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Analysis of the Silica Sol Surface Structure by X-Ray Scattering Method

Abstract

The structure of the planar surface of colloidal solutions of amorphous 27-nm silica sol particles enriched with heavy K+, Rb+, and Cs+ alkali ions is studied by the methods of reflectometry and diffuse (nonspecular) scattering of synchrotron radiation. For liquid-phase systems, we have used a self-consistent approach that makes it possible to reconstruct from experimental data the electron density profiles perpendicular to the hydrosol surface, as well as the spectra of the height–height correlation function in the plane of the surface without using any a priori information about the near-surface structure. Analysis represented here shows that for high values of pH, alkali cations with a large radius and a surface concentration of (5 ± 1) × 1018 m–2 replace Na+ ions with a smaller radius. This result is in qualitative agreement with the dependence of the Kharkats–Ukstrup single-ion electrostatic free energy on the ion radius and in good quantitative agreement with the results obtained by other authors using the capillary-wave approach. The integrated value of  the effective height of interface roughness (3.2 ± 0.5 Å) coincides to within the measuring error with the prediction of the capillary-wave theory; however, the experimental spectra of the height-to-height correlation function basically differ from the theoretical spectra in the range of low spatial frequencies ν < 10–3 nm–1. The approximation of the spectra by the sum of two K-correlation distributions indicates a transition from the natural roughness of the compact layer of alkali metal ions to the capillary roughness of the liquid surface in the correlation length range of about 1 μm. In our opinion, the aggregate of available data indicates the dispersion of this layer into 2D clusters (Wigner islands).

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REFERENCES

  1. 1

    P. Becher, Emulsions: Theory and Practice, 3rd ed. (Am. Chem. Soc., Oxford Univ. Press, Washington, D.C., 2001).

  2. 2

    C. M. Starks, C. L. Liotta, and M. Halpern, Phase Transfer Catalysis (Chapman and Hall, New York, 1994).

    Book  Google Scholar 

  3. 3

    E. Bitto, M. Li, A. M. Tikhonov, M. L. Schlossman, and W. Cho, Biochemistry 39, 13469 (2000).

    Article  Google Scholar 

  4. 4

    Yu. A. Ermakov, V. A. Asadchikov, Yu. V. Volkov, A. D. Nuzhdin, B. S. Roshchin, V. Honkimaki, and A. M. Tikhonov, JETP Lett. 109, 334 (2019).

    ADS  Article  Google Scholar 

  5. 5

    I. Benjamin, Chem. Rev. 96, 1449 (1996).

    Article  Google Scholar 

  6. 6

    Yu. B. Vysotsky, E. S. Kartashynska, E. A. Belyaeva, V. B. Fainerman, D. Vollhardt, and R. Miller, Phys. Chem. Chem. Phys. 17, 28901 (2015).

    Article  Google Scholar 

  7. 7

    A. Moghimikheirabadi, L. M. Sagis, and P. Ilg, Phys. Chem. Chem. Phys. 20, 16238 (2018).

    Article  Google Scholar 

  8. 8

    P. S. Pershan and M. L. Schlossman, Liquid Surfaces and Interfaces: Synchrotron X-Ray Methods (Cambridge Univ. Press, Cambridge, UK, 2012).

    Book  Google Scholar 

  9. 9

    J. Als-Nielsen, Synchrotr. Radiat. News 12 (2), 5 (1999).

    Article  Google Scholar 

  10. 10

    Yu. A. Ermakov, V. E. Asadchikov, B. S. Roschin, Yu. O. Volkov, D. A. Khomich, A. M. Nesterenko, and A. M. Tikhonov, Langmuir 35, 12326 (2019).

    Article  Google Scholar 

  11. 11

    V. M. Kaganer, H. Mohwald, and P. Dutta, Rev. Mod. Phys. 71, 779 (1999).

    ADS  Article  Google Scholar 

  12. 12

    M. L. Schlossman and A. M. Tikhonov, Ann. Rev. Phys. Chem. 59, 153 (2008).

    ADS  Article  Google Scholar 

  13. 13

    A. M. Tikhonov, J. Exp. Theor. Phys. 110, 1055 (2010).

    ADS  Article  Google Scholar 

  14. 14

    M. F. Toney, J. N. Howard, J. Richer, G. L. Borges, J. G. Gordon, O. R. Melroy, D. G. Wiesler, D. Yee, and L. B. Sorensen, Nature (London, U.K.) 444, 368 (1994).

