. Araújo, G. Wurm, H. Hermann, and T. Shinbrot, Self-charging of identical grains in the absence of an external field, Sci. Rep. 7, 39996 (2017).
  28. G. Grosjean and S. Waitukaitis, Single-collision statistics reveal a global mechanism driven by sample history for contact electrification in granular media, Phys. Rev. Lett. 130, 098202 (2023).
  29. J. Lowke and F. Alessandro, Onset corona fields and electrical breakdown criteria, J. Phys. D: Appl. Phys. 36, 2673 (2003).
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/37yf-n6f7 for additional experimental details and simulation parameters, which includes Refs. [37, 38].
  31. R. Färber, Y. Lu, M. Balmelli, O. Sefl, and C. Franck, Static breakdown threshold modeling of quasi-uniform gas gaps with a focus on the PDIV of contacting enameled wire pairs, J. Phys. D: Appl. Phys. 56, 435204 (2023).
  32. B. Techaumnat and T. Takuma, Analysis of the electrostatic force on a dielectric particle with partial charge distribution, J. Electrost. 67, 686 (2009).
  33. J. Jackson, Classical Electrodynamics, 3rd ed. (Wiley & Sons, New York, 1999).
  34. Y. Zhang, T. Pähtz, Y. Liu, X. Wang, R. Zhang, Y. Shen, R. Ji, and B. Cai, Electric field and humidity trigger contact electrification, Phys. Rev. X 5, 011002 (2015).
  35. H. Hinrichsen, Non-equilibrium critical phenomena and phase transitions into absorbing states, Adv. Phys. 49, 815 (2000).
  36. J. Teiser, J. Penner, K. Joeris, F. Onyeagusi, J. Kollmer, D. Daab, and G. Wurm, The growth of super-large pre-planetary pebbles to an impact erosion limit, Nat. Astron. 9, 535 (2025).
  37. J. Townsend, The Theory of Ionization of Gases by Collision (London, Constable & Co., London, UK, 1910).
  38. H. Herrmann and S. Luding, Modeling granular media on the computer, Continuum Mech. Thermodyn. 10, 189 (1998).

Outline

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Phys. Rev. E 114, L033402– Published 29 September, 2026
  • Received 24 March 2026
  • Accepted 8 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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