Advertisement

Journal of Biological Physics

, Volume 38, Issue 1, pp 121–152 | Cite as

Structure of the nanobubble clusters of dissolved air in liquid media

  • Nikolai F. Bunkin
  • Stanislav O. Yurchenko
  • Nikolai V. Suyazov
  • Alexey V. Shkirin
Original Paper

Abstract

A qualitative model of the nucleation of stable bubbles in water at room temperature is suggested. This model is completely based on the property of the affinity of water at the nanometer scale; it is shown that under certain conditions the extent of disorder in a liquid starts growing, which results in a spontaneous decrease of the local density of the liquid and in the formation of nanometer-sized voids. These voids can serve as nuclei for the following generation of the so-called bubstons (the abbreviation for bubbles, stabilized by ions). The model of charging the bubstons by the ions, which are capable of adsorption, and the screening by a cloud of counter-ions, which are incapable of adsorption, is analyzed. It was shown that, subject to the charge of bubston, two regimes of such screening can be realized. At low charge of bubston the screening is described in the framework of the known linearized Debye–Huckel approach, when the sign of the counter-ion cloud preserves its sign everywhere in the liquid surrounding the bubston, whereas at large charge this sign is changed at some distance from the bubston surface. This effect provides the mechanism of the emergence of two types of compound particles having the opposite polarity, which leads to the aggregation of such compound particles by a ballistic kinetics.

Keywords

Nanobubbles Structure of aqueous media Breathing of marine organisms 

Notes

Acknowledgements

The authors are very grateful to V.A. Kozlov and A.V. Starosvetskij for assistance in preparing the manuscript.

