Nanotechnologies — Evaluation of the mean size of nano-objects in liquid dispersions by static multiple light scattering (SMLS)

This document provides guidance and requirements for the determination of the mean (spherical) equivalent diameter of nano-objects (i.e. particles, droplets or bubbles) dispersed in liquids using the static multiple light scattering (SMLS) technique. The technique is applicable to a wide range of materials and does not require dilution of concentrated samples.

Nanotechnologies — Évaluation de la taille moyenne des nano-objets dans les dispersions liquides par diffusion statique multiple de la lumière (DSML)

Le présent document présente des recommandations et des exigences pour la détermination du diamètre équivalent moyen (sphérique) de nano-objets (particules, gouttelettes ou bulles) dispersés dans des liquides au moyen de la technique de diffusion statique multiple de la lumière (DSML). La technique est applicable à une large gamme de matériaux et n’exige pas la dilution des échantillons concentrés.

General Information

Status
Published
Publication Date
13-Jan-2022
Current Stage
6060 - International Standard published
Start Date
14-Jan-2022
Due Date
05-Sep-2021
Completion Date
14-Jan-2022
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TECHNICAL ISO/TS
SPECIFICATION 21357
First edition
2022-01
Corrected version
2022-03
Nanotechnologies — Evaluation of the
mean size of nano-objects in liquid
dispersions by static multiple light
scattering (SMLS)
Nanotechnologies — Évaluation de la taille moyenne des nano-objets
dans les dispersions liquides par diffusion statique multiple de la
lumière (DSML)
Reference number
ISO/TS 21357:2022(E)
© ISO 2022
---------------------- Page: 1 ----------------------
ISO/TS 21357:2022(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2022

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on

the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below

or ISO’s member body in the country of the requester.
ISO copyright office
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CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
© ISO 2022 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/TS 21357:2022(E)
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 Principles ..................................................................................................................................................................................................................... 3

5.1 Relevant theory ...................................................................................................................................................................................... 3

5.2 Key measurands .................................................................................................................................................................................... 5

5.3 Method applicability and limitations ................................................................................................................................. 6

5.3.1 General ........................................................................................................................................................................................ 6

5.3.2 Sample concentration .................................................................................................................................................... 6

5.3.3 Mean equivalent particle diameter .................................................................................................................... 7

5.3.4 Sample homogeneity and stability ..................................................................................................................... 7

5.4 Method characteristics ................................................................................................................................................................... 7

6 Apparatus .................................................................................................................................................................................................................... 8

7 Measurement procedure ............................................................................................................................................................................. 9

7.1 Instrument preparation ................................................................................................................................................................. 9

7.2 Sample handling .................................................................................................................................................................................... 9

7.3 System settings ................................................................................................................................................................................... 10

7.3.1 General ..................................................................................................................................................................................... 10

7.3.2 Procedure to verify sample homogeneity ................................................................................................. 10

7.3.3 Volume fraction ................................................................................................................................................................ 10

7.3.4 Refractive index ............................................................................................................................................................... 10

8 Performance qualification .....................................................................................................................................................................11

9 Data record .............................................................................................................................................................................................................11

10 Measurement uncertainty ......................................................................................................................................................................11

Annex A (informative) I and I versus l* and l ...................................................................................................................................13

BS T

Annex B (informative) I and I as a function of D for titanium dioxide and melamine resin

BS T

particles ......... .......................... ...................................................................................................................................................................................14

Annex C (informative) Instrument qualification .................................................................................................................................16

Annex D (informative) Comparative analysis of Latex suspensions at various concentrations .......17

Annex E (informative) Analysis of titanium dioxide suspensions at different concentrations .........18

Annex F (informative) Results of an interlaboratory comparison study ..................................................................20

Bibliography .............................................................................................................................................................................................................................23

iii
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ISO/TS 21357:2022(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www.iso.org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to

the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see

www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 229, Nanotechnologies.

This corrected version of ISO/TS 21357:2022 incorporates the following correction:

— the IEC logo has been removed from the cover page.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www.iso.org/members.html.
© ISO 2022 – All rights reserved
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ISO/TS 21357:2022(E)
Introduction

Dispersions of nanoparticles in liquids are widely used in industry. Nanoparticles dispersed in liquids

interact via a variety of weak and strong forces, which can lead to aggregation or agglomeration of

objects (primary particles, agglomerates, aggregates, etc.). As a result, the dispersion state and the

apparent mean particle size and size distribution can differ from those determined during product

manufacturing, storage, and processing, particularly when using measurements requiring sample

dilution or extensive preparation. Sample preparation can result in breaking or formation of aggregates

or agglomerates and in some cases can also affect morphology of primary particles. Industrial

stakeholders require analytical methods that are applicable to dispersions in their native state for

reasons of product development, quality control and regulatory compliance.