    Google Scholar 

  15. 15

    M. J. Regan, P. S. Pershan, O. M. Magnussen, B. M. Ocko, M. Deutsch, and L. E. Berman, Phys. Rev. B 55, 15874 (1997).

    ADS  Article  Google Scholar 

  16. 16

    P. Dutta, J. B. Peng, B. Lin, J. B. Ketterson, M. Prakash, P. Georgopoulous, and S. Ehrlich, Phys. Rev. Lett. 58, 2228 (1987).

    ADS  Article  Google Scholar 

  17. 17

    T. Graham, Trans. R. Soc. London 151, 183 (1861).

    ADS  Google Scholar 

  18. 18

    I. V. Kozhevnikov, Crystallogr. Rep. 57, 490 (2012).

    ADS  Article  Google Scholar 

  19. 19

    A. M. Tikhonov, V. E. Asadchikov, Yu. O. Volkov, B. S. Roshchin, V. Honkimäki, and M. Blanco, JETP Lett. 107, 384 (2018).

    ADS  Article  Google Scholar 

  20. 20

    F. P. Buff, R. A. Lovett, and F. H. Stillinger, Phys. Rev. Lett. 15, 621 (1965).

    ADS  Article  Google Scholar 

  21. 21

    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media (Nauka, Moscow, 1982; Pergamon, New York, 1984).

  22. 22

    C. Wagner, Phys. Z. 25, 474 (1924).

    Google Scholar 

  23. 23

    L. Onsager and N. N. T. Samaras, J. Chem. Phys. 2, 528 (1934).

    ADS  Article  Google Scholar 

  24. 24

    G. Gouy, J. Phys. 9, 457 (1910).

    Google Scholar 

  25. 25

    D. L. Chapman, Philos. Mag. 25, 475 (1913).

    Article  Google Scholar 

  26. 26

    E. J. W. Verwey and K. F. Nielsen, Philos. Mag. 28, 435 (1935).

    Article  Google Scholar 

  27. 27

    O. Stern, Z. Elektrochem. 30, 508 (1924).

  28. 28

    A. G. Volkov, D. W. Dreamer, D. L. Tanelli, and V. S. Markin, Prog. Surf. Sci. 53, 1 (1996).

    ADS  Article  Google Scholar 

  29. 29

    A. N. Frumkin, Z. Phys. Chem. 34, 109 (1924).

    Google Scholar 

  30. 30

    A. N. Frumkin, in Collection of Articles on Pure and Applied Chemistry (NKhTI, Petrograd, 1924), p. 106 [in Russian].

  31. 31

    V. S. Markin and A. G. Volkov, J. Phys. Chem. B 106, 11810 (2002).

    Article  Google Scholar 

  32. 32

    Y. I. Kharkats and J. Ulstrup, J. Electroanal. Chem. 308, 17 (1991).

    Article  Google Scholar 

  33. 33

    J. Ulstrup and Yu. I. Kharkats, Russ. J. Electrochem. 29, 299 (1993).

    Google Scholar 

  34. 34

    B. S. Gourary and F. S. Adrian, Solid State Phys. 10, 127 (1960).

    Article  Google Scholar 

  35. 35

    J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry: Principles of Structure and Reactivity, 4th ed. (Harper Collins, New York, USA, 1993).

    Google Scholar 

  36. 36

    K. Wu, M. J. Iedema, G. K. Schenter, and J. P. Cowin, J. Phys. Chem. B 105, 2483 (2001).

    Article  Google Scholar 

  37. 37

    B. S. Gourary and F. S. Adrian, Solid State Phys. 10, 127 (1960).

    Article  Google Scholar 

  38. 38

    E. Sloutskin, J. Baumert, B. M. Ocko, I. Kuzmenko, A. Checco, L. Tamam, E. Ofer, T. Gog, and M. Deutsch, J. Chem. Phys. 126, 054704 (2007).