References

  1. 1.
    Epstein, P.S., Plesset, M.S.: On the stability of gas bubbles in liquid-gas solutions. J. Chem. Phys. 18(11), 1505–1509 (1950)ADSCrossRefGoogle Scholar
  2. 2.
    Ljunggren, S., Eriksson, J.C.: The lifetime of a colloid-sized gas bubble in water and the cause of the hydrophobic attraction. Colloids Surf. A 129130, 151–155 (1997)CrossRefGoogle Scholar
  3. 3.
    Crum, L.A.: Tensile strength of water. Nature (London) 278, 148–149 (1979)ADSCrossRefGoogle Scholar
  4. 4.
    Crum, L.A.: Acoustic cavitation thresholds in water. In: Lauterborn, W. (ed.) Cavitation and Inhomogeneities in Underwater Acoustics, pp. 3–12. Springer-Verlag, New York (1980)Google Scholar
  5. 5.
    Crum, L.A.: Nucleation and stabilization of micro-bubbles in liquids. Appl. Sci. Res. 38, 101–115 (1982)CrossRefGoogle Scholar
  6. 6.
    Crum, L.A.: Nucleation and stabilization of microbubbles in liquids. In: van Wijngaarden, L. (ed.) Mechanics and Physics of Bubbles in Liquids, pp. 101–115. Martinus Nijhoff Publishers, The Hague (1982)CrossRefGoogle Scholar
  7. 7.
    Sirotyuk, M.G.: Experimental investigations of ultrasonic cavitation. In: Rozenberg, L.D. (ed.) High Intensity Ultrasonic Fields, pp. 319–337. Plenum Press, New York (1971)Google Scholar
  8. 8.
    Washburn, E.W. (ed.): International Critical Tables, vol. 4. McGraw-Hill, New York (1928)Google Scholar
  9. 9.
    Wagner, C.: Die Oberflächenspannung verdünnter elektrolytlösungen. Phys. Z. 25, 474–477 (1924)Google Scholar
  10. 10.
    Onsager, L., Samaras, N.N.T.: The surface tension of Debye-Hiickel electrolytes. J. Chem. Phys. 2, 528–536 (1934)ADSCrossRefGoogle Scholar
  11. 11.
    Bunkin, N.F., Bunkin, F.V.: Bubbstons: stable microscopic gas bubbles in very dilute electrolytic solutions. J. Exp. Theor. Phys. 74, 271–278 (1992)Google Scholar
  12. 12.
    Bunkin, N.F., Bunkin, F.V.: Screening of strongly charged macroparticles in liquid electrolyte solutions. J. Exp. Theor. Phys. 96, 730–746 (2003)ADSCrossRefGoogle Scholar
  13. 13.
    Bunkin, N.F., Bunkin, F.V.: Adsorption and desorption of ions at the surface of liquid. Z. Phys. Chem. 215, 111–132 (2001)CrossRefGoogle Scholar
  14. 14.
    Bunkin, N.F., Lobeyev, A.V., Lyakhov, G.A., Ninham, B.W.: Mechanism of low-threshold hypersonic cavitation stimulated by broadband laser pump. Phys. Rev. E 60, 1681–1690 (1999)ADSCrossRefGoogle Scholar
  15. 15.
    Bunkin, N.F., Suyazov, N.V., Shkirin, A.V., Ignatiev, P.S., Indukaev, K.V.: Nanoscale structure of dissolved air bubbles in water as studied by measuring the elements of the scattering matrix. J. Chem. Phys. 130, 134308 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    Bunkin, N.F., Suyazov, N.V., Shkirin, A.V., Ignatiev, P.S., Indukaev, K.V.: Screening of strongly charged macroparticles in liquid electrolyte solutions. JETP 108, 800–816 (2009)ADSCrossRefGoogle Scholar
  17. 17.
    Bunkin, N.F., Shkirin, A.V., Kozlov, V.A., Starosvetskiy, A.V.: Laser scattering in water and aqueous solutions of salts. Proc. SPIE 7376, 73761D (2010)ADSCrossRefGoogle Scholar
  18. 18.
    Bunkin, N.F., Ninham, B.W., Shkirin, A.V., Ignatiev, P.S., Kozlov, V.A., Starosvetskij, A.V.: Long-living nanobubbles of dissolved gas in aqueous solutions of salts and erythrocyte suspensions. J. Biophotonics 4(3), 150–164 (2011)CrossRefGoogle Scholar
  19. 19.
    Bunkin, N.F., Bunkin, F.V.: The new concepts in the optical breakdown of transparent liquids. Laser Phys. 3, 63–78 (1993)Google Scholar
  20. 20.