While many methods exist for characterization of nanoparticle properties, in particular their size and

size distribution, these methods typically require a specific and frequently complex sample preparation

(e.g. dilution, stirring, shearing or pumping) and, therefore, do not yield characteristics specific to as-

received dispersions. In addition, some experiments do not require measurement of a full particle

size distribution with the mean particle size being the main measurand. Using the mean particle size

measurement, it is possible to monitor other dispersion parameters of the system such as the state of

agglomeration, aggregation or dissolution.

Static multiple light scattering (SMLS) based methods do not require sample preparation allowing,

within limitations outlined in this document, direct measurement of the mean equivalent particle

diameter in the native (as-received) state of dispersion. In addition, and beyond the scope of this

document, SMLS is capable in some cases of monitoring in real time the temporal evolution of mean

equivalent particle diameter due to agglomeration or aggregation processes.

This document describes a standardized method for evaluating the mean equivalent particle diameter

in various sample types (including as-received samples) having a wide range of concentrations using

the SMLS based method.
© ISO 2022 – All rights reserved
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TECHNICAL SPECIFICATION ISO/TS 21357:2022(E)
Nanotechnologies — Evaluation of the mean size of nano-
objects in liquid dispersions by static multiple light
scattering (SMLS)
1 Scope

This document provides guidance and requirements for the determination of the mean (spherical)

equivalent diameter of nano-objects (i.e. particles, droplets or bubbles) dispersed in liquids using

the static multiple light scattering (SMLS) technique. The technique is applicable to a wide range of

materials and does not require dilution of concentrated samples.
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/TS 80004-1, Nanotechnologies — Vocabulary — Part 1: Core terms
ISO/TS 80004-2, Nanotechnologies — Vocabulary — Part 2: Nano-objects
ISO/TS 80004-4, Nanotechnologies — Vocabulary — Part 4: Nanostructured materials

ISO/TS 80004-6, Nanotechnologies — Vocabulary — Part 6: Nano-object characterization

3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO/TS 80004-1, ISO/TS 80004-2,

ISO/TS 80004-4, ISO/TS 80004-6 and the following 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
static multiple light scattering
SMLS

technique in which transmitted or backscattered light intensity is measured after multiple successive

scattering events of incident light in a random scattering medium
3.2
transport mean free path

average distance that a photon travels before its direction vector in its initial direction of motion is

reduced to 1/e of its initial magnitude by elastic scattering alone

[SOURCE: ISO 18115-1:2013, 4.299, modified — "an energetic particle" has been changed to "a photon";

"momentum" has been changed to "direction vector"; "initial value" has been changed to "initial

magnitude"; notes to entry have been deleted.]
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ISO/TS 21357:2022(E)
3.3
mean free path
mean distance between photon scattering events in a dispersion

[SOURCE: ISO 22493:2014, 3.2.4, modified — "electron" has been changed to "photon".]

3.4
volume fraction
quotient of the volume of a specified component and the total sample volume
3.5
refractive index

ratio of the speed of light (more exactly, the phase velocity) in a vacuum to the speed of that same light

in a material

[SOURCE: ISO 18369-1:2017, 3.1.6.3, modified — “(more exactly, the phase velocity)” has been added;

the alternative preferred term "index of refraction" and note 1 to entry have been deleted.]

3.6
equivalent particle diameter

diameter of the sphere with defined characteristics which behaves under defined conditions in exactly

the same way as the particle being described
[SOURCE: ISO 21501-1:2009, 2.4]
3.7
absorption
reduction of intensity of a light beam not due to scattering
[SOURCE: ISO 13320:2020, 3.1.1]
4 Symbols and abbreviated terms
I backscattered light intensity
I transmitted light intensity
transport mean free path
mean free path
asymmetry factor
Q extinction efficiency factor
volume fraction
mean equivalent particle diameter
wavelength of the incident light (in vacuum)
R sample half thickness
n refractive index
T light flux transmitted by the continuous phase
TEM transmission electron microscopy
CCD charge-coupled device
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ISO/TS 21357:2022(E)
CMOS complementary metal–oxide–semiconductor
ILC interlaboratory comparison
RM reference material
VAMAS Versailles Project on Advanced Materials and Standards
5 Principles
5.1 Relevant theory

The SMLS technique is based on the principle of elastic light scattering from dispersed objects in a

liquid. Incident light is scattered multiple times successively, which results in a loss of correlation

of the incident light direction. The I or I light depends on the incident light wavelength, particle

BS T

concentration, particle size and shape, optical properties (n and absorption of both the continuous and

dispersed phases), and the measurement geometry.

