Skip to main content

Fractal Behaviour of Porous Glasses

  • Chapter
Disordered Solids

Part of the book series: Ettore Majorana International Science Series ((PHYSC,volume 46))

  • 83 Accesses

Abstract

Fractal geometry provides a measure of randomness and permits characterization of porous materials and systems having rough surfaces. Fractal objects show dilation symmetry implying that the essential geometric features are invariant to scale changes such as magnification factors. Theoretical background and experimental methods for studying fractal structure such as low-angle neutron and X-ray scattering, adsorption and energy transfer between donor and acceptor molecules embedded in fractal structures are presented. It will be shown that results obtained today by various methods provide different answers about the fractal dimensionality. A proposition is made for unifying the different methods.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B.B. Mandelbrot, “Fractals: Form, Chance and Dimension”, W.H. Freeman, San Francisco, 1977.

    Google Scholar 

  2. D.W. Schaefer and K.D. Keefer, Phys. Rev. Lett. 53, 1383 (1984).

    Article  ADS  Google Scholar 

  3. D.W. Schaefer, J.E. Martin, P. Wiltzius and D.S. Cannell, Phys. Rev. Lett. 52, 2371 (1984).

    Article  ADS  Google Scholar 

  4. P. Pfeifer and D. Avnir, J. Chem. Phys. 79, 3558–3566 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  5. H.D. Bale and P.W. Schmidt, Phys. Rev. Lett. 53, 596 (1984).

    Article  ADS  Google Scholar 

  6. U. Even, K. Rademann, J. Jortner, N. Manor and R. Reisfeld, Phys. Rev. Lett. 52, 2164 (1984).

    Article  ADS  Google Scholar 

  7. D.W. Schaefer and K.D. Keefer, Structure of random silicates: Polymers, colloids and porous solids, in “Fractals in Physics”, Eds. L. Pietronero and E. Tosatti, North-Holland, Amsterdam - Oxford - New York - Tokyo, 1986. Part II, p 39.

    Google Scholar 

  8. S. Alexander and R. Orbach, J. Phys. Lett. (Paris) 4a, L625 (1982).

    Article  Google Scholar 

  9. R. Rammal and G. Toulouse, J. Phys. Lett. 44, L-13 (1983).

    Article  Google Scholar 

  10. B.B. Mandelbrot, “The Fractal Geometry of Nature”, W.H. Freeman, San Francisco, 1982.

    Google Scholar 

  11. J.P. Allen, J.J. Colvin, D.G. Stimson, C.P. Flynn and H.J. Stapleton, J. Biophys. 38, 299 (1982)

    Article  Google Scholar 

  12. H.J. Stapleton, J.P.Allen, C.P.Flynn, D.G. Stimson and S.R. Kurz, Phys. Rev. Lett. 45, 1456 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  13. a) P.W. Kylmko and R. Kopelman, J. Phys. Chem. 8, 4565 (1983)

    Google Scholar 

  14. P. Argyrakis and R. Kopelman, Phys. Rev. B: Condens. Matter 2, 511 (1984).

    Article  ADS  Google Scholar 

  15. P. Argyrakis and R. Kopelman, J. Chem. Phys. 81, 1015 (1984).

    Article  ADS  Google Scholar 

  16. a) P. Evesque, J. Phys. (Les Ulis, Fr) 44, 1217 (1983).

    Google Scholar 

  17. P. Evesque and J. Duran, J. Chem. Phys. 80, 3016 (1984).

    Article  ADS  Google Scholar 

  18. S. Alexander, C. Laermans, R. Orbach and H.M. Rosenberg, Phys. Rev. B 28, 4615 (1983).

    Article  ADS  Google Scholar 

  19. P.F. Tua, S.J. Puttermann and R. Orbach, Phys. Lett. 98A, 357 (1983).

    Article  Google Scholar 

  20. B. Berrida, R. Orbach and K.-W. Yu, Phys. Rev. B 29, 6645 (1984).

    Article  ADS  Google Scholar 

  21. A. Aharony, S. Alexander, O. Entin-Wohlman and R. Orbach, Phys. Rev. B. 31, 2565 (1985).

    Article  ADS  Google Scholar 

  22. R. Rammal and G. Toulouse, J. Phys. Lett. (Paris) 41, L625 (1982).

    Google Scholar 

  23. S. Kelham and H.M. Rosenberg, J. Phys. C 14, 1737 (1981).

    Article  ADS  Google Scholar 

  24. U. Buchenau, N. Nucker and A.J. Dianoux, Phys. Rev. Lett. 51, 2316 (1984).

    Article  ADS  Google Scholar 

  25. J. Klafter and A. Blumen, J. Chem. Phys. 80, 875 (1984).

    Article  ADS  Google Scholar 

  26. D. Rojanski, D. Huppert, H.D. Bale, Xie Dacai, P.W. Schmidt, D. Farin, A, Seri-Levy and D. Avnir, Phys. Rev. Lett. 2, 2505 (1986).