    Bunkin, N.F., Lobeyev, A.V.: Bubbston-cluster structure under conditions of optical breakdown in a liquid. Quantum Electron. 24, 297–301 (1994)ADSCrossRefGoogle Scholar
  21. 21.
    Vinogradova, O.I., Bunkin, N.F., Churaev, N.V., Kiseleva, O.A., Lobeyev, A.V., Ninham, B.W.: Submicrocavity structure of water between hydrophobic and hydrophilic walls as revealed by optical cavitation. J. Colloid Interface Sci. 173, 443–447 (1995)CrossRefGoogle Scholar
  22. 22.
    Bunkin, N.F., Lyakhov, G.A.: Microbubbles of dissolved gas in water: physical studies and possible applications in biological technologies and medicine. Phys. Wave Phenom. 13, 61–80 (2005)Google Scholar
  23. 23.
    Bunkin, N.F., Bakum, S.I.: Role of a dissolved gas in the optical breakdown of water. Quant. Electron. 36, 117–124 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    Bunkin, N.F., Kochergin, A.V., Lobeyev, A.V., Ninham, B.W., Vinogradova, O.I.: Existence of charged submicrobubble clusters in polar liquids as revealed by correlation between optical cavitation and electrical conductivity. Colloid Surf. A 110, 207–212 (1996)CrossRefGoogle Scholar
  25. 25.
    Bunkin, N.F., Kiseleva, O.A., Lobeyev, A.V., Movchan, T.G., Ninham, B.W., Vinogradova, O.I.: Effect of salts and dissolved gas on optical cavitation near hydrophobic and hydrophilic surfaces. Langmuir 13, 3024–3028 (1997)CrossRefGoogle Scholar
  26. 26.
    Bunkin, N.F., Ninham, B.W., Babenko, V.A., Suyazov, N.V., Sychev, A.A.: Role of dissolved gas in optical breakdown of water: differences between effects due to helium and other gases. J. Phys. Chem. B 114, 7743–7752 (2010)CrossRefGoogle Scholar
  27. 27.
    Chattoraj, D.K., Birdi, K.S.: Adsorption and the Gibbs Surface Excess. Plenum Press, New York (1984)Google Scholar
  28. 28.
    Wilson, M.A., Pohorille, A., Pratt, L.R.: Molecular-dynamics of the water liquid vapor interface. J. Phys. Chem. 91, 4873–4878 (1987)CrossRefGoogle Scholar
  29. 29.
    Wilson, M.A., Pohorille, A.: Interaction of monovalent ions with the water liquid vapor interface—a molecular dynamic study. J. Chem. Phys. 95, 6005–6013 (1991)ADSCrossRefGoogle Scholar
  30. 30.
    Benjamin, I.: Theoretical-study of ion solvation at the water liquid–vapor interface. J. Chem. Phys. 95, 3698–3709 (1991)ADSCrossRefGoogle Scholar
  31. 31.
    Jungwirth, P., Tobias, D.J.: Surface effects on aqueous ionic solvation: a molecular dynamics simulation study of NaCl at the air/water interface from infinite dilution to saturation. J. Phys. Chem. B 104, 7702–7706 (2000)CrossRefGoogle Scholar
  32. 32.
    Jungwirth, P., Tobias, D.J.: Molecular structure of salt solutions: a new view of the interface with implications for heterogeneous atmospheric chemistry. J. Phys. Chem. B 105, 10468–10472 (2001)CrossRefGoogle Scholar
  33. 33.
    Mucha, M., Frigato, T., Levering, L.M., Allen, H.C., Tobias, D.J., Dang, L.X., Yungwirth, P.: Unified molecular picture of the surfaces of aqueous acid, base, and salt solutions. J. Phys. Chem. B 109, 7617–7623 (2005)CrossRefGoogle Scholar
  34. 34.
    Kniping, E.M., Lakin, M.J., Foster, K.L., Yungwirth, P., Tobias, D.J., Dabdub, R.B., Finlayson-Pitts, B.J.: Experiments and simulations of ion-enhanced interfacial chemistry on aqueous NaCl aerosols. Science 288, 301–306 (2000)ADSCrossRefGoogle Scholar
  35. 35.
    Stuart, S.J., Berne, B.J.: Surface curvature effects in the aqueous ionic solvation of the chloride ion. J. Phys. Chem. A 103, 10300–10307 (1999)CrossRefGoogle Scholar
  36. 36.
    Herce, D.H., Perera, L., Darden, T.A., Sagui, C.: Surface solvation for an ion in a water cluster. J. Chem. Phys. 122, 024513 (2005)CrossRefGoogle Scholar
  37. 37.
    Vrbka, L., Mucha, M., Minofar, B., Yungwirth, P., Brown, E.C., Tobias, D.J.: Propensity of soft ions for the air/water interface. Curr. Opin. Colloid Interface Sci. 9, 67–73 (2004)CrossRefGoogle Scholar
  38. 38.
    Jungwirth, P., Tobias, D.J.: Specific ion effects at the air/water interface. Chem. Rev. 106, 1259–1281 (2006)CrossRefGoogle Scholar
  39. 39.
    Baldelli, S., Schnitzer, C., Shultz, M.J.: The structure of water on HCl solutions studied with sum frequency generation. Chem. Phys. Lett. 302, 157–163 (1999)ADSCrossRefGoogle Scholar
  40. 40.
    Schnitzer, C., Baldelli, S., Shultz, M.J.: Sum frequency generation of water on NaCl, NaNO3, KHSO4, HCl, HNO3, and H2SO4 aqueous solutions. J. Phys. Chem. B 104, 585–590 (2000)CrossRefGoogle Scholar
  41. 41.
    Shultz, M.J., Schnitzer, C., Simonelli, D., Baldelli, S.: Sum frequency generation spectroscopy of the aqueous interface: ionic and soluble molecular solutions. Int. Rev. Phys. Chem. 19, 123–153 (2000)CrossRefGoogle Scholar
  42. 42.
    Shultz, M.J., Baldelli, S., Schnitzer, C., Simonelli, D.: Aqueous solution/air interfaces probed with sum frequency generation spectroscopy. J. Phys. Chem. B 106, 5313–5324 (2002)CrossRefGoogle Scholar
  43. 43.
    Liu, D.F., Ma, G.; Levering, L.M., Allen, H.C.: Vibrational Spectroscopy of aqueous sodium halide solutions and air-liquid interfaces: observation of increased interfacial depth. J. Phys. Chem. B 108, 2252–2260 (2004)CrossRefGoogle Scholar
  44. 44.
    Scatena L.F., Richmond, G.L.: Isolated molecular ion solvation at an oil/water interface investigated by vibrational sum-frequency spectroscopy. J. Phys. Chem. B 108, 12518–12528 (2004)CrossRefGoogle Scholar
  45. 45.
    Petersen, P.B., Saykally, R.J.: Confirmation of enhanced anion concentration at the liquid water surface. Chem. Phys. Lett. 397, 51–55 (2004)ADSCrossRefGoogle Scholar
  46. 46.
    Petersen, P.B., Johnson, J.C., Knutsen, K.P., Saykally, R.J.: Direct experimental validation of the Jones-Ray effect. Chem. Phys. Lett. 397, 46–50 (2004)ADSCrossRefGoogle Scholar
  47. 47.
    Weber, R., Winter, B., Schmidt, P.M., Widdra, W., Hertel, I.V., Dittmar, M., Faubel, M.: Photoemission from aqueous alkali-metal-iodide salt solutions using EUV synchrotron radiation. J. Phys. Chem. B 108, 4729–4736 (2004)CrossRefGoogle Scholar
  48. 48.
    Winter, B., Weber, R., Schmidt, P.M., Hertel, I.V., Faubel, M., Vrbka, M., Yungwirth, P.: Molecular structure of surface-active salt solutions: photoelectron spectroscopy and molecular dynamics simulations of aqueous tetrabutylammonium iodide. J. Phys. Chem. B 108, 14558–14564 (2004)CrossRefGoogle Scholar
  49. 49.
    Ghosal, S., Shbeeb, A., Hemminger, J.C.: Surface segregation of bromine in bromide doped NaCl: implications for the seasonal variations in Arctic ozone. Geophys. Res. Lett. 27, 1879–1882 (2000)ADSCrossRefGoogle Scholar
  50. 50.
    Finlayson-Pitts, B.J., Hemminger, J.C.: Physical chemistry of airborne sea salt particles and their components. J. Phys. Chem. A 104, 11463–11477 (2000)CrossRefGoogle Scholar
  51. 51.
    Kelsall, G.H., Tang, S., Yurdakul, S., Smith, A.: Electrophoretic behaviour of bubbles in aqueous electrolytes. J. Chem. Soc. Faraday Trans. 92, 3887–3893 (1996)CrossRefGoogle Scholar
  52. 52.
    Bernal, J.D., Fowler, R.H.: A theory of water and ionic solutions, with particular reference to hydrogen and hydroxyl ions. J. Chem. Phys. 1, 515–548 (1933)ADSCrossRefGoogle Scholar
  53. 53.
    Eisenberg, D., Kauzmann, W.: The Structure and Properties of Water. Oxford University Press, London (1969)Google Scholar
