ISO 23484:2023

INTERNATIONAL ISO
STANDARD 23484
First edition
2023-07
Determination of particle
concentration by small-angle X-ray
scattering (SAXS)
Détermination de la concentration de particules par diffusion des
rayons X aux petits angles (SAXS)
Reference number
© ISO 2023
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Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms.2
5 Principle of the method . 3
5.1 Particle size detection limits . 4
5.2 Particle concentration detection limits . 4
5.3 Effects of polydispersity . 5
6 Apparatus . 6
7 Preliminary procedures and instrument set-up . 7
8 Sample preparation .7
9 Measurement and data correction procedures . 8
10 Determination of the particle concentration . 8
11 Repeatability .11
12 Documentation and test report .11
12.1 Test report . 11
12.2 Technical records .12
Annex A (informative) Inter-laboratory comparison .13
Bibliography .14
iii
Foreword
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This document was prepared by Technical Committee ISO/TC 24, Particle characterization including
sieving, Subcommittee SC 4, Particle characterization.
Any feedback or questions on this document should be directed to the user’s national standards body. A
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iv
Introduction
Small-angle X-ray scattering (SAXS) is a well-established method to obtain structural information on
inhomogeneities in materials at the nanoscale, typically between 1 nm and 100 nm, and is thus perfectly
suited for nanoparticulate systems. Under certain conditions, the upper limit can be extended to
200 nm and beyond. For sufficiently monodisperse spherical particles, the observed oscillations of the
scattered intensity as a function of the momentum transfer, which is directly related to the scattering
angle and the wavelength of the incident X-rays, enable the size determination of nanoparticles. In
order to determine their concentration in a liquid (also called suspending medium, solvent or matrix),
the absolute differential scattering cross section has to be determined, thus the ratio of the scattered
intensity to the incident intensity. Assumptions on the particle shape are required, which can be based
on microscopic techniques like electron microscopy. Furthermore, the electron density difference
between the particles and the liquid needs to be known.
The concentration of nanoparticles, thus particles in the size range between about 1 nm to 100 nm, is
one of the most important parameters for nanoparticle use in industry, medicine and research, and is
expected to become relevant as well for regulatory purposes, especially in the pharmaceutic sector.
The application of SAXS for the determination of the mean particle size and size distribution has been
described in ISO 17867. This document covers the extension to obtain the nanoparticle concentration
as well from SAXS measurements. User-friendly commercial SAXS instruments are available worldwide
from several manufacturers for both routine and more sophisticated analyses, and state-of-the-art
research instruments are available at synchrotron radiation facilities.
As in all particle size measurement techniques, care is required in all aspects of the use of the
instrument, collection of data, and further interpretation. Therefore, there is a need for a document
that allows users to obtain good inter-laboratory agreement on the accuracy and reproducibility of the
technique.
Since all illuminated particles present in the X-ray beam are measured simultaneously, SAXS results are
ensemble and time averaged across all the particle orientations which are present in the sample.
v
INTERNATIONAL STANDARD ISO 23484:2023(E)
Determination of particle concentration by small-angle
X-ray scattering (SAXS)
1 Scope
This document deals with the application of small-angle X-ray scattering (SAXS) for the measurement
of the particle concentration in suspensions. In this document, only the concentration of sufficiently
monodisperse spherical particles is treated, which means that the width of the size distribution is
typically below about 50 % of the mean diameter. Here, the differential scattering cross section can be
calculated based on the form factor, which depends only on the momentum transfer q and the particle
radius r. Furthermore, this document is limited to dilute systems. A dilute system in the sense of SAXS
means that particle interactions are absent. In case of long-range interactions (Coulomb forces between
the particles), special care needs to be taken and a reduction of the concentration can be necessary.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 17867, Particle size analysis — Small angle X-ray scattering (SAXS)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
particle
minute piece of matter with defined physical boundaries
Note 1 to entry: A physical boundary can also be described as an interface.
Note 2 to entry: A particle can move as a unit.
Note 3 to entry: This definition applies to nano-objects.
[SOURCE: ISO/TS 80004-6:2021, 3.9]
3.2
particle size
linear dimension of a particle (3.1) determined by a specified measurement method and under specified
measurement conditions
Note 1 to entry: Different methods of analysis are based on the measurement of different physical properties.
Independent of the particle property actually measured, the particle size can be reported as a linear dimension,
e.g. as an equivalent spherical diameter.
[SOURCE: ISO/TS 80004-6:2021, 4.1.1]
3.3
particle size distribution
distribution of particles (3.1) as a function of particle size (3.2)
Note 1 to entry: Particle size distribution may be expressed as cumulative distribution or a distribution density
(distribution of the fraction of material in a size class, divided by the width of that class).
[SOURCE: ISO/TS 80004-6:2021, 4.1.2]
3.4
suspension
heterogeneous mixture of materials comprising a liquid and a finely dispersed solid material
[SOURCE: ISO/TS 80004-6:2021, 3.13]
3.5
concentration
amount-of-substance of a component divided by the volume of the system
[SOURCE: ISO 18113-1:2022, 3.2.12]
3.6
particle number concentration
number of particles per unit of volume of suspension
Note 1 to entry: The particle number concentration can also be given as number of particles per unit of mass of
suspension. Literature values for the density of the liquid can be used for the conversion as, in most cases, the
low content of particles for which this document is applicable will not affect the sample density significantly.
[SOURCE: ISO 29464:2017, 3.2.131]
4 Symbols and abbreviated terms
The symbols and abbreviated terms used in this document are listed in Table 1.
Table 1 — Symbols
Symbol Description Unit (with prefix)
-1
C Particle number concentration l
Median of lognormal size distribution nm
d
ln
Number-weighted mean particle diameter nm
d
num
f , f Atomic scattering factors
1 2
g (r) Number-weighted particle size distribution
num
I Primary beam intensity without sample
in
I(q) Scattered intensity (or scattering intensity)
M Molar mass g/mol
N Number of particles
-1
N Avogadro constant mol
A
P(q, r) Particle form factor as functions of q-value and particle radius, r
Momentum transfer or q-value, magnitude of the scattering vector given
-1
q nm
by q = (4π /λ) sin θ
r Particle radius nm
r Thomson radius fm
e
S(q,r) Structure factor as functions of q-value and particle radius, r
T Transmission
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbol Description Unit (with prefix)
t Optimum sample thickness mm
o
w Sample thick
...