Skip to main content
SpringerLink
Log in

Mean-Field Theory of the Electrical Double Layer in Ionic Liquids

  • Reference work entry
  • First Online:
Encyclopedia of Ionic Liquids

Introduction

Ionic liquids (ILs) are superconcentrated electrolytes of great interest in energy storage devices. The lack of electrolysable solvents, since ILs are solely composed of cations and anions, means the voltages that ILs can withstand (∼3 V) are roughly twice that of conventional aqueous electrolytes [1]. As the energy stored increases with the voltage, ILs are promising candidates as electrolytes for electrical double layer supercapacitors.

In such a capacitor, electrodes are in contact with an electrolyte. The ions in the electrolyte redistribute such that they reside in energetically favorable electrostatic environments, forming a layer rich in countercharges that screens the electrostatic fields arising from the charged electrodes. This structure is commonly referred to as the electrical double layer (EDL). The work done separating charges in the EDL is stored as energy in EDL capacitors.

The intensive study of EDL capacitors with ILs has burgeoned theories for the EDL....

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 799.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 999.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Fedorov MV, Kornyshev AA (2014) Ionic liquids at electrified interfaces. Chem Rev 114:2978–3036

    Article  CAS  Google Scholar 

  2. Bazant MZ, Kilic MS, Storey BD, Ajdari A (2009) Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions. Adv Colloid Interf Sci 152(1–2):48–88

    Article  CAS  Google Scholar 

  3. Bazant MZ, Thornton K, Ajdari A (2004) Diffuse-charge dynamics in electrochemical systems. Phys Rev E 70:021506

    Article  Google Scholar 

  4. Weingärtner H (2008) Understanding ionic liquids at the molecular level: facts, problems, and controversies. Angew Chem Int Ed 47:654–670

    Article  Google Scholar 

  5. Fedorov MV, Kornyshev AA (2008) Towards understanding the structure and capacitance of electrical double layer in ionic liquids. Electrochim Acta 53:6835–6840

    Article  CAS  Google Scholar 

  6. Fedorov MV, Kornyshev AA (2008) Ionic liquid near a charged wall: structure and capacitance of electrical double layer. J Phys Chem B 112:11868–11872

    Article  CAS  Google Scholar 

  7. Bazant MZ, Storey BD, Kornyshev AA (2011) Double layer in ionic liquids: Overscreening versus crowding. Phys Rev Lett 109:046102

    Article  Google Scholar 

  8. Kornyshev AA (2007) Double-layer in ionic liquids: paradigm change? J Phys Chem B 111:5545–5557

    Article  CAS  Google Scholar 

  9. Pedro de Souza J, Goodwin ZAH, McEldrew M, Kornyshev AA, Bazant MZ (2020) Interfacial layering in the electrical double layer of ionic liquids. Phys Rev Lett 125:116001

    Article  Google Scholar 

  10. Fedorov MV, Georgi N, Kornyshev AA (2010) Double layer in ionic liquids: the nature of the camel shape of capacitance. Electrochem Commun 12:296–299

    Article  CAS  Google Scholar 

  11. Kilic MS, Bazant MZ, Ajdari A (2007) Steric effects in the dynamics of electrolytes at large applied voltages. i. double-layer charging. Phys Rev E 75:021502

    Article  Google Scholar 

  12. Bikerman JJ (1942) Structure and capacity of electrical double layer. Philos Mag 33:384–397

    Article  CAS  Google Scholar 

  13. Borukhov T, Andelman D, Orland H (1997) Steric effects in electrolytes: a modified poisson-boltzmann equation. Phys Rev Lett 79:435

    Article  CAS  Google Scholar 

  14. Freise V (1952) Theorie der diffusen doppelschicht (theory of the diffuse double layer). Z Elektrochem 56:822–827

    CAS  Google Scholar 

  15. Goodwin ZAH, Feng G, Kornyshev AA (2017) Mean-field theory of electrical double layer in ionic liquids with account of short-range correlations. Electrochim Acta 225:190–196

    Article  CAS  Google Scholar 

  16. Leote de Carvalho RJF, Evans R (1994) The decay of correlations in ionic fluids. Mol Phys 83:619–654

    Article  Google Scholar 

  17. Friedl J, Markovits IIE, Herpich M, Feng G, Kornyshev AA, Stimming U (2017) Interface between an au(111) surface and an ionic liquid: the influence of water on the double-layer capacitance. ChemElectroChem 4:216–220

    Article  CAS  Google Scholar 

  18. Fawcett WR, Ryan PJ (2010) An improved version of the kornyshev-eigen-wicke model for the di_use double layer in concentrated electrolytes. Phys Chem Chem Phys 12:9816–9821

    Article  CAS  Google Scholar 

  19. Han Y, Huang S, Yan T (2014) A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes. J Phys Condens Matter 26:284103

    Article  Google Scholar 

  20. Gongadze E, Iglič A (2015) Asymmetric size of ions and orientational ordering of water dipoles in electric double layer model – an analytical mean-field approach. Electrochim Acta 178:541–545