  54. 54.
    Pauling, L.: The structure of water. In: Hadzi, D., Thompson, H.W. (eds.) Hydrogen Bonding, pp. 1–6. Pergamon Press Ltd, London (1959)Google Scholar
  55. 55.
    Kamb, B.: Ice polymorphism and the structure of water. In: Rich, A., Davidson, N. (eds.) Structural Chemistry and Molecular Biology, pp. 507–542. W.H. Freeman, San Francisco (1968)Google Scholar
  56. 56.
    Dore, J.C.: Structural studies of water and other hydrogen-bonded liquids by neutron-diffraction. J. Mol. Struct. 250, 193–211 (1991)ADSCrossRefGoogle Scholar
  57. 57.
    Boutron, P., Alben, A.: Structural model for amorphous solid water. J. Chem. Phys. 62, 4848–4853 (1975)ADSCrossRefGoogle Scholar
  58. 58.
    Svishchev, I.M., Kusalik, P.G.: Structure in liquid water - a study of spatial-distribution functions. J. Chem. Phys. 99, 3049–3058 (1993)ADSCrossRefGoogle Scholar
  59. 59.
    Kusalik, P.G., Svishchev, I.M.: The spatial structure in liquid water. Science 265, 1219–1221 (1994)ADSCrossRefGoogle Scholar
  60. 60.
    Narten, A.H., Thiessen W., Blum, L.: Atom pair distribution-functions of liquid water at 25-degrees-c from neutron-diffraction. Science 217, 1033–1034 (1982)ADSCrossRefGoogle Scholar
  61. 61.
    Chialvo, A.A., Cummings, P.T., Simonson, J.M., Mesmer, J.M., Cochran, H.D.: Interplay between molecular simulation and neutron scattering in developing new insights into the structure of water. Ind. Eng. Chem. Res. 37, 3021–3025 (1998)CrossRefGoogle Scholar
  62. 62.
  63. 63.
    Balescu, R.: Equilibrium and Nonequilibrium Statistical Mechanics. Wiley, New York, (1975)MATHGoogle Scholar
  64. 64.
    Landau, L.D., Lifshitz, E.M.: Theory of Elasticity. Butterworth-Heinemann, Oxford (1986)Google Scholar
  65. 65.
    Landau, L.D., Lifshitz, E.M.: Statistical Physics, Part 1. Butterworth-Heinemann, Oxford (1980)Google Scholar
  66. 66.
    Pitaevskii, L.P., Lifshitz, E.M.: Physical Kinetics. Pergamon Press Ltd, London (1981)Google Scholar
  67. 67.
    Archer, A.J., Wilding, N.B.: Phase behavior of a fluid with competing attractive and repulsive interactions. Phys. Rev. E 76, 031501 (2007)ADSCrossRefGoogle Scholar
  68. 68.
    Lugli, F., Hofinger, S., Zerbetto, F.: The collapse of nanobubbles in water. J. Am. Chem. Soc. 127, 8020–8021 (2005)CrossRefGoogle Scholar
  69. 69.
    Fabelinskii, I.L.: Molecular Scattering of Light. Plenum Press, New York (1968)Google Scholar
  70. 70.
    Conway, B.E.: The evaluation and use of properties of individual ions in solutions. J. Solution Chem. 7, 721 (1978)CrossRefGoogle Scholar
  71. 71.
    Debye, P.W., Huckel, E.: Zur theorie der elektrolyte II. Das grenzgesetz für die elektrishe leitfähigkeit. Physik Z. 24, 305–325 (1923)Google Scholar
  72. 72.
    Ise, N., Okubo, T.: Ordered distribution of electrically charged solutes in dilute solutions. Accounts Chem. Res. 13, 303–309 (1980)CrossRefGoogle Scholar
  73. 73.
    Kepler, G.M., Fraden, S.: Attractive potential between confined colloids at low ionic-strength. Phys. Rev. Lett. 73, 356–359 (1994)ADSCrossRefGoogle Scholar
  74. 74.
    Dosho, S., Ise, N., Ito, K., Iwai, S., et al.: Recent study of polymer latex dispersions. Langmuir 9, 394–411 (1993)CrossRefGoogle Scholar
  75. 75.
    Matsuoka, Y., Harada, T., Yamaoka, H.: An exact evaluation of salt concentration-dependence of interparticle distance in colloidal crystals by ultra-small-angle x-ray-scattering. Langmuir 10, 4423–4425 (1994)CrossRefGoogle Scholar
  76. 76.
