Analytical and Bioanalytical Chemistry

, Volume 408, Issue 28, pp 7897–7903 | Cite as

Volume determination of irregularly-shaped quasi-spherical nanoparticles

  • Ravi Kiran AttotaEmail author
  • Eileen Cherry Liu
Rapid Communication


Nanoparticles (NPs) are widely used in diverse application areas, such as medicine, engineering, and cosmetics. The size (or volume) of NPs is one of the most important parameters for their successful application. It is relatively straightforward to determine the volume of regular NPs such as spheres and cubes from a one-dimensional or two-dimensional measurement. However, due to the three-dimensional nature of NPs, it is challenging to determine the proper physical size of many types of regularly and irregularly-shaped quasi-spherical NPs at high-throughput using a single tool. Here, we present a relatively simple method that determines a better volume estimate of NPs by combining measurements from their top-down projection areas and peak heights using two tools. The proposed method is significantly faster and more economical than the electron tomography method. We demonstrate the improved accuracy of the combined method over scanning electron microscopy (SEM) or atomic force microscopy (AFM) alone by using modeling, simulations, and measurements. This study also exposes the existence of inherent measurement biases for both SEM and AFM, which usually produce larger measured diameters with SEM than with AFM. However, in some cases SEM measured diameters appear to have less error compared to AFM measured diameters, especially for widely used IS-NPs such as of gold, and silver. The method provides a much needed, proper high-throughput volumetric measurement method useful for many applications.

Graphical Abstract

The combined method for volume determination of irregularly-shaped quasi-spherical nanoparticles


Nanoparticles Characterization Irregularly-shaped nanoparticles Quasi-spherical nanoparticles Spherical volume equivalent diameter Nanotechnology 



The authors would like to thank John Kramar for the useful discussions, Andras Vladar for providing high-quality SEM images of Au nanoparticles used in Ref. [29], and the Summer Undergraduate Research Fellowship (SURF) program of NIST and NSF for providing an internship to Eileen Liu.

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.

Supplementary material

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Copyright information

© Springer-Verlag Berlin Heidelberg (outside the USA) 2016

Authors and Affiliations

  1. 1.Engineering Physics Division, Physical Measurement LaboratoryNational Institute of Standards and TechnologyGaithersburgUSA

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