Journal of Solid State Electrochemistry

, Volume 18, Issue 5, pp 1365–1376 | Cite as

Attractive forces in microporous carbon electrodes for capacitive deionization

  • P. M. Biesheuvel
  • S. Porada
  • M. Levi
  • M. Z. Bazant
Original Paper


The recently developed modified Donnan (mD) model provides a simple and useful description of the electrical double layer in microporous carbon electrodes, suitable for incorporation in porous electrode theory. By postulating an attractive excess chemical potential for each ion in the micropores that is inversely proportional to the total ion concentration, we show that experimental data for capacitive deionization (CDI) can be accurately predicted over a wide range of applied voltages and salt concentrations. Since the ion spacing and Bjerrum length are each comparable to the micropore size (few nanometers), we postulate that the attraction results from fluctuating bare Coulomb interactions between individual ions and the metallic pore surfaces (image forces) that are not captured by mean-field theories, such as the Poisson-Boltzmann-Stern model or its mathematical limit for overlapping double layers, the Donnan model. Using reasonable estimates of the micropore permittivity and mean size (and no other fitting parameters), we propose a simple theory that predicts the attractive chemical potential inferred from experiments. As additional evidence for attractive forces, we present data for salt adsorption in uncharged microporous carbons, also predicted by the theory.


Cell Voltage Porous Electrode Activate Carbon Powder Image Force Charge Efficiency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Part of this work was performed in the cooperation framework of Wetsus, Centre of Excellence for Sustainable Water Technology ( Wetsus is co-funded by the Dutch Ministry of Economic Affairs and Ministry of Infrastructure and Environment, the European Union Regional Development Fund, the Province of Fryslân, and the Northern Netherlands Provinces. The authors like to thank the participants of the research theme Capacitive Deionization for fruitful discussions and financial support. We thank Michiel van Soestbergen for providing unpublished theoretical results used in section “Analysis of data for adsorption of salt in uncharged carbon—measuring μatt”.


  1. 1.
    Arnold BB, Murphy GW (1961) J Phys Chem 65:135–138CrossRefGoogle Scholar
  2. 2.
    Farmer JC, Fix DV, Mack GV, Pekala RW, Poco JF (1996) J Electrochem Soc 143:159–169CrossRefGoogle Scholar
  3. 3.
    Johnson AM, Newman J (1971) J Electrochem Soc 118:510–517CrossRefGoogle Scholar
  4. 4.
    Soffer A, Folman M (1972) J Electroanal Chem Interface Electrochem 38:25–43CrossRefGoogle Scholar
  5. 5.
    Suss ME, Baumann TF, Bourcier WL, Spadaccini CM, Rose KA, Santiago JG, Stadermann M (2012) Energy Environ Sci 5:9511–9519CrossRefGoogle Scholar
  6. 6.
    Rica RA, Ziano R, Salerno D, Mantegazza F, Brogioli D (2012) Phys Rev Lett 109:156103CrossRefGoogle Scholar
  7. 7.
    Porada S, Zhao R, van der Wal A, Presser V, Biesheuvel PM (2013) Prog Mater Sci 58:1388–1442CrossRefGoogle Scholar
  8. 8.
    Jeon S-I, Park H-R, Yeo J-G, Yang S, Cho CH, Han MH, Kim D-K (2013) Energy Environ Sci 6:1471–1475CrossRefGoogle Scholar
  9. 9.
    Jande YAC, Kim WS (2013) Desalination 329:29–34CrossRefGoogle Scholar
  10. 10.
    Jande YAC, Kim WS (2013) Sep Purif Technol 115:224–230CrossRefGoogle Scholar
  11. 11.
    Garcia-Quismondo E, Gomez R, Vaquero F, Cudero AL, Palma J, Anderson MA (2013) Phys Chem Chem Phys 15:7648–7656CrossRefGoogle Scholar
  12. 12.
    Wang G, Qian B, Dong Q, Yang J, Zhao Z, Qiu J (2013) Sep Purif Technol 103:216–221CrossRefGoogle Scholar
  13. 13.
    Oren Y, Soffer A (1983) J Appl Electrochem 13:473–487CrossRefGoogle Scholar
  14. 14.
    Levi MD, Salitra G, Levy N, Aurbach D, Maier J (2009) Nat Mater 8:872–875CrossRefGoogle Scholar
  15. 15.
    Avraham E, Bouhadana Y, Soffer A, Aurbach D (2009) J Electrochem Soc 156:95–99CrossRefGoogle Scholar
  16. 16.