    ADS  Article  Google Scholar 

  39. 39

    J. W. Ryznar, Colloidal Chemistry: Theoretical and Applied, Ed. by J. B. Alexander (Reinhold, New York, 1946), Vol. 6.

    Google Scholar 

  40. 40

    R. K. Iler, The Chemistry of Silica (Wiley-Interscience, New York, 1979).

    Google Scholar 

  41. 41

    A. M. Tikhonov, J. Phys. Chem. B 110, 2746 (2006).

    Article  Google Scholar 

  42. 42

    G. A. Parks, Chem. Rev. 65, 177 (1965).

    Article  Google Scholar 

  43. 43

    R. H. Yoon, T. Salman, and G. Donnay, J. Colloid Interface Sci. 70, 483 (1979).

    ADS  Article  Google Scholar 

  44. 44

    F. Dumont, J. Warlus, and A. Watillon, J. Colloid Interface Sci. 138, 543 (1990).

    ADS  Article  Google Scholar 

  45. 45

    A. M. Tikhonov, J. Chem. Phys. 124, 164704 (2006).

    ADS  Article  Google Scholar 

  46. 46

    A. M. Tikhonov, J. Phys. Chem. C 111, 930 (2007).

    Article  Google Scholar 

  47. 47

    V. S. Pingali, T. Takiue, G. Guangming, A. M. Tikhonov, N. Ikeda, M. Aratono, and M. L. Schlossman, J. Dispers. Sci. Technol. 27, 715 (2006).

    Article  Google Scholar 

  48. 48

    A. M. Tikhonov and M. L. Schlossman, J. Phys.: Condens. Matter 19, 375101 (2007).

    Google Scholar 

  49. 49

    E. S. Wu and W. W. Webb, Phys. Rev. A 8, 2065 (1973).

    ADS  Article  Google Scholar 

  50. 50

    J. D. Weeks, J. Chem. Phys. 67, 3106 (1977).

    ADS  Article  Google Scholar 

  51. 51

    A. M. Tikhonov, J. Chem. Phys 126, 171102 (2007).

    ADS  Article  Google Scholar 

  52. 52

    A. M. Tikhonov, J. Chem. Phys. 130, 024512 (2009).

    ADS  Article  Google Scholar 

  53. 53

    V. S. Edel’man, Sov. Phys. Usp. 23, 227 (1980).

    ADS  Article  Google Scholar 

  54. 54

    A. Madsen, O. Konovalov, A. Robert, and G. Grubel, Phys. Rev. E 64, 061406 (2001).

    ADS  Article  Google Scholar 

  55. 55

    A. M. Tikhonov, V. E. Asadchikov, Yu. O. Volkov, B. S. Roshchin, I. S. Monakhov, and I. S. Smirnov, JETP Lett. 104, 873 (2016).

    ADS  Article  Google Scholar 

  56. 56

    V. E. Asadchikov, V. V. Volkov, Yu. O. Volkov, K. A. Dembo, I. V. Kozhevnikov, B. S. Roshchin, D. A. Frolov, and A. M. Tikhonov, JETP Lett. 94, 585 (2011).

