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Updated: May 12, 2026

Nanoparticle Tracking Analysis of Gold Nanoparticles in Aqueous Media through an Inter-Laboratory Comparison
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Measuring absolute nanoparticle number concentrations from particle count time series.

M Röding1, H Deschout, K Braeckmans

  • 1Department of  Mathematical Statistics, Chalmers University of Technology and Gothenburg University, Gothenburg, Sweden. roding@chalmers.se

Journal of Microscopy
|April 17, 2013
PubMed
Summary

Accurate nanoparticle concentration measurement is vital. A new method uses particle count fluctuations (Smoluchowski process) to estimate absolute concentrations without precise tracking or volume calibration, simplifying nanoparticle characterization.

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Last Updated: May 12, 2026

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Published on: May 22, 2020

Area of Science:

  • Nanotechnology
  • Physical Chemistry
  • Materials Science

Background:

  • Accurate characterization of nanoparticulate matter is essential for various scientific and industrial applications.
  • Precise concentration measurements are critical for understanding nanoparticle behavior and performance.
  • Current methods often require complex calibration or unambiguous particle tracking.

Purpose of the Study:

  • To introduce a novel method for estimating absolute number concentrations of nanoparticles in dispersions.
  • To simplify nanoparticle concentration measurement by avoiding the need for unambiguous particle tracking or pre-calibrated detection volumes.
  • To provide a robust method applicable to various nanoparticle sizes and types.

Main Methods:

  • Utilizes a fluctuating time series of particle counts, modeled as a Smoluchowski process.
  • Requires separate estimation of the particle diffusion coefficient.
  • Estimates the detection region volume directly from observational data, eliminating the need for pre-calibration.

Main Results:

  • The proposed method successfully estimates absolute number concentrations in nanoparticle dispersions.
  • Evaluated through simulation studies and experimental data of polymer nanospheres (0.2- and 0.5-μm).
  • Achieved very good agreement with established reference concentration values.

Conclusions:

  • The Smoluchowski process-based method offers a simplified yet accurate approach to nanoparticle concentration determination.
  • This technique reduces experimental complexity by not requiring particle tracking or volume calibration.
  • The method holds significant potential for routine nanoparticle characterization in research and industry.