    Zhao R, Biesheuvel PM, Miedema H, Bruning H, van der Wal A (2010) J Phys Chem Lett 1:205–210CrossRefGoogle Scholar
  17. 17.
    Levi MD, Levy N, Sigalov S, Salitra G, Aurbach D, Maier J (2010) J Am Chem Soc 132:13220–13222CrossRefGoogle Scholar
  18. 18.
    Kastening B, Heins M (2001) Phys Chem Chem Phys 3:372–373CrossRefGoogle Scholar
  19. 19.
    Han L, Karthikeyan KG, Anderson MA, Gregory K, Wouters JJ, Abdel-Wahab A (2013) Electrochim Acta 90:573–581CrossRefGoogle Scholar
  20. 20.
    Mossad M, Zou L (2013) Chem Eng J 223:704–713CrossRefGoogle Scholar
  21. 21.
    Zhao R, Biesheuvel PM, Van der Wal A (2012) Energy Environ Sci 5:9520–9527CrossRefGoogle Scholar
  22. 22.
    Wu P, Huang J, Meunier V, Sumpter BG, Qiao R (2012) J Phys Chem Lett 3:1732–1737CrossRefGoogle Scholar
  23. 23.
    Bazant MZ, Thornton K, Ajdari A (2004) Phys Rev E 70:021506Google Scholar
  24. 24.
    Biesheuvel PM, Bazant MZ (2010) Phys Rev E 81:031502Google Scholar
  25. 25.
    Zhao R, van Soestbergen M, Rijnaarts HHM, van der Wal A, Bazant MZ, Biesheuvel PM (2012) J Colloid Interface Sci 384:38–44CrossRefGoogle Scholar
  26. 26.
    Yang K-L, Ying T-Y, Yiacoumi S, Tsouris C, Vittoratos ES (2001) Langmuir 17:1961–1969CrossRefGoogle Scholar
  27. 27.
    Gabelich CJ, Tran TD, Suffet IH (2002) Environ Sci Technol 36:3010–3019CrossRefGoogle Scholar
  28. 28.
    Hou C-H, Liang C, Yiacoumi S, Dai S, Tsouris C (2006) J Colloid Interface Sci 302:54–61CrossRefGoogle Scholar
  29. 29.
    Xu P, Drewes JE, Heil D, Wang G (2008) Water Res 42:2605–2617CrossRefGoogle Scholar
  30. 30.
    Li L, Zou L, Song H, Morris G (2009) Carbon 47:775–781CrossRefGoogle Scholar
  31. 31.
    Gabelich CJ, Xu P, Cohen Y (2010) Sustain Sci Eng 2:295–326CrossRefGoogle Scholar
  32. 32.
    Tsouris C, Mayes R, Kiggans J, Sharma K, Yiacoumi S, DePaoli D, Dai S (2011) Environ Sci Technol 45:10243–10249CrossRefGoogle Scholar
  33. 33.
    Porada S, Weinstein L, Dash R, van der Wal A, Bryjak M, Gogotsi Y, Biesheuvel PM (2012) ACS Appl Mater Interfaces 4:1194–1199CrossRefGoogle Scholar
  34. 34.
    Porada S, Borchardt L, Oschatz M, Bryjak M, Atchison J, Keesman KJ, Kaskel S, Biesheuvel M, Presser V (2013) Energy Environ Sci 6:3700–3712CrossRefGoogle Scholar
  35. 35.
    Lin C, Ritter JA, Popov BN (1999) J Electrochem Soc 146:3639–3643CrossRefGoogle Scholar
  36. 36.
    Kim T, Yoon J (2013) J Electroanal Chem 704:169–174CrossRefGoogle Scholar
  37. 37.
    Sharma K, Mayes RT, Kiggans JO Jr, Yiacoumi S, Gabitto J, DePaoli DW, Dai S, Tsouris C (2013) Sep Purif Technol 116:206–213CrossRefGoogle Scholar
  38. 38.
    Biesheuvel PM, Zhao R, Porada S, van der Wal A (2011) J Colloid Interface Sci 360:239–248CrossRefGoogle Scholar
  39. 39.
    Porada S, Bryjak M, van der Wal A, Biesheuvel PM (2012) Electrochim Acta 75:148–156CrossRefGoogle Scholar
  40. 40.
    Rica RA, Brogioli D, Ziano R, Salerno D, Mantegazza F (2012) J Phys Chem C 116:16934–16938CrossRefGoogle Scholar
  41. 41.
