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Attractive forces in microporous carbon electrodes for capacitive deionization

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Abstract

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.

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References

  1. Arnold BB, Murphy GW (1961) J Phys Chem 65:135–138

    Article  CAS  Google Scholar 

  2. Farmer JC, Fix DV, Mack GV, Pekala RW, Poco JF (1996) J Electrochem Soc 143:159–169

    Article  CAS  Google Scholar 

  3. Johnson AM, Newman J (1971) J Electrochem Soc 118:510–517

    Article  CAS  Google Scholar 

  4. Soffer A, Folman M (1972) J Electroanal Chem Interface Electrochem 38:25–43

    Article  CAS  Google Scholar 

  5. Suss ME, Baumann TF, Bourcier WL, Spadaccini CM, Rose KA, Santiago JG, Stadermann M (2012) Energy Environ Sci 5:9511–9519

    Article  CAS  Google Scholar 

  6. Rica RA, Ziano R, Salerno D, Mantegazza F, Brogioli D (2012) Phys Rev Lett 109:156103

    Article  CAS  Google Scholar 

  7. Porada S, Zhao R, van der Wal A, Presser V, Biesheuvel PM (2013) Prog Mater Sci 58:1388–1442

    Article  CAS  Google Scholar 

  8. Jeon S-I, Park H-R, Yeo J-G, Yang S, Cho CH, Han MH, Kim D-K (2013) Energy Environ Sci 6:1471–1475

    Article  CAS  Google Scholar 

  9. Jande YAC, Kim WS (2013) Desalination 329:29–34

    Article  CAS  Google Scholar 

  10. Jande YAC, Kim WS (2013) Sep Purif Technol 115:224–230

    Article  CAS  Google Scholar 

  11. Garcia-Quismondo E, Gomez R, Vaquero F, Cudero AL, Palma J, Anderson MA (2013) Phys Chem Chem Phys 15:7648–7656

    Article  CAS  Google Scholar 

  12. Wang G, Qian B, Dong Q, Yang J, Zhao Z, Qiu J (2013) Sep Purif Technol 103:216–221

    Article  CAS  Google Scholar 

  13. Oren Y, Soffer A (1983) J Appl Electrochem 13:473–487

    Article  CAS  Google Scholar 

  14. Levi MD, Salitra G, Levy N, Aurbach D, Maier J (2009) Nat Mater 8:872–875

    Article  CAS  Google Scholar 

  15. Avraham E, Bouhadana Y, Soffer A, Aurbach D (2009) J Electrochem Soc 156:95–99

    Article  Google Scholar 

  16. Zhao R, Biesheuvel PM, Miedema H, Bruning H, van der Wal A (2010) J Phys Chem Lett 1:205–210

    Article  CAS  Google Scholar 

  17. Levi MD, Levy N, Sigalov S, Salitra G, Aurbach D, Maier J (2010) J Am Chem Soc 132:13220–13222

    Article  CAS  Google Scholar 

  18. Kastening B, Heins M (2001) Phys Chem Chem Phys 3:372–373

    Article  CAS  Google Scholar 

  19. Han L, Karthikeyan KG, Anderson MA, Gregory K, Wouters JJ, Abdel-Wahab A (2013) Electrochim Acta 90:573–581

    Article  CAS  Google Scholar 

  20. Mossad M, Zou L (2013) Chem Eng J 223:704–713

    Article  CAS  Google Scholar 

  21. Zhao R, Biesheuvel PM, Van der Wal A (2012) Energy Environ Sci 5:9520–9527

    Article  CAS  Google Scholar 

  22. Wu P, Huang J, Meunier V, Sumpter BG, Qiao R (2012) J Phys Chem Lett 3:1732–1737

    Article  CAS  Google Scholar 

  23. Bazant MZ, Thornton K, Ajdari A (2004) Phys Rev E 70:021506

    Google Scholar 

  24. Biesheuvel PM, Bazant MZ (2010) Phys Rev E 81:031502

    Google Scholar 

  25. Zhao R, van Soestbergen M, Rijnaarts HHM, van der Wal A, Bazant MZ, Biesheuvel PM (2012) J Colloid Interface Sci 384:38–44

    Article  CAS  Google Scholar 

  26. Yang K-L, Ying T-Y, Yiacoumi S, Tsouris C, Vittoratos ES (2001) Langmuir 17:1961–1969

    Article  CAS  Google Scholar 

  27. Gabelich CJ, Tran TD, Suffet IH (2002) Environ Sci Technol 36:3010–3019

    Article  CAS  Google Scholar 

  28. Hou C-H, Liang C, Yiacoumi S, Dai S, Tsouris C (2006) J Colloid Interface Sci 302:54–61

    Article  CAS  Google Scholar 

  29. Xu P, Drewes JE, Heil D, Wang G (2008) Water Res 42:2605–2617

    Article  CAS  Google Scholar 

  30. Li L, Zou L, Song H, Morris G (2009) Carbon 47:775–781

    Article  CAS  Google Scholar 

  31. Gabelich CJ, Xu P, Cohen Y (2010) Sustain Sci Eng 2:295–326

    Article  Google Scholar 

  32. Tsouris C, Mayes R, Kiggans J, Sharma K, Yiacoumi S, DePaoli D, Dai S (2011) Environ Sci Technol 45:10243–10249

    Article  CAS  Google Scholar 

  33. Porada S, Weinstein L, Dash R, van der Wal A, Bryjak M, Gogotsi Y, Biesheuvel PM (2012) ACS Appl Mater Interfaces 4:1194–1199

    Article  CAS  Google Scholar 

  34. Porada S, Borchardt L, Oschatz M, Bryjak M, Atchison J, Keesman KJ, Kaskel S, Biesheuvel M, Presser V (2013) Energy Environ Sci 6:3700–3712

    Article  CAS  Google Scholar 

  35. Lin C, Ritter JA, Popov BN (1999) J Electrochem Soc 146:3639–3643

    Article  CAS  Google Scholar 

  36. Kim T, Yoon J (2013) J Electroanal Chem 704:169–174

    Article  CAS  Google Scholar 

  37. Sharma K, Mayes RT, Kiggans JO Jr, Yiacoumi S, Gabitto J, DePaoli DW, Dai S, Tsouris C (2013) Sep Purif Technol 116:206–213

    Article  CAS  Google Scholar 

  38. Biesheuvel PM, Zhao R, Porada S, van der Wal A (2011) J Colloid Interface Sci 360:239–248

    Article  CAS  Google Scholar 

  39. Porada S, Bryjak M, van der Wal A, Biesheuvel PM (2012) Electrochim Acta 75:148–156

    Article  CAS  Google Scholar 

  40. Rica RA, Brogioli D, Ziano R, Salerno D, Mantegazza F (2012) J Phys Chem C 116:16934–16938

    Article  CAS  Google Scholar 

  41. Porada S, Sales BB, Hamelers HVM, Biesheuvel PM (2012) J Phys Chem Lett 3:1613–1618

    Article  CAS  Google Scholar 

  42. Andersen MB, van Soestbergen M, Mani A, Bruus H, Biesheuvel PM, Bazant MZ (2012) Phys Rev Lett 109:108301

    Article  CAS  Google Scholar 

  43. Galama AH, Post JW, Cohen Stuart MA, Biesheuvel PM (2013) J Membr Sci 442:131–139

    Article  CAS  Google Scholar 

  44. Biesheuvel PM, de Vos WM, Amoskov VM (2008) Macromolecules 41:6254–6259

    Article  CAS  Google Scholar 

  45. de Vos WM, Biesheuvel PM, de Keizer A, Kleijn JM, Cohen Stuart MA (2009) Langmuir 25:9252–9261