    Article  CAS  Google Scholar 

  21. Maggs AC, Podgornik R (2016) General theory of asymmetric steric interactions in electrostatic double layers. Soft Mater 12:1219–1229

    Article  CAS  Google Scholar 

  22. Popović M, Šiber A (2013) Lattice-gas poisson-boltzmann approach for sterically asymmetric electrolytes. Phys Rev E 88:022302

    Article  Google Scholar 

  23. Yin L, Huang Y, Chen H, Yan T (2018) A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes. ii. accounts of ionic interactions. Phys Chem Chem Phys 20:17606–17614

    Article  CAS  Google Scholar 

  24. Pedro de Souza J, Bazant MZ (2020) Continuum theory of electrostatic correlations at charged surfaces. J Phys Chem C 124:11414–11421

    Article  Google Scholar 

  25. Gavish N, Yochelis A (2016) Theory of phase separation and polarization for pure ionic liquids. J Phys Chem Lett 7:1121–1126

    Article  CAS  Google Scholar 

  26. Limmer DT (2015) Interfacial ordering and accompanying divergent capacitance at ionic liquid-metal interfaces. Phys Rev Lett 115:256102

    Article  Google Scholar 

  27. Roth R (2010) Fundamental measure theory for hard-sphere mixtures: a review. J Phys Condens Matter 22(6):063102

    Article  Google Scholar 

  28. Härtel A (2017) Structure of electric double layers in capacitive systems and to what extent (classical) density functional theory describes it. J Phys Condes Matter 29:423002

    Article  Google Scholar 

  29. Wu J, Jiang T, Jiang D, Jin Z, Henderson D (2011) A classical density functional theory for interfacial layering of ionic liquids. Soft Matter 7(23):11222–11231

    Article  CAS  Google Scholar 

  30. Härtel A, Samin S, van Roij R (2016) Dense ionic fluids confined in planar capacitors: in- and out-of-plane structure from classical density functional theory. J Phys Condes Matter 28:244007

    Article  Google Scholar 

  31. Li H-K, de Souza JP, Zhang Z, Martis J, Sendgikoski K, Cumings J, Bazant MZ, Majumdar A (2020) Imaging arrangements of discrete ions at liquid–solid interfaces. Nano Lett 20:7927–7932

    Article  CAS  Google Scholar 

  32. Adar RM, Safran SA, Diamant H, Andelman D (2019) Screening length for finite-size ions in concentrated electrolytes. Phys Rev E 100(4):042615

    Article  CAS  Google Scholar 

  33. Lauw Y, Horne MD, Rodopoulos T, Leermakers FAM (2009) Room-temperature ionic liquids: excluded volume and ion polarizability effects in the electrical double-layer structure and capacitance. Phys Rev Lett 103:117801

    Article  CAS  Google Scholar 

  34. Forsman J, Woodward CE, Trulsson M (2011) A classical density functional theory of ionic liquids. J Phys Chem B 115:4606–4612

    Article  CAS  Google Scholar 

  35. McEldrew M, Goodwin ZAH, Kornyshev AA, Bazant MZ (2018) Theory of the double layer in water-in-salt electrolytes. J Phys Chem Lett 9:5840–5846

    Article  CAS  Google Scholar 

  36. Budkov YA, Kolesnikov AL, Goodwin ZAH, Kiselev MG, Kornyshev AA (2018) Theory of electrosorption of water from ionic liquids. Electrochim Acta 284:346–354

    Article  CAS  Google Scholar 

  37. Feng G, Jiang X, Qiao R, Kornyshev AA (2014) Water in ionic liquids at electrified interfaces: the anatomy of electrosorption. ACS Nano 8:11685–11694

    Article  CAS  Google Scholar 

  38. Bi S, Wang R, Liu S, Yan J, Mao B, Kornyshev AA, Feng G (2018) Minimizing the electrosorption of water from humid ionic liquids on electrodes. Nature Comm 9:5222

    Article  Google Scholar 

  39. Budkov YA, Kolesnikov AL, Kiselev MG (2016) On the theory of electric double layer with explicit account of a polarizable co-solvent. J Chem Phys 114:184703

    Article  Google Scholar 

  40. Smith AM, Lee AA, Perkin S (2016) The electrostatic screening length in concentrated electrolytes increases with concentration. J Phys Chem Lett 7:2157–2163

    Article  CAS  Google Scholar 

  41. Gebbie MA, Valtiner M, Banquy X, Fox ET, Henderson WA, Israelachvili JN (2013) Ionic liquids behave as dilute electrolyte solutions. PNAS 110:9674–9679

    Article  CAS  Google Scholar 

  42. Lee AA, Perez-Martinez CS, Smith AM, Perkin S (2017) Underscreening in concentrated electrolytes. Faraday Discuss 199:239–259