    Porada S, Sales BB, Hamelers HVM, Biesheuvel PM (2012) J Phys Chem Lett 3:1613–1618CrossRefGoogle Scholar
  42. 42.
    Andersen MB, van Soestbergen M, Mani A, Bruus H, Biesheuvel PM, Bazant MZ (2012) Phys Rev Lett 109:108301CrossRefGoogle Scholar
  43. 43.
    Galama AH, Post JW, Cohen Stuart MA, Biesheuvel PM (2013) J Membr Sci 442:131–139CrossRefGoogle Scholar
  44. 44.
    Biesheuvel PM, de Vos WM, Amoskov VM (2008) Macromolecules 41:6254–6259CrossRefGoogle Scholar
  45. 45.
    de Vos WM, Biesheuvel PM, de Keizer A, Kleijn JM, Cohen Stuart MA (2009) Langmuir 25:9252–9261CrossRefGoogle Scholar
  46. 46.
    Biesheuvel PM (2004) J Phys Condens Matter 16:L499–L504CrossRefGoogle Scholar
  47. 47.
    Spruijt E, Biesheuvel PM (2014) J Phys Condens Matter 26:075101Google Scholar
  48. 48.
    Huang J, Qiao R, Feng G, Sumpter BG, Meunier V (2013) Modern Theories of Carbon-Based Electrochemical Capacitors, in Supercapacitors. Wiley, New York, pp 167–206Google Scholar
  49. 49.
    Garten VA, Weiss DE (1955) Aust J Chem 8:68–95CrossRefGoogle Scholar
  50. 50.
    Garten VA, Weiss DE (1957) Rev Pure Appl Chem 7:69–122Google Scholar
  51. 51.
    Attard P, Mitchell DJ, Ninham BW (1988) J Chem Phys 89:4358–4367CrossRefGoogle Scholar
  52. 52.
    Skinner B, Loth MS, Shklovskii BI (2010) Phys Rev Lett 104:128302CrossRefGoogle Scholar
  53. 53.
    Biesheuvel PM, Fu YQ, Bazant MZ (2011) Phys Rev E 83:061507Google Scholar
  54. 54.
    Biesheuvel PM, Fu Y, Bazant MZ (2012) Russ J Electrochem 48:580–592CrossRefGoogle Scholar
  55. 55.
    Rica RA, Ziano R, Salerno D, Mantegazza F, Bazant MZ, Brogioli D (2013) Electrochim Acta 92:304–314CrossRefGoogle Scholar
  56. 56.
    Hou C-H, Patricia T-S, Yiacoumi S, Tsouris C (2008) J Chem Phys 129:224703–224709CrossRefGoogle Scholar
  57. 57.
    Feng G, Qiao R, Huang J, Sumpter BG, Meunier V (2010) ACS Nano 4:2382–2390CrossRefGoogle Scholar
  58. 58.
    Bonthuis DJ, Gekle S, Netz RR (2011) Phys Rev Lett 107:166102CrossRefGoogle Scholar
  59. 59.
    Feng G, Cummings PT (2011) J Phys Chem Lett 2:2859–2864CrossRefGoogle Scholar
  60. 60.
    Kondrat S, Kornyshev A (2011) J Phys Condens Matter 23:022201CrossRefGoogle Scholar
  61. 61.
    Jadhao V, Solis FJ, de la Cruz MO (2013) J Chem Phys 138:054119-13CrossRefGoogle Scholar
  62. 62.
    Jiménez ML, Fernández MM, Ahualli S, Iglesias G, Delgado AV (2013) J Colloid Interface Sci 402:340–349CrossRefGoogle Scholar
  63. 63.
    Wang H, Thiele A, Pilon L (2013) J Phys Chem C 117:18286–18297CrossRefGoogle Scholar
  64. 64.
    Kobrak MN (2013) J Phys Condens Matter 25:095006CrossRefGoogle Scholar
  65. 65.
    Kastening B, Heins M (2005) Electrochim Acta 50:2487–2498CrossRefGoogle Scholar
  66. 66.
    Suss, M.E., T.F., Baumann, M.A. Worsley, K.A. Rose, T.F. Jaramillo, M. Stadermann, J.G. Santiago (2013) J Power Sources 241: 266–273Google Scholar
  67. 67.
    Grahame DC (1947) Chem Rev 41:441–501CrossRefGoogle Scholar
  68. 68.
    Bazant MZ, Chu KT, Bayly BJ (2005) SIAM J Appl Math 65:1463–1484CrossRefGoogle Scholar
  69. 69.
