SAXS Determination of Particle Size Distribution for FD100 Silica ERM
The morphology of pharmaceutical excipients and API in nanoscale range may be of critical
importance for the manufacturability, dissolution and bioavailability of a pharmaceutical product.
Small Angle X-Ray Scattering (SAXS) is applied at DANNALAB to determine the particle
size, pore size and specific surface of nanomaterials, both in bulk and in dispersion.
Liquid dispersions of nanoscale particulates are currently used in many applications of drug
delivery and labelling and as ingredients in pharmaceutical and cosmetic formulations. The
development and validation of efficient methods for particle/pore sizing
together with evaluation of standard reference materials, is one of the areas of activity at DANNALAB.
Below we describe the test case of particle sizing for a fraction of silica nanoparticles in
aqueous dispersion, conducted within a collaborative project with IRMM. 
Several different definitions of particle-size distribution are currently in use: number-weighted, volume-weighted and intensity-weighted. Volume-weighted and intensity-weighted distributions are defined as Dv(r)~Dn(r)V(r) and DI(r)~Dn(r)V2(r), where Dn(r) is a number-weighted particle size distribution and V(r) is a function of particle volume. Function
Dn(r) is derived, for example, from TEM measurements.
Prospective colloidal silica standard material ERM FD100 developed by IRMM JRC EU was used
When investigated by TEM, particles form the single-mode distribution with an 18 nm modal
diameter (number-weighted distribution).
Figure 1. A mono-modal particle population with a
modal diameter of 18[nm] estimated with number-weighted particle size distributions by TEM.
During the SAXS characterisation, multiple samples containing an aqueous
dispersion of FD100 were evaluated together with blanks, providing a total of 18 differential patterns.
Several different methods of analysis were used to obtain parameters of number-, volume- and intensity-weighted distributions from the experimental SAXS data.
First, the volume-weighted size distribution function Dv
(r) was reconstructed by the inverse Fourier transform of the differential scattering
pattern. The typical form of the reconstructed distribution is shown in Figure 2.
Figure 2. Volume-weighted particle size distribution
Dv(r) for aqueous dispersion of FD100 shows a well-defined single-mode distribution. Particle radius is
shown as abscissa.
From the recovered Dv(r) function, we
reconstructed the functions of DI(r) and Dn(R)
and obtained the following values for the
particle diameter taken as the maximum of
DI(D): maximum = 210±13 [A]
Dv(D): maximum = 196±13 [A]
Dn(D): maximum = 181±12 [A]
The value for number-weighted distribution
obtained from the SAXS data closely match the
data obtained by TEM.
Figure 3. Theoretical, simulated based on the
Gaussian distribution scattering curve (blue) is shown versus the experimental differential scattering curve (black).
The shape of particle size distribution was found to be close to the Gauss function. The
simulated scattering curve based on the Gauss model closely fits the experimental differential curve, as shown in Figure 3.
Currently this silica dispersion is certified as ERM FD100 (European Reference Material)
and routinely used at DANNALAB and many other laboratories for quality control and method validation.
 The EasySAXS software package is developed by PANalytical BV in cooperation
with DANNALAB and EMBL
 Report: Certification of Equivalent Spherical Diameters of Silica Nanoparticles in Water
ERM®-FD100, IRMM JRC EU
 Certificate of Analysis, ERM®-FD100