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Advances in Condensed Matter Physics
Volume 2015, Article ID 501281, 5 pages
http://dx.doi.org/10.1155/2015/501281
Research Article

Microscale Fragmentation and Small-Angle Scattering from Mass Fractals

1Joint Institute for Nuclear Research, Dubna 141980, Russia
2Horia Hulubei National Institute of Physics and Nuclear Engineering, 077125 Bucharest-Magurele, Romania

Received 21 April 2015; Revised 29 July 2015; Accepted 30 July 2015

Academic Editor: Fajun Zhang

Copyright © 2015 E. M. Anitas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. B. Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman, 1983.
  2. J.-F. Gouyet, Physics and Fractal Structures, Springer, 1996. View at MathSciNet
  3. T. Vicsek, Fractal Growth Phenomena, World Scientific Publishing Co., Inc., Teaneck, NJ, Singapore, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  4. M. Bittelli, G. S. Campbell, and M. Flury, “Characterization of particle-size distribution in soils with a fragmentation model,” Soil Science Society of America Journal, vol. 63, no. 4, pp. 782–788, 1999. View at Publisher · View at Google Scholar · View at Scopus
  5. D. L. Turcotte, “Fractals and fragmentation,” Journal of Geophysical Research, vol. 91, no. 2, pp. 1921–1926, 1986. View at Publisher · View at Google Scholar · View at Scopus
  6. D. L. Turcotte, Fractals and Chaos in Geology and Geophysics, Cambridge University Press, 2nd edition, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  7. H. W. Baac, J. G. Ok, A. Maxwell et al., “Carbon-nanotube optoacoustic lens for focused ultrasound generation and high-precision targeted therapy,” Scientific Reports, vol. 2, article 989, 2012. View at Publisher · View at Google Scholar · View at Scopus
  8. O. Glatter and O. Kratky, Small-Angle X-Ray Scattering, Academic Press, London, UK, 1982.
  9. L. A. Feigin and D. I. Svergun, Structure Analysis by Small-Angle X-Ray and Neutron Scattering, Springer, New York, NY, USA, 1987. View at Publisher · View at Google Scholar
  10. J. E. Martin and A. J. Hurd, “Scattering from fractals,” Journal of Applied Crystallography, vol. 20, no. 2, pp. 61–78, 1987. View at Publisher · View at Google Scholar
  11. P. W. Schmidt, “Small-angle scattering studies of disordered, porous and fractal systems,” Journal of Applied Crystallography, vol. 24, part 5, pp. 414–435, 1991. View at Publisher · View at Google Scholar
  12. M. Balasoiu, E. M. Anitas, I. Bica et al., “SANS of interacting magnetic micro-sized Fe particles in a Stomaflex creme polymer matrix,” Optoelectronics and Advanced Materials—Rapid Communications, vol. 2, no. 11, pp. 730–734, 2008. View at Google Scholar
  13. E. M. Anitas, M. Balasoiu, I. Bica, V. A. Osipov, and A. I. Kuklin, “Small-angle neutron scattering analysis of the microstructure of stomaflex crème—ferrofluid based elastomers,” Optoelectronics and Advanced Materials—Rapid Communications, vol. 3, no. 6, pp. 621–625, 2009. View at Google Scholar · View at Scopus
  14. V. Maneeratana, J. D. Bass, T. Azaïs et al., “Fractal inorganic−organic interfaces in hybrid membranes for efficient proton transport,” Advanced Functional Materials, vol. 23, no. 22, pp. 2872–2880, 2013. View at Publisher · View at Google Scholar · View at Scopus
  15. H. Amjad, Z. Khan, and V. V. Tarabara, “Fractal structure and permeability of membrane cake layers: effect of coagulation-flocculation and settling as pretreatment steps,” Separation and Purification Technology, vol. 143, pp. 40–51, 2015. View at Publisher · View at Google Scholar · View at Scopus
  16. A. Das, S. Mazumder, D. Sen et al., “Small-angle neutron scattering as a probe to decide the maximum limit of chemical waste immobilization in a cement matrix,” Journal of Applied Crystallography, vol. 47, no. 1, pp. 421–429, 2014. View at Publisher · View at Google Scholar · View at Scopus
  17. K. Cho, P. Biswas, and P. Fraundorf, “Characterization of nanostructured pristine and Fe- and V-doped titania synthesized by atomization and bubbling,” Journal of Industrial and Engineering Chemistry, vol. 20, no. 2, pp. 558–563, 2014. View at Publisher · View at Google Scholar · View at Scopus
  18. M.-L. Craus, A. K. Islamov, E. M. Anitas, N. Cornei, and D. Luca, “Microstructural, magnetic and transport properties of La0.5Pr0.2Pb0.3-xSrx MnO3 manganites,” Journal of Alloys and Compounds, vol. 592, pp. 121–126, 2014. View at Publisher · View at Google Scholar · View at Scopus
  19. T. Naito, H. Yamamoto, K. Okuda et al., “Magnetic ordering of spin systems having fractal dimensions: experimental study,” The European Physical Journal B, vol. 86, article 410, 2014. View at Publisher · View at Google Scholar
  20. I. Yadav, S. Kumar, V. K. Aswal, and J. Kohlbrecher, “Small-angle neutron scattering study of differences in phase behavior of silica nanoparticles in the presence of lysozyme and bovine serum albumin proteins,” Physical Review E, vol. 89, no. 3, Article ID 032304, 9 pages, 2014. View at Publisher · View at Google Scholar
  21. R. Gebhardt, “Effect of filtration forces on the structure of casein micelles,” Journal of Applied Crystallography, vol. 47, no. 1, pp. 29–34, 2014. View at Publisher · View at Google Scholar
  22. J. Maji, S. M. Bhattacharjee, F. Seno, and A. Trovato, “Melting behavior and different bound states in three-stranded DNA models,” Physical Review E, vol. 89, no. 1, Article ID 012121, 2014. View at Publisher · View at Google Scholar
  23. H. D. Bale and P. W. Schmidt, “Small-angle X-ray-scattering investigation of submicroscopic porosity with fractal properties,” Physical Review Letters, vol. 53, no. 6, pp. 596–599, 1984. View at Publisher · View at Google Scholar
  24. P. W. Schmidt and X. Dacai, “Calculation of the small-angle x-ray and neutron scattering from nonrandom (regular) fractals,” Physical Review A, vol. 33, article 560, 1986. View at Publisher · View at Google Scholar · View at Scopus
  25. J. Teixeira, “Small-angle scattering by fractal systems,” Journal of Applied Crystallography, vol. 21, no. 6, pp. 781–785, 1988. View at Publisher · View at Google Scholar
  26. A. Y. Cherny, E. M. Anitas, V. A. Osipov, and A. I. Kuklin, “Deterministic fractals: extracting additional information from small-angle scattering data,” Physical Review E, vol. 84, no. 3, Article ID 036203, 2011. View at Publisher · View at Google Scholar
  27. D. Günther, D. Y. Borin, S. Günther, and S. Odenbach, “X-ray micro-tomographic characterization of field-structured magnetorheological elastomers,” Smart Materials and Structures, vol. 21, no. 1, Article ID 015005, 2012. View at Publisher · View at Google Scholar
  28. A. Y. Cherny, E. M. Anitas, V. A. Osipov, and A. I. Kuklin, “Small-angle scattering from multiphase fractals,” Journal of Applied Crystallography, vol. 47, no. 1, pp. 198–206, 2014. View at Publisher · View at Google Scholar · View at Scopus
  29. E. M. Anitas, “Small-angle scattering from fat fractals,” The European Physical Journal B, vol. 87, p. 139, 2014. View at Publisher · View at Google Scholar
  30. I. Bica, E. M. Anitas, L. M. E. Averis, and M. Bunoiu, “Magnetodielectric effects in composite materials based on paraffin, carbonyl iron and graphene,” Journal of Industrial and Engineering Chemistry, vol. 21, pp. 1323–1327, 2015. View at Publisher · View at Google Scholar · View at Scopus
  31. E. M. Anitas, “Scattering structure factor from fat fractals,” Romanian Journal of Physics, vol. 60, no. 5-6, p. 647, 2015. View at Google Scholar
  32. R. Wengeler, F. Wolf, N. Dingenouts, and H. Nirschl, “Characterizing dispersion and fragmentation of fractal, pyrogenic silica nanoagglomerates by small-angle X-ray scattering,” Langmuir, vol. 23, no. 8, pp. 4148–4154, 2007. View at Publisher · View at Google Scholar · View at Scopus
  33. G. Beaucage, “Approximations leading to a unified exponential/power-law approach to small-angle scattering,” Journal of Applied Crystallography, vol. 28, no. 6, pp. 717–728, 1995. View at Publisher · View at Google Scholar