    ADS  Article  Google Scholar 

  57. 57

    A. E. Kryukova, A. C. Kozlova, P. V. Konarev, V. V. Volkov, and V. E. Asadchikov, Crystallogr. Rep. 63, 531 (2018).

    ADS  Article  Google Scholar 

  58. 58

    L. H. Allen and E. Matijevic, J. Colloid Interface Sci. 31, 287 (1969).

    ADS  Article  Google Scholar 

  59. 59

    J. Depasse and A. Watillon, J. Colloid Interface Sci. 33, 430 (1970).

    ADS  Article  Google Scholar 

  60. 60

    A. C. J. H. Johnson, P. Greenwood, M. Hagstrom, Z. Abbas, and S. Wall, Langmuir 24, 12798 (2008).

    Article  Google Scholar 

  61. 61

    V. V. Volkov, private commun.

  62. 62

    V. Honkimäki, H. Reichert, J. Okasinski, and H. Dosch, J. Synchrotr. Rad. 13, 426 (2006).

    Google Scholar 

  63. 63

    C. Ponchut, J. Rigal, J. Clément, E. Papillon, A. Homs, and S. Petitdemange, J. Instrum. 6, C01069 (2011).

    Article  Google Scholar 

  64. 64

    I. V. Kozhevnikov and M. V. Pyatakhin, J. X-Ray Sci. Technol. 8, 253 (2000).

    Google Scholar 

  65. 65

    I. V. Kozhevnikov, Nucl. Instrum. Methods Phys. Res., Sect. A 508, 519 (2003).

    Google Scholar 

  66. 66

    I. V. Kozhevnikov, L. Peverini, and E. Ziegler, Phys. Rev. B 85, 125439 (2012).

    ADS  Article  Google Scholar 

  67. 67

    A. M. Tikhonov, JETP Lett. 92, 356 (2010).

    ADS  Article  Google Scholar 

  68. 68

    A. M. Tikhonov, V. E. Asadchikov, and Yu. O. Volkov, JETP Lett. 102, 478 (2015).

    ADS  Article  Google Scholar 

  69. 69

    A. M. Tikhonov and Yu. O. Volkov, J. Exp. Theor. Phys. 129, 368 (2019).

    ADS  Article  Google Scholar 

  70. 70

    I. V. Kozhevnikov, Doctoral (Phys. Math.) Dissertation (IK RAN, 2013).

  71. 71

    R. Kanwal, Generalized Functions: Theory and Technique, 2nd ed. (Birkhäuser, Basel, 1998).

    MATH  Google Scholar 

  72. 72

    L. G. Parratt, Phys. Rev. 95, 359 (1954).

    ADS  Article  Google Scholar 

  73. 73

    B. L. Henke, E. M. Gullikson, and J. C. Davis, At. Data Nucl. Data Tables 54, 181 (1993).

    ADS  Article  Google Scholar 

  74. 74

    J. C. Stover, Optical Scattering: Measurement and Analysis, 3rd ed. (SPIE Press, 2012).

    Google Scholar 

  75. 75

    A. V. Vinogradov, I. A. Brytov, and A. Ya. Grudskii, Mirror X-Ray Optics (Mashinostroenie, Leningrad, 1989) [in Russian].

    Google Scholar 

  76. 76

    A. Yu. Karabekov and I. V. Kozhevnikov, J. X-ray Sci. Technol. 4, 37 (1993).

    Article  Google Scholar 

  77. 77

    A. Yu. Karabekov and I. V. Kozhevnikov, Proc. SPIE 2453, 176 (1995).

    ADS  Article  Google Scholar 

  78. 78

    A. Braslau, P. S. Pershan, G. Swislow, B. M. Ocko, and J. Als-Nielsen, Phys. Rev. A 38, 2457 (1988).

    ADS  Article  Google Scholar 

  79. 79

    L. Nevot and P. Croce, Rev. Phys. Appl. 15, 761 (1980).

    Article  Google Scholar 

  80. 80

    J. Nocedal and S. Wright, Numerical Optimization, 2nd ed. (Springer, New York, 2006).

    MATH  Google Scholar 

  81. 81

    D. K. Schwartz, M. L. Schlossman, E. H. Kawamoto, G. J. Kellogg, P. S. Pershan, and B. M. Ocko, Phys. Rev. A 41, 5687 (1990).

    ADS  Article  Google Scholar 

  82. 82

    M. Sanyal, S. Sinha, K. Huang, and B. Ocko, Phys. Rev. Lett. 66, 628 (1991).

    ADS  Article  Google Scholar 

  83. 83

    B. R. McClain, D. D. Lee, B. L. Carvalho, S. G. J. Mochrie, S. H. Chen, and J. D. Litster, Phys. Rev. Lett. 72, 246 (1994).

