Quantification of nanoparticle dispersion within polymer matrix using gap statistics

K. Anane-Fenin, E. T. Akinlabi, N. Perry

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


This study was prompted by the inadequacy of most dispersion quantification techniques to address issues pertaining to scalability, implementation complexity, accuracy/error, uncertainty factors and versatility. Therefore, a method for quantifying dispersion based on gap statistics was developed. A dispersion quantity ( D ) was formulated from a Gap factor Particle spacing dispersity ( PSD 1) and Particle size dispersity ( PSD 2) factors. The summation of the factors resulted in the dispersion parameter ( D p) which must be equal to one for an ideal or uniformly distributed condition. The state of dispersion increases as D → 100%. The concept was tested with simulated models having uniform dispersion, random dispersion, small aggregate, three large aggregate and one large aggregate were successfully quantified to show 99.34%, 82.42%, 34.17%, 8.95% and 3.65% respectively. For validation of concept, the state of dispersion when samples with (scenario 1) and without (scenario 4) silane treatment were quantified as 32,02% and 7.72% respectively. The concepts were then validated using real microscopy images. This approach is robust, versatile and easy to implement.

Original languageEnglish
Article number075310
JournalMaterials Research Express
Issue number7
Publication statusPublished - 5 Apr 2019


  • agglomeration
  • dispersion
  • gap statistics
  • image segmentation
  • nanoparticles

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Surfaces, Coatings and Films
  • Polymers and Plastics
  • Metals and Alloys


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