    Crocker, J.C., Grier, D.G.: Microscopic measurement of the pair interaction potential of charge-stabilized colloid. Phys. Rev. Lett. 73, 352–355 (1994)ADSCrossRefGoogle Scholar
  77. 77.
    Crocker, J.C., Grier, D.G.: When like charges attract: the effects of geometrical confinement on long-range colloidal interactions. Phys. Rev. Lett. 77, 1897–1900 (1996)ADSCrossRefGoogle Scholar
  78. 78.
    Larsen, A.E., Grier, D.G.: Like-charge attractions in metastable colloidal crystallites. Nature 385, 230–233 (1997)ADSCrossRefGoogle Scholar
  79. 79.
    Ise, N.: When does like like like? Microscopic inhomogeneity in homogeneous ionic systems. Proc. Jpn. Acad. B 78, 129–137 (2002)CrossRefGoogle Scholar
  80. 80.
    Zheng, J., Pollack, G.H.: Long-range forces extending from polymer-gel surfaces. Phys. Rev. E 68, 031408 (2003)ADSCrossRefGoogle Scholar
  81. 81.
    Gomez-Guzman, O., Ruiz-Garcia, J.: Attractive interactions between like-charged colloidal particles at the air/water interface. J. Colloid Interface Sci. 291, 1–6 (2005)CrossRefGoogle Scholar
  82. 82.
    Zheng, J., Chin, W., Khijniak, E., Khijniak Jr., E., Pollack, G.H.: Surfaces and interfacial water: evidence that hydrophilic surfaces have long-range impact. Adv. Colloid Interface Sci. 127, 19–27 (2006)CrossRefGoogle Scholar
  83. 83.
    Liang, Y., Hilal, N., Langston, P., Starov, V.: Interaction forces between colloidal particles in liquid: theory and experiment. Adv. Colloid Interface Sci. 134135, 151–166 (2007)CrossRefGoogle Scholar
  84. 84.
    Zheng, J., Wexler, A., Pollack, G.H.: Effect of buffers on aqueous solute-exclusion zones around ion-exchange resins. J. Colloid Interface Sci. 332, 511–514 (2009)CrossRefGoogle Scholar
  85. 85.
    Nagornyak, E., Yoo, H., Pollack, G.H.: Mechanism of attraction between like-charged particles in aqueous solution. Soft Matter 5, 3850–3857 (2009)CrossRefADSGoogle Scholar
  86. 86.
    Derjaguin, B.V., Landau, L.D.: Theory of stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes. Acta Physicochimica (USSR) 14, 633–645 (1941)Google Scholar
  87. 87.
    Verwey, E.J., Overbeek, J.T.G.: Theory of the Stabilization of Lyophobic Colloids. Elsevier, Amsterdam (1948)Google Scholar
  88. 88.
    Yoon, R., Yordan, J.L.: Zeta-potential measurements on microbubbles generated using various surfactants. J. Colloid Interface Sci. 113, 430–438 (1986)CrossRefGoogle Scholar
  89. 89.
    Li, C., Somasundaran, P.: Reversal of bubble charge in multivalent inorganic salt-solutions—effect of magnesium. J. Colloid Interface Sci. 146, 215–218 (1991)CrossRefGoogle Scholar
  90. 90.
    Li, C., Somasundaran, P.: Reversal of bubble charge in multivalent inorganic salt-solutions—effect of lanthanum. Colloid Surf. A 81, 13–15 (1993)CrossRefGoogle Scholar
  91. 91.
    Mateescu, E.M., Jeppesen, C., Pincus, P.: Overcharging of a spherical macroion by an oppositely charged polyelectrolyte. Europhys. Lett. 46, 493–498 (1999)ADSCrossRefGoogle Scholar
  92. 92.
    Park, S.Y., Bruinsma, R.F., Gelbart, W.M.: Spontaneous overcharging of macro-ion complexes. Europhys. Lett. 46, 454–460 (1999)ADSCrossRefGoogle Scholar
  93. 93.
    Joanny, J.F.: Polyelectrolyte adsorption and charge inversion. Eur. J. Phys. B 9, 117–122 (1999)ADSCrossRefGoogle Scholar
  94. 94.
    Perel, V.I., Shklovskii, B.I.: Screening of a macroion by multivalent ions: a new boundary condition for the Poisson-Boltzmann equation and charge inversion. Physica A (Amsterdam) 274, 446–453 (1999)ADSGoogle Scholar
  95. 95.
    Shklovskii, B.I.: Screening of a macroion by multivalent ions: correlation-induced inversion of charge. Phys. Rev. E 60, 5802–5811 (1999)ADSCrossRefGoogle Scholar