    Kalluri RK, Biener MM, Suss ME, Merrill MD, Stadermann M, Santiago JG, Baumann TF, Biener J, Striolo A (2013) Phys Chem Chem Phys 15:2309–2320CrossRefGoogle Scholar
  70. 70.
    Andersen PS, Fuchs M (1975) Biophys J 15:795–830CrossRefGoogle Scholar
  71. 71.
    Grosberg AY, Nguyen TT, Shklovskii BI (2002) Rev Mod Phys 74:329–345CrossRefGoogle Scholar
  72. 72.
    Santangelo CD (2006) Phys Rev E 73:041512CrossRefGoogle Scholar
  73. 73.
    Hatlo MM, Lue L (2010) EPL Europhys Lett 89:25002CrossRefGoogle Scholar
  74. 74.
    Bazant MZ, Storey BD, Kornyshev AA (2011) Phys Rev Lett 106:046102CrossRefGoogle Scholar
  75. 75.
    Jackson, J.D. (1975) Classical electrodynamics. Second edition ed: Wiley. 848Google Scholar
  76. 76.
    Zhao R, Satpradit O, Rijnaarts HHM, Biesheuvel PM, van der Wal A (2013) Water Res 47:1941–1952CrossRefGoogle Scholar
  77. 77.
    Zhao R, Porada S, Biesheuvel PM, van der Wal A (2013) Desalination 330:35–41CrossRefGoogle Scholar
  78. 78.
    Levi MD, Sigalov S, Aurbach D, Daikhin L (2013) J Phys Chem C 117:14876–14889CrossRefGoogle Scholar
  79. 79.
    Müller M, Kastening B (1994) J Electroanal Chem 374:149–158CrossRefGoogle Scholar
  80. 80.
    Gupta VK, Pathania D, Sharma S, Singh P (2013) J Colloid Interface Sci 401:125–132CrossRefGoogle Scholar
  81. 81.
    Aghakhani A, Mousavi SF, Mostafazadeh-Fard B, Rostamian R, Seraji M (2011) Desalination 275:217–223CrossRefGoogle Scholar
  82. 82.
    Tarazona P (1985) Phys Rev A 31:2672–2679CrossRefGoogle Scholar
  83. 83.
    Dlugolecki P, van der Wal A (2013) Environ Sci Technol 47:4904–4910CrossRefGoogle Scholar
  84. 84.
    Liang P, Yuan L, Yang X, Zhou S, Huang X (2013) Water Res 47:2523–2530CrossRefGoogle Scholar
  85. 85.
    Kim Y-J, Kim J-H, Choi J-H (2013) J Membr Sci 429:52–57CrossRefGoogle Scholar
  86. 86.
    Yeo J-H, Choi J-H (2013) Desalination 320:10–16CrossRefGoogle Scholar
  87. 87.
    Hamelers, H.V.M., O. Schaetzle, J.M. Paz-García, P.M. Biesheuvel, and C.J.N. Buisman (2014) Environ Sci Technol Lett 1:31–35Google Scholar
  88. 88.
    Paz-Garcia, J.M., O. Schaetzle, P.M. Biesheuvel, H.V.M. Hamelers (2014) J Colloid Interface Sci 418:200–207Google Scholar
  89. 89.
    Grochowski P, Trylska J (2008) Biopolymers 89:93–113CrossRefGoogle Scholar
  90. 90.
    Levitt DG (1986) Annu Rev Biophys Biophys Chem 15:29–57CrossRefGoogle Scholar
  91. 91.
    Levi MD, Sigalov S, Salitra G, Aurbach D, Maier J (2011) ChemPhysChem 12:854–862CrossRefGoogle Scholar
  92. 92.
    Levi MD, Sigalov S, Salitra G, Elazari R, Aurbach D (2011) J Phys Chem Lett 2:120–124CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • P. M. Biesheuvel
    • 1
    • 2
    • 3
  • S. Porada
    • 1
  • M. Levi
    • 4
  • M. Z. Bazant
    • 5
    • 6
  1. 1.Wetsus, Centre of Excellence for Sustainable Water TechnologyLeeuwardenThe Netherlands
  2. 2.Laboratory of Physical Chemistry and Colloid ScienceWageningen UniversityWageningenThe Netherlands
  3. 3.Department of Environmental TechnologyWageningen UniversityWageningenThe Netherlands
  4. 4.Department of ChemistryBar-Ilan UniversityRamat-GanIsrael
  5. 5.Department of Chemical EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  6. 6.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations