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A Method for the Quantification of Nanoparticle Dispersion in Nanocomposites Based on Fractal Dimension

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Advances in Material Sciences and Engineering

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

Dispersion quantification provides critical insight and towards understanding and improving the influence of nanoparticle dispersion on the behaviour of the nanocomposite at macro and nanoscale level. This study was precipitated by the limitations of most methods for quantifying dispersion to sufficiently handle issues regarding scalability, complexity, consistency and versatility. A quantity (D0) based on the variance of the fractal dimension was used to quantify dispersion successfully. The concept was validated using real microscopy images. The approach is simple and versatile to implement.

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References

  1. DeLeon VH, Nguyen TD, Nar M, D’Souza NA, Golden TD (2012) Polymer nanocomposites for improved drug delivery efficiency. Mater Chem Phys 132:409–415

    Article  Google Scholar 

  2. Cong H, Radosz M, Towler BF, Shen Y (2007) Polymer-inorganic nanocomposite membranes for gas separation. Sep Purif Technol 55:281–291

    Article  Google Scholar 

  3. Hule R a, Pochan DJ. (2007) Polymer nanocomposites for biomedical applications. MRS Bull 32(4):354–358

    Article  Google Scholar 

  4. Paul DR, Robeson LM (2008) Polymer nanotechnology: nanocomposites. Polymer 49:3187–3204

    Article  Google Scholar 

  5. Dresselhaus MS, Dresselhaus G, Avouris P (2001) Carbon nanotubes. Carbon nanotubes synthesis, structure, properties, and applications. Springer 1–427

    Google Scholar 

  6. Iijima S (1991) Helical microtubules of graphitic carbon. Nature 354(6348):56–58

    Article  Google Scholar 

  7. Meyer RR, Sloan J, Dunin-Borkowski RE, Kirkland AI, Novotny MC, Bailey SR et al (2000) Discrete atom imaging of one-dimensional crystals formed within single-walled carbon nanotubes. Science (80-) 289(5483):1324–1326

    Article  Google Scholar 

  8. Smith BW, Monthioux M, Luzzi DE (1998) Encapsulated C60 in carbon nanotubes. Nature 396(6709):323–324

    Article  Google Scholar 

  9. Esawi AMK, Morsi K, Sayed A, Taher M, Lanka S (2010) Effect of carbon nanotube (CNT) content on the mechanical properties of CNT-reinforced aluminium composites. Compos Sci Technol 70(16):2237–2241

    Article  Google Scholar 

  10. Šupová M, Martynková GS, Barabaszová K (2011) Effect of nanofillers dispersion in polymer matrices: a review. Sci Adv Mater 3(1):1–25

    Article  Google Scholar 

  11. Sandler J, Shaffer MSP, Prasse T, Bauhofer W, Schulte K, Windle AH (1999) Development of a dispersion process for carbon nanotubes in an epoxy matrix and the resulting electrical properties. Polymer (Guildf) 40(21):5967–5971

    Article  Google Scholar 

  12. Huang YY, Terentjev EM (2012) Dispersion of carbon nanotubes: mixing, sonication, stabilization, and composite properties. Polymers. Mol Divers Preserv Int 4:275–295

    Google Scholar 

  13. Bensadoun F, Kchit N, Billotte C, Bickerton S, Trochu F, Ruiz E (2011) A study of nanoclay reinforcement of biocomposites made by liquid composite molding. Int J Polym Sci 2011:1–10

    Article  Google Scholar 

  14. Rastogi R, Kaushal R, Tripathi SK, Sharma AL, Kaur I, Bharadwaj LM (2008) Comparative study of carbon nanotube dispersion using surfactants. J Colloid Interface Sci 328(2):421–428

    Article  Google Scholar 

  15. Xie S, Harkin-Jones E, Shen Y, Hornsby P, McAfee M, McNally T et al (2010) Quantitative characterization of clay dispersion in polypropylene-clay nanocomposites by combined transmission electron microscopy and optical microscopy. Mater Lett 64(2):185–188

    Article  Google Scholar 

  16. Lillehei PT, Kim J-W, Gibbons LJ, Park C (2009) A quantitative assessment of carbon nanotube dispersion in polymer matrices. Nanotechnology 20(32):32–57

    Article  Google Scholar 

  17. Trionfi A, Scrymgeour DA, Hsu JWP, Arlen MJ, Tomlin D, Jacobs JD et al (2008) Direct imaging of current paths in multiwalled carbon nanofiber polymer nanocomposites using conducting-tip atomic force microscopy. J Appl Phys 104(8):28–37

    Article  Google Scholar 

  18. Haslam MD, Raeymaekers B (2013) A composite index to quantify dispersion of carbon nanotubes in polymer-based composite materials. Compos Part B Eng 55(1):16–21

    Article  Google Scholar 

  19. Clark PJ, Evans FC (1954) Distance to nearest neighbor as a measure of spatial relationships in populations. Ecology 35(4):445–453

    Article  Google Scholar 

  20. Luo ZP, Koo JH (2007) Quantifying the dispersion of mixture microstructures. J Microsc 225(2):118–125

    Article  MathSciNet  Google Scholar 

  21. Bakshi SR, Batista RG, Agarwal A (2009) Quantification of carbon nanotube distribution and property correlation in nanocomposites. Compos Part A Appl Sci Manuf 40(8):1311–1318

