A Better Method for Volume Determination of Regularly and Irregularly   Shaped Nanoparticles with Enhanced Accuracy
  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 NPs (IS-NPs) at high-throughput using a single tool. Here, we present a relatively simple method that statistically determines a better volume estimate of many types 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) and atomic force microscopy (AFM) by using both modeling and measurements. This study also shows that SEM provides a more accurate estimate of size than AFM for most IS-NP size measurements. The method provides a much needed, proper high-throughput volumetric measurement method useful for many applications. 
Ravi Kiran Attota
cond-mat.mes-hall