    Article  Google Scholar 

  46. Biesheuvel PM (2004) J Phys Condens Matter 16:L499–L504

    Article  CAS  Google Scholar 

  47. Spruijt E, Biesheuvel PM (2014) J Phys Condens Matter 26:075101

    Google Scholar 

  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 167–206

    Google Scholar 

  49. Garten VA, Weiss DE (1955) Aust J Chem 8:68–95

    Article  CAS  Google Scholar 

  50. Garten VA, Weiss DE (1957) Rev Pure Appl Chem 7:69–122

    CAS  Google Scholar 

  51. Attard P, Mitchell DJ, Ninham BW (1988) J Chem Phys 89:4358–4367

    Article  CAS  Google Scholar 

  52. Skinner B, Loth MS, Shklovskii BI (2010) Phys Rev Lett 104:128302

    Article  Google Scholar 

  53. Biesheuvel PM, Fu YQ, Bazant MZ (2011) Phys Rev E 83:061507

    Google Scholar 

  54. Biesheuvel PM, Fu Y, Bazant MZ (2012) Russ J Electrochem 48:580–592

    Article  CAS  Google Scholar 

  55. Rica RA, Ziano R, Salerno D, Mantegazza F, Bazant MZ, Brogioli D (2013) Electrochim Acta 92:304–314

    Article  CAS  Google Scholar 

  56. Hou C-H, Patricia T-S, Yiacoumi S, Tsouris C (2008) J Chem Phys 129:224703–224709

    Article  Google Scholar 

  57. Feng G, Qiao R, Huang J, Sumpter BG, Meunier V (2010) ACS Nano 4:2382–2390

    Article  CAS  Google Scholar 

  58. Bonthuis DJ, Gekle S, Netz RR (2011) Phys Rev Lett 107:166102

    Article  Google Scholar 

  59. Feng G, Cummings PT (2011) J Phys Chem Lett 2:2859–2864

    Article  CAS  Google Scholar 

  60. Kondrat S, Kornyshev A (2011) J Phys Condens Matter 23:022201

    Article  CAS  Google Scholar 

  61. Jadhao V, Solis FJ, de la Cruz MO (2013) J Chem Phys 138:054119-13

    Article  Google Scholar 

  62. Jiménez ML, Fernández MM, Ahualli S, Iglesias G, Delgado AV (2013) J Colloid Interface Sci 402:340–349

    Article  Google Scholar 

  63. Wang H, Thiele A, Pilon L (2013) J Phys Chem C 117:18286–18297

    Article  CAS  Google Scholar 

  64. Kobrak MN (2013) J Phys Condens Matter 25:095006

    Article  Google Scholar 

  65. Kastening B, Heins M (2005) Electrochim Acta 50:2487–2498

    Article  CAS  Google Scholar 

  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: 266–273

    Google Scholar 

  67. Grahame DC (1947) Chem Rev 41:441–501

    Article  CAS  Google Scholar 

  68. Bazant MZ, Chu KT, Bayly BJ (2005) SIAM J Appl Math 65:1463–1484

    Article  CAS  Google Scholar 

  69. Kalluri RK, Biener MM, Suss ME, Merrill MD, Stadermann M, Santiago JG, Baumann TF, Biener J, Striolo A (2013) Phys Chem Chem Phys 15:2309–2320