    Article  ADS  Google Scholar 

  27. U. Even, K. Rademann, J. Jortner, N. Manor and R. Reisfeld, Phys. Rev. Lett. 58, 285 (1987).

    Article  ADS  Google Scholar 

  28. U. Even, K. Rademann, J. Jortner, N. Manor and R. Reisfeld, J. Luminescence 31 /32, 634 (1984).

    Article  ADS  Google Scholar 

  29. D. Avnir, D. Farin and P. Pfeifer, Nature 308, 261 (1984).

    Article  ADS  Google Scholar 

  30. V.R. Kaufman and D. Avnir, Langmuir 2, 717 (1986).

    Article  Google Scholar 

  31. D. Farin and D. Avnir, The fractal nature of molecule-surface chemical activities and physical interactions in porous materials. Proc. IUPAC Symp. Characterization of Porous Solids, FRG, April 1987. K.K. Unger et al. Eds. Elsevier, Amsterdam, 1987.

    Google Scholar 

  32. P.W. Schmidt, Small-angle scattering studies of porous solids. Proc. IUPAC Symp. Characterization of Porous Solids, FRG, April 1987. K.K. Unger et al. Eds. Elsevier, Amsterdam, 1987.

    Google Scholar 

  33. A. Guinier, G. Fournet, C.B. Walker and K.L. Yudowitch, “Small-Angle Scattering of X-Rays”. Wiley, New York, 1955.

    Google Scholar 

  34. O. Glatter and O. Kratky, “Small-Angle X-Ray Scattering”. Academic Press, New York, 1982.

    Google Scholar 

  35. Ref. 30, pp. 3–4.

    Google Scholar 

  36. Ref. 31, Chapter 6, especially pp.197–199.

    Google Scholar 

  37. Ref. 30, pp. 5–30.

    Google Scholar 

  38. D.W. Schaefer, B.C. Bunker and J.P. Wilcoxon, Phys. Rev. Lett. 58, 284 (1987).

    Article  ADS  Google Scholar 

  39. S.K. Sinha, J.M. Drake, P. Levitz and G. Grest, unpublished research and paper RRI presented at the meeting of the American Physical Society, New York, March 20, 1987.

    Google Scholar 

  40. D. Avnir, D. Farin and P. Pfeifer, J. Chem. Phys. 79, 3566 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  41. A.J. Katz and A.H. Thompson, Phys. Rev. Lett. 54, 1325 (1985).

    Article  ADS  Google Scholar 

  42. D.L. Huber, Dynamics of incoherent transfer, in “Laser Specroscopy of Solids”, Eds. W.M. Yen and P.M. Selzer, Topics in Applied Physics, Vol. 49, Springer-Verlag, Berlin, Heidelberg, New York, 1981. p 83.

    Google Scholar 

  43. M. Inokuti and F. Hirayama, J. Chem. Phys. 4a, 1978 (1985).

    Google Scholar 

  44. M. Yokota and I. Tanimoto, J. Phys. Soc. (JPN) 22, 779 (1967).

    Article  ADS  Google Scholar 

  45. A. Blumen, J. Klafter, B.S. White and G. Zumofen, Phys. Rev. Lett. 53, 1301 (1984).

    Article  ADS  Google Scholar 

  46. J. Klafter, A. Blumen and G. Zumofen, J. Luminescence 31, 32, 627 (1984).

    Google Scholar 

  47. R. Kopelman, J. Statistical Phys. 42, 185 (1986).

    Article  ADS  Google Scholar 

  48. P. Levitz and J.M. Drake, Phys. Rev. Lett. 58, 686 (1987).

    Article  ADS  Google Scholar 

  49. D. Pines-Rojanski, D. Huppert and D. Avnir, Pore size effects on the fractal distribution of adsorbed molecules as revealed by electronic energy transfer on silica surfaces. Submitted to Chem. Phys. Lett. 1987.

    Google Scholar 

  50. C.L. Yang, P. Evesque and M.A. El-Sayed, J. Phys. Che (1985).

    Google Scholar 

  51. R. Reisfeld, M. Eyal, C.K. Jorgensen and C. Jacoboni, Lett. 129, 392 (1986).

    Google Scholar 

  52. M. Eyal, R. Reisfeld, C.K. Jorgensen and C. Jacoboni, Lett. 129, 550 (1986).

    Google Scholar 

  53. R. Reisfeld and M. Eyal, Acta Physica Polonia, to be

    Google Scholar 

  54. D. Levy, R. Reisfeld and D. Avnir, Chem. Phys. Lett. (1984).

    Google Scholar 

  55. R. Reisfeld, M. Eyal and R. Gvishi, Spectroscopic behaviour of fluorescein and its di(mercury acetate) adduct in glasses. Chem. Phys. Lett., (1987) in publication.

    Google Scholar 

  56. D. Brusilovsky and R. Reisfeld, Comparison of gelation mechanisms of TEOS and TMOS by spectroscopic measurements. Chem. Phys. Lett. submitted.

    Google Scholar 

  57. D. Avnir, D. Levy and R. Reisfeld, J. Phys. Chem. 88, 5956 (1984).

    Article  Google Scholar 

  58. D. Avnir, V.R. Kaufman and R. Reisfeld, J. Noncryst. Solids Z, 395 (1985).

    Google Scholar 

  59. M. Eyal and R. Reisfeld, to be published in Chem. Phys. Lett.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Plenum Press, New York

About this chapter

Cite this chapter

Reisfeld, R. (1989). Fractal Behaviour of Porous Glasses. In: Di Bartolo, B., Özen, G., Collins, J.M. (eds) Disordered Solids. Ettore Majorana International Science Series, vol 46. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5475-8_15

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-5475-8_15

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-5477-2

  • Online ISBN: 978-1-4684-5475-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics