Journal of Materials Science

, Volume 46, Issue 19, pp 6437–6452 | Cite as

Quantifying nanoparticle dispersion: application of the Delaunay network for objective analysis of sample micrographs

  • D. J. BrayEmail author
  • S. G. Gilmour
  • F. J. Guild
  • T. H. Hsieh
  • K. Masania
  • A. C. Taylor


Measuring quantitatively the nanoparticle dispersion of a composite material requires more than choosing a particular parameter and determining its correspondence to good and bad dispersion. It additionally requires anticipation of the measure’s behaviour towards imperfect experimental data, such as that which can be obtained from a limited number of samples. It should be recognised that different samples from a common parent population can give statistically different responses due to sample variation alone and a measure of the likelihood of this occurring allows a decision on the dispersion to be made. It is also important to factor into the analysis the quality of the data in the micrograph with it: (a) being incomplete because some of the particles present in the micrograph are indistinguishable or go unseen; (b) including additional responses which are false. With the use of our preferred method, this article investigates the effects on the measured dispersion quality of nanoparticles of the micrograph’s magnification settings, the role of the fraction of nanoparticles visible and the number of micrographs used. It is demonstrated that the best choice of magnification, which gives the clearest indication of dispersion type, is dependent on the type of nanoparticle structure present. Furthermore, it is found that the measured dispersion can be modified by particle loss, through the limitations of micrograph construction, and material/microscope imperfections such as cut marks and optical aberrations which could lead to the wrong conclusions being drawn. The article finishes by showing the versatility of the dispersion measure by characterising various different spatial features.


Silica Nanoparticles Area Fraction Rubber Particle Dispersion Quality Voronoi Polygon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors would like to thank the EPSRC for providing research funding under the grant EP/H00582X and Nanoresins for supplying materials.


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • D. J. Bray
    • 1
    • 2
    Email author
  • S. G. Gilmour
    • 3
  • F. J. Guild
    • 1
  • T. H. Hsieh
    • 1
  • K. Masania
    • 1
  • A. C. Taylor
    • 1
  1. 1.Department of Mechanical EngineeringImperial College LondonLondonUK
  2. 2.School of Mathematical ScienceQueen Mary University of LondonLondonUK
  3. 3.Statistical Sciences Research InstituteUniversity of SouthamptonSouthamptonUK

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