  96. 96.
    Nguyen, T.T., Grosberg, F.Yu., Shklovskii, B.I.: Screening of a charged particle by multivalent counterions in salty water: strong charge inversion. J. Chem. Phys. 113, 1110–1125 (2000)ADSCrossRefGoogle Scholar
  97. 97.
    Nguyen, T.T., Grosberg, F.Yu., Shklovskii, B.I.: Macroions in salty water with multivalent ions: giant inversion of charge. Phys. Rev. Lett. 85, 1568–1571 (2000)ADSCrossRefGoogle Scholar
  98. 98.
    Levin, Y.: Electrostatic correlations: from plasma to biology. Rep. Prog. Phys. 65, 1577–1632 (2002)ADSCrossRefGoogle Scholar
  99. 99.
    Quesada-Perez, M., Gonzalez-Tovar, E., Martin-Molina, A., Lozada-Cassou, M., Hidalgo-Alvarez, R.: Overcharging in colloids: beyond the Poisson-Boltzmann approach. ChemPhysChem 4, 235–248 (2003)CrossRefGoogle Scholar
  100. 100.
    Grosberg, F.Yu., Nguyen, T.T., Shklovskii, B.I.: Colloquium: the physics of charge inversion in chemical and biological systems. Rev. Mod. Phys. 74, 329–345 (2002)ADSCrossRefGoogle Scholar
  101. 101.
    Zhang, R.; Shklovskii, B.I.: Long-range polarization attraction between two different like-charged macroions. Phys. Rev. E 72, 021405 (2005)ADSCrossRefGoogle Scholar
  102. 102.
    Pittler, J., Bu, W., Vakhnin, D., Travesset, A., McGillivray, D.J., Losche, M.: Charge inversion at minute electrolyte concentrations. Phys. Rev. Lett. 97, 046102 (2006)ADSCrossRefGoogle Scholar
  103. 103.
    Gracheva, M.E., Leburton, J.P.: Electrolytic charge inversion at the liquid-solid interface in a nanopore in a doped semiconductor membrane. Nanotechnology 18, 145704 (2007)ADSCrossRefGoogle Scholar
  104. 104.
    Faraudo, J., Travesset, A.: The many origins of charge inversion in electrolyte solutions: effects of discrete interfacial charges. J. Phys. Chem. C 111, 987–994 (2007)CrossRefGoogle Scholar
  105. 105.
    Calero, C., Faraudo, J.: Enhancement of charge inversion by multivalent interfacial groups. Phys. Rev. E 80, 042601 (2009)ADSCrossRefGoogle Scholar
  106. 106.
    Terao, T., Nakayama, T.: Charge inversion of colloidal particles in an aqueous solution: screening by multivalent ions. Phys. Rev. E 63, 041401 (2001)ADSCrossRefGoogle Scholar
  107. 107.
    Wang, Z.Y., Ma, Y.Q.: Monte Carlo determination of mixed electrolytes next to a planar dielectric interface with different surface charge distributions. J. Chem. Phys. 131, 244715 (2009)ADSCrossRefGoogle Scholar
  108. 108.
    Wang, Z.Y., Ma, Y.Q.: Insights from Monte Carlo simulations on charge inversion of planar electric double layers in mixtures of asymmetric electrolytes. J. Chem. Phys. 133, 064704 (2010)CrossRefGoogle Scholar
  109. 109.
    Dukhin, S.S., Deryaguin, B.V.: Electrophoresis. Nauka, Moscow (1976, in Russian)Google Scholar
  110. 110.
    Landau, L.D., Lifshitz, E.M.: Fluid Mechanics. Pergamon Press, Oxford (1987)MATHGoogle Scholar
  111. 111.
    Langevin, P.: Sur la théorie du mouvement brownien. Coptes Rendus (Paris) 146, 530–533 (1908)MATHGoogle Scholar
  112. 112.
    Tikhonov, V.I.: Outliers in Random Processes. Nauka, Moscow (1970, in Russian)Google Scholar
  113. 113.
    Jullien, R.: Aggregation phenomena and fractal aggregates. Cont. Phys. 28, 477–493 (1987)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Nikolai F. Bunkin
    • 1
  • Stanislav O. Yurchenko
    • 2
  • Nikolai V. Suyazov
    • 1
  • Alexey V. Shkirin
    • 1
  1. 1.A.M.Prokhorov General Physics Institute of Russian Academy of SciencesMoscowRussia
  2. 2.Bauman Moscow State Technical UniversityMoscowRussia

Personalised recommendations