    Article  CAS  Google Scholar 

  43. Ma K, Forsman J, Woodward CE (2015) Influence of ion pairing in ionic liquids on electrical double layer structures and surface force using classical density functional approach. J Chem Phys 142:174704

    Article  Google Scholar 

  44. Lee AA, Vella D, Perkin S, Goriely A (2015) Are room-temperature ionic liquids dilute electrolytes? J Phys Chem Lett 6:159–163

    Article  CAS  Google Scholar 

  45. Chen M, Goodwin ZAH, Feng G, Kornyshev AA (2018) On the temperature dependence of the double layer capacitance of ionic liquids. J Electroanal Chem 819:347–358

    Article  CAS  Google Scholar 

  46. Feng G, Chen M, Bi S, Goodwin ZAH, Postnikov EB, Brilliantov N, Urbakh M, Kornyshev AA (2019) Free and bound states of ions in ionic liquids, conductivity, and underscreening paradox. Phys Rev X 9:021024

    CAS  Google Scholar 

  47. Kirchner B, Malberg F, Firaha DS, Hollóczki O (2015) Ion pairing in ionic liquids. J Phys Condens Matter 27:463002

    Article  Google Scholar 

  48. Del Pópolo MG, Voth GA (2004) On the structure and dynamics of ionic liquids. J Phys Chem B 108:1744–1752

    Article  Google Scholar 

  49. Damaskin BB, Frumkin AN (1974) Potentials of zero charge, interaction of metals with water and adsorption of organic substances—iii. the role of the water dipoles in the structure of the dense part of the electric double layer. Electrochim Acta 19:173–176

    Article  CAS  Google Scholar 

  50. Zhang Y, Ye T, Chen M, Goodwin ZAH, Feng G, Huang J, Kornyshev AA (2020) Enforced freedom: electric-field-induced declustering of ionic-liquid ions in the electrical double layer. Energy Environ Mater 3:414–420

    Article  CAS  Google Scholar 

  51. Avni Y, Adar RM, Andelman D (2020) Charge oscillations in ionic liquids: a microscopic cluster model. Phys Rev E 101(1):010601

    Article  CAS  Google Scholar 

  52. McEldrew M, Goodwin ZAH, Bi S, Bazant MZ, Kornyshev AA (2020) Theory of ion aggregation and gelation in super-concentrated electrolytes. J Chem Phys 152:234506

    Article  CAS  Google Scholar 

  53. Blum L, Rosenfeld Y (1991) Relation between the free energy and the direct correlation function in the mean spherical approximation. J Stat Phys 63(5):1177–1190

    Google Scholar 

  54. May S, Iglic A, Reščič J, Maset S, Bohinc K (2008) Bridging like-charged macroions through long divalent rodlike ions. J Phys Chem B 112(6):1685–1692

    Google Scholar 

  55. Wang ZG (2010) Fluctuation in electrolyte solutions: the self energy. Phys Rev E 81(2):021501

    Google Scholar 

  56. Frydel D, Levin Y (2013) The double-layer of penetrable ions: an alternative route to charge reversal. J Chem Phys 138(17):17490

    Google Scholar 

  57. Frydel D (2016) The double-layer structure of overscreened surfaces by smeared-out ions. J Chem Phys 145(18):184703

    Google Scholar 

  58. Roth R, Gillespie D (2016) Shells of charge: a density functional theory for charged hard spheres. J Phys Condens Matt 28(24):244006

    Google Scholar 

  59. Jiang J, Gillespie D (2021) Revisiting the charged shell model: a density functional theory for electrolytes. J Chem Theory Comput 17(4):2409–2416

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, Imperial College of London, Molecular Science Research Hub, London, UK

    Zachary A. H. Goodwin & Alexei A. Kornyshev

  2. Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    J. Pedro de Souza & Martin Z. Bazant

  3. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Martin Z. Bazant

  4. Institute of Molecular Science and Engineering, Imperial College of London, London, UK

    Alexei A. Kornyshev

Authors
  1. Zachary A. H. Goodwin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Pedro de Souza
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Martin Z. Bazant
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alexei A. Kornyshev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexei A. Kornyshev .

Editor information

Editors and Affiliations

  1. Institute of Process Engineering, Chinese Academy of Sciences, Beijing, China

    Suojiang Zhang

  2. Henan University, Zhengzhou, China

    Suojiang Zhang

Section Editor information

  1. Huazhong University of Science and Technology (HUST), Wuhan, China

    Guang Feng

  2. Chemical and Biomolecular Engineering, Vanderbilt University, Nashville, USA

    Peter T. Cummings

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Singapore Pte Ltd.

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Goodwin, Z.A.H., de Souza, J.P., Bazant, M.Z., Kornyshev, A.A. (2022). Mean-Field Theory of the Electrical Double Layer in Ionic Liquids. In: Zhang, S. (eds) Encyclopedia of Ionic Liquids. Springer, Singapore. https://doi.org/10.1007/978-981-33-4221-7_62

Download citation

Publish with us

Policies and ethics

Search

Navigation