    Article  CAS  Google Scholar 

  70. Andersen PS, Fuchs M (1975) Biophys J 15:795–830

    Article  CAS  Google Scholar 

  71. Grosberg AY, Nguyen TT, Shklovskii BI (2002) Rev Mod Phys 74:329–345

    Article  CAS  Google Scholar 

  72. Santangelo CD (2006) Phys Rev E 73:041512

    Article  Google Scholar 

  73. Hatlo MM, Lue L (2010) EPL Europhys Lett 89:25002

    Article  Google Scholar 

  74. Bazant MZ, Storey BD, Kornyshev AA (2011) Phys Rev Lett 106:046102

    Article  Google Scholar 

  75. Jackson, J.D. (1975) Classical electrodynamics. Second edition ed: Wiley. 848

  76. Zhao R, Satpradit O, Rijnaarts HHM, Biesheuvel PM, van der Wal A (2013) Water Res 47:1941–1952

    Article  CAS  Google Scholar 

  77. Zhao R, Porada S, Biesheuvel PM, van der Wal A (2013) Desalination 330:35–41

    Article  CAS  Google Scholar 

  78. Levi MD, Sigalov S, Aurbach D, Daikhin L (2013) J Phys Chem C 117:14876–14889

    Article  CAS  Google Scholar 

  79. Müller M, Kastening B (1994) J Electroanal Chem 374:149–158

    Article  Google Scholar 

  80. Gupta VK, Pathania D, Sharma S, Singh P (2013) J Colloid Interface Sci 401:125–132

    Article  CAS  Google Scholar 

  81. Aghakhani A, Mousavi SF, Mostafazadeh-Fard B, Rostamian R, Seraji M (2011) Desalination 275:217–223

    Article  CAS  Google Scholar 

  82. Tarazona P (1985) Phys Rev A 31:2672–2679

    Article  CAS  Google Scholar 

  83. Dlugolecki P, van der Wal A (2013) Environ Sci Technol 47:4904–4910

    Article  CAS  Google Scholar 

  84. Liang P, Yuan L, Yang X, Zhou S, Huang X (2013) Water Res 47:2523–2530

    Article  CAS  Google Scholar 

  85. Kim Y-J, Kim J-H, Choi J-H (2013) J Membr Sci 429:52–57

    Article  CAS  Google Scholar 

  86. Yeo J-H, Choi J-H (2013) Desalination 320:10–16

    Article  CAS  Google Scholar 

  87. Hamelers, H.V.M., O. Schaetzle, J.M. Paz-García, P.M. Biesheuvel, and C.J.N. Buisman (2014) Environ Sci Technol Lett 1:31–35

    Google Scholar 

  88. Paz-Garcia, J.M., O. Schaetzle, P.M. Biesheuvel, H.V.M. Hamelers (2014) J Colloid Interface Sci 418:200–207

    Google Scholar 

  89. Grochowski P, Trylska J (2008) Biopolymers 89:93–113

    Article  CAS  Google Scholar 

  90. Levitt DG (1986) Annu Rev Biophys Biophys Chem 15:29–57

    Article  CAS  Google Scholar 

  91. Levi MD, Sigalov S, Salitra G, Aurbach D, Maier J (2011) ChemPhysChem 12:854–862

    Article  CAS  Google Scholar 

  92. Levi MD, Sigalov S, Salitra G, Elazari R, Aurbach D (2011) J Phys Chem Lett 2:120–124

    Article  CAS  Google Scholar 

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Acknowledgments

Part of this work was performed in the cooperation framework of Wetsus, Centre of Excellence for Sustainable Water Technology (www.wetsus.nl). 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”.

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Authors and Affiliations

  1. Wetsus, Centre of Excellence for Sustainable Water Technology, Agora 1, 8934 CJ, Leeuwarden, The Netherlands

    P. M. Biesheuvel & S. Porada

  2. Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703 HB, Wageningen, The Netherlands

    P. M. Biesheuvel

  3. Department of Environmental Technology, Wageningen University, Bornse Weilanden 9, 6708 WG, Wageningen, The Netherlands

    P. M. Biesheuvel

  4. Department of Chemistry, Bar-Ilan University, Ramat-Gan, 52900, Israel

    M. Levi

  5. Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    M. Z. Bazant

  6. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    M. Z. Bazant

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  1. P. M. Biesheuvel
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  2. S. Porada
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  3. M. Levi
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Correspondence to P. M. Biesheuvel.

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Biesheuvel, P.M., Porada, S., Levi, M. et al. Attractive forces in microporous carbon electrodes for capacitive deionization. J Solid State Electrochem 18, 1365–1376 (2014). https://doi.org/10.1007/s10008-014-2383-5

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  • DOI: https://doi.org/10.1007/s10008-014-2383-5

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