    Article  Google Scholar 

  22. Kim SH, Il Lee W, Park JM (2009) Assessment of dispersion in carbon nanotube reinforced composites using differential scanning calorimetry. Carbon 47(11):2699–2703

    Article  Google Scholar 

  23. Kim D, Lee JS, Barry CMF, Mead JL (2007) Microscopic measurement of the degree of mixing for nanoparticles in polymer nanocomposites by TEM images. Microsc Res Tech 70(6):539–546

    Article  Google Scholar 

  24. Gleason HA (1920) Society some applications of the Quadrat method. Bull Torrey Bot Club 47(1):21–33

    Article  Google Scholar 

  25. Yazdanbakhsh A, Grasley Z, Tyson B, Abu Al-Rub RK (2011) Dispersion quantification of inclusions in composites. Compos Part A Appl Sci Manuf 42(1):75–83

    Article  Google Scholar 

  26. Fan LT, Chen YM, Lai FS (1990) Recent developments in solids mixing. Powder Technol 61(3):255–287

    Article  Google Scholar 

  27. Rhodes M (2008) Introduction to particle technology. Chem Eng Process 7:450

    Google Scholar 

  28. Broughton WR, Koukoulas T, Woolliams P, Williams J, Rahatekar SS (2013) Assessment of nanoparticle loading and dispersion in polymeric materials using optical coherence tomography. Polym Test. 32(7):1290–1298

    Article  Google Scholar 

  29. Nayak SR, Mishra J, Palai G (2018) A modified approach to estimate fractal dimension of gray scale images. Optik (Stuttg) 161:136–145

    Article  Google Scholar 

  30. Asvestas P, Matsopoulos GK, Nikita KS (1998) A power differentiation method of fractal dimension estimation for 2-D signals. J Vis Commun Image Represent 9(4):392–400

    Article  Google Scholar 

  31. Lin KH, Lam KM, Siu WC (2001) Locating the eye in human face images using fractal dimensions. IEE Proc Vis Image Sig Process 148(6):413–421

    Article  Google Scholar 

  32. Voss RF (1986) Characterization and measurement of random fractals. Phys Scr 13:27–32

    Article  Google Scholar 

  33. Keller JM, Crownover RM, Chen RY (1987) Characteristics of natural scenes related to the fractal dimension. IEEE Trans Pattern Anal Mach Intell 9(5):621–627

    Article  Google Scholar 

  34. Keller JM, Chen S, Crownover RM (1989) Texture description and segmentation through fractal geometry. Comput Vis Graph Image Process 45(2):150–166

    Article  Google Scholar 

  35. Gagnepain JJ, Roques-Carmes C (1986) Fractal approach to two-dimensional and three-dimensional surface roughness. Wear 109(1–4):119–126

    Article  Google Scholar 

  36. Chen W-S, Yuan S-Y, Hsieh C-M (2003) Two algorithms to estimate fractal dimension of gray-level images. Opt Eng 42(8):2452

    Article  Google Scholar 

  37. Xu S, Weng Y (2006) A new approach to estimate fractal dimensions of corrosion images. Pattern Recognit Lett 27(16):1942–1947

    Article  Google Scholar 

  38. Moisy F (2008) Fractal dimension using the “box-counting” method for 1D, 2D and 3D sets. Available from https://www.mathworks.com/matlabcentral/fileexchange/13063-boxcount?focused=5083247&tab=example

  39. Ma PC, Siddiqui NA, Marom G, Kim JK (2010) Dispersion and functionalization of carbon nanotubes for polymer-based nanocomposites: a review. Compos Part A Appl Sci Manuf 41(10):1345–1367

    Article  Google Scholar 

  40. Naguib HM, Ahmed MA, Abo-Shanab ZL (2018) Silane coupling agent for enhanced epoxy-iron oxide nanocomposite. J Mater Res Technol 7(1):21–28

    Article  Google Scholar 

  41. Dalod ARM, Henriksen L, Grande T, Einarsrud M-A (2017) Functionalized TiO2 nanoparticles by single-step hydrothermal synthesis: the role of the silane coupling agents. Beilstein J Nanotechnol 8:304–312

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering Science, Faculty of Engineering and the Built Environment, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, Johannesburg, South Africa

    K. Anane-Fenin & Esther T. Akinlabi

  2. Arts et Métiers ParisTech, CNRS, 12M Bordeaux, Esplanade des Arts et Métiers, Talence, France

    N. Perry

Authors
  1. K. Anane-Fenin
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  2. Esther T. Akinlabi
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  3. N. Perry
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Corresponding author

Correspondence to K. Anane-Fenin .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Universiti Teknologi PETRONAS, Seri Iskandar, Perak, Malaysia

    Mokhtar Awang

  2. Department of Mechanical Engineering, Universiti Teknologi PETRONAS, Seri Iskandar, Perak, Malaysia

    Seyed Sattar Emamian

  3. Department of Mechanical Engineering, University of Malaya, Kuala Lumpur, Malaysia

    Farazila Yusof

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Anane-Fenin, K., Akinlabi, E.T., Perry, N. (2020). A Method for the Quantification of Nanoparticle Dispersion in Nanocomposites Based on Fractal Dimension. In: Awang, M., Emamian, S., Yusof, F. (eds) Advances in Material Sciences and Engineering. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-8297-0_57

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  • DOI: https://doi.org/10.1007/978-981-13-8297-0_57

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-8296-3

  • Online ISBN: 978-981-13-8297-0

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