Calculation of Nanoparticle Filler Content in Solid or Liquid Dispersions

R.L. Khalfin, Y. Cohen
Technion – Israel Institute of Technology, IL

Keywords: smaall X-ray scattering, dispersion, nano particles, content


Nano composites have unique properties which depend to a large extent on the quality of the nanoparticle dispersion. An outstanding issue is the quantitative measure of fillers that are actually dispersed to dimensions below a particular aggregate size by the mixing processes. We have developed two variants of a method for evaluating the content of dispersed nano-sized particles using small angle X-ray scattering (SAXS). We therefore use the well known Porod integral of the measured intensity. In our experiments the range of scattering vectors h is from 0.1 to 3 nm-1 (dimensional range of about 2 – 100 nm). The ratio of the filler volume fraction WF calculated from the Porod integral to the actual filler volume fraction‎ (WD) provides a quantitative estimation of the quality of the nano-scale dispersion process, as the fraction of nano-fillers that were successfully dispersed to a scale below about 100 nm. In the case of significant impurities in the matrix, this calculation may be incorrect. If the particle shape is known and the SAXS pattern has a distinctive peak, the quantitative estimation of the dispersion quality (nano index: WF/WD) can be estimated by the experimental and calculated (from WD) peak area comparison.