    ADS  Article  Google Scholar 

  84. 84

    P. S. Pershan, Synchrotr. Rad. News 12 (2), 17 (1999).

    Article  Google Scholar 

  85. 85

    D. M. Mitrinovic, A. M. Tikhonov, M. Li, Z. Huang, and M. L. Schlossman, Phys. Rev. Lett. 85, 582 (2000).

    ADS  Article  Google Scholar 

  86. 86

    M. Li, D. J. Chaiko, A. M. Tikhonov, and M. L. Schlossman, Phys. Rev. Lett. 86, 5934 (2001).

    ADS  Article  Google Scholar 

  87. 87

    M. Li, A. M. Tikhonov, and M. L. Schlossman, Europhys. Lett. 58, 80 (2002).

    ADS  Article  Google Scholar 

  88. 88

    A. M. Tikhonov, M. Li, and M. L. Schlossman, J. Phys. Chem. B 105, 8065 (2001).

    Article  Google Scholar 

  89. 89

    A. M. Tikhonov, JETP Lett. 104, 309 (2016).

    ADS  Article  Google Scholar 

  90. 90

    A. M. Tikhonov, JETP Lett. 106, 743 (2017).

    ADS  Article  Google Scholar 

  91. 91

    F. Family and T. Vicsek, J. Phys. A 18, L75 (1985).

    ADS  Article  Google Scholar 

  92. 92

    A.-L. Barabasi and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge Univ. Press, Cambridge, 1995).

    MATH  Book  Google Scholar 

  93. 93

    G. Palasantzas, Phys. Rev. B 48, 14472 (1993).

    ADS  Article  Google Scholar 

  94. 94

    P. Jungwirth and D. J. Tobias, J. Phys. Chem. B 106, 6361 (2002).

    Article  Google Scholar 

  95. 95

    C. D. Wick and L. X. Dang, J. Chem. Phys. 133, 024705 (2010).

    ADS  Article  Google Scholar 

  96. 96

    M. Manciu and E. Ruckenstein, Colloids Surf. A 404, 93 (2012).

    Article  Google Scholar 

  97. 97

    M. A. Vorotyntsev and S. N. Ivanov, Sov. Phys. JETP 61, 1028 (1985).

    Google Scholar 

  98. 98

    E. Wigner, Phys. Rev. 46, 1002 (1934).

    ADS  Article  Google Scholar 

  99. 99

    E. Wigner, Trans. Faraday Soc. 34, 678 (1938).

    Article  Google Scholar 

  100. 100

    I. Rouzina and V. A. Bloomfield, J. Phys. Chem. 100, 9977 (1996).

    Article  Google Scholar 

  101. 101

    N. Gronbech-Jensen, R. J. Mashl, R. F. Bruinsma, and W. M. Gelbart, Phys. Rev. Lett. 78, 2477 (1997).

    ADS  Article  Google Scholar 

  102. 102

    B. I. Shklovskii, Phys. Rev. Lett. 82, 3268 (1999).

    ADS  Article  Google Scholar 

  103. 103

    J. H. Chu and I. Lin, Phys. Rev. Lett. 72, 4009 (1994).

    ADS  Article  Google Scholar 

  104. 104

    A. Melzer, Phys. Rev. E 67, 016411 (2003).

    ADS  Article  Google Scholar 

  105. 105

    J. N. Tan, J. J. Bollinger, B. Jelenkovic, and D. J. Wineland, Phys. Rev. Lett. 75, 4198 (1995).

    ADS  Article  Google Scholar 

  106. 106

    J. M. Saint, C. Even, and C. Guthmann, Europhys. Lett. 55, 45 (2001).

    ADS  Article  Google Scholar 

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ACKNOWLEDGMENTS

The authors are grateful to H. Isern, T. Buslaps, and F. Russello (ESPF) for their help in preparing experiments and to H. Reichert, I.V. Kozhevnikov, and Yu.A. Ermakov for their keen interest and fruitful discussions of experimental results.

Funding

Experiments at the ID31 station were performed under research projects SC-4246, SC-4461, and SC-4845 of the European Synchrotron Radiation Facility (ESRF), Grenoble, France. This study was supported by the Ministry of Science and Higher Education of the Russian Federation under State assignment for the Institutes of the Russian Academy of Sciences. The theoretical part of this work was supported by the Russian Science Foundation (project no. 18-12-00108).

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Tikhonov, A.M., Asadchikov, V.E., Volkov, Y.O. et al. Analysis of the Silica Sol Surface Structure by X-Ray Scattering Method. J. Exp. Theor. Phys. 132, 1–17 (2021). https://doi.org/10.1134/S1063776120120110

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