Light propagation in concentrated dispersions (Figure 1) can be characterised by two parameters: the

[8],[9],[11]

mean free path (Formula (1)), l , and the transport mean free path, l . The mean free path

characterizes scattering phenomena at the microscopic level, while l describes multiple scattering at a

macroscopic level as the penetration depth of radiation in a random medium (i.e. no significant

[14]

correlation between scattering objects). Both parameters l and l are related by the Mie theory

[11]
under the hypothesis where l>λ :
l= (1)
3ϕQ

where D is the mean equivalent particle diameter, ϕ is the volume fraction of the material and Q is the

extinction efficiency factor.
l = (2)
1− g

NOTE 1 The anisotropic scattering of light by an object can be characterized by the asymmetry factor g, which

is the average cosine (cos θ) of the scattering angles weighted by the phase function or scattering diagram of the

[14]

scatterer (e.g. g = 0 for isotropic Rayleigh scatterers and 0 < g < 1 for Mie scatterers) . Q takes into account

scattering efficiency and light absorption phenomena.
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ISO/TS 21357:2022(E)
Key
1 high I signal 2 low I signal
T BS
3 low I signal 4 high I signal
T BS
NOTE The I dependence on the volume fraction is depicted.
Figure 1 — Schematic representation of the I , I , l and l
BS T
[8],[14]

Both Q and g are described by the Mie theory and depend on optical properties of the particles

and the medium, particle size and wavelength of light.

The Mie theory is then used to determine either equivalent particle diameter or volume fraction,

provided that the other is known, from I or I . This is accomplished by comparing the experimental

T BS
values of l or l with the values determined from the Mie theory.
[13]

For measuring (for instance) I from the incident light, it is possible to derive an approximate :

31ϕ()−gQ
α  
2 e
I =+βα= +β (3)
 
l  

Due to the influence of experimental geometry and the optical detector, an output calibration to convert

the raw I and the raw I (e.g. voltage signal) into an exploitable unit is used. The gain α and offset β

BS T

in Formula (3) are determined with a set of samples of different volume fraction with known l

(calculated theoretically with the Mie theory).
[15]
The light-flux transmitted through a sample can be expressed as :
3RQϕ
 
  e
 
 
   
Il(),RT==eeT (4)
T 0 0

NOTE 2 Variations of I and I as a function of l and l respectively are illustrated in Annex A. Variations of

BS T

I and I on mean equivalent particle diameter D for TiO and melamine resin nanoparticles are illustrated in

BS T 2
Annex B.
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ISO/TS 21357:2022(E)
5.2 Key measurands

The measurand used in SMLS is a volume weighted mean equivalent (spherical) particle diameter. For a

polydisperse suspension case, an effective l is defined that takes into account contributions to the

signal from individual particles of various sizes (as described in 5.1). The diameter corresponding to

the effective l is called the mean equivalent (spherical) particle diameter, also see Formula (2).

It can be shown that for particles smaller than the wavelength of light, the measured mean equivalent

[10],[11]

particle diameter linearly correlates with the mean volume diameter, D . In this case,

backscattered light intensity scales approximately as D , meaning that “larger” (but still smaller than

λ ) particles contribute more to the signal.

The dependence of I and I on the mean equivalent particle diameter is shown in Figure 2 by way

BS T

of example. It is the calculated I and I as a function of mean equivalent particle diameter in a 5 %

BS T
volume fraction titanium dioxide aqueous dispersion.
Key
X D [nm] I
Y intensity of light [%] I

Figure 2 — Calculated I and I as a function of particle diameter for an aqueous dispersion

BS T
(n = 1,33) of titanium dioxide (n = 2,50, φ = 5 %, λ = 880 nm)

The I and I signals are instrument and sample dependent. Thus, as a rule of thumb, mean equivalent

T BS

particle diameter estimation is obtained from I signal provided that it is not null and I signal when

T BS
I is null.

NOTE Although outside the scope of the document, for particles larger than λ , the measured mean

[9],[10]

equivalent particle diameter correlates with the mean surface diameter D . In this case, the I signal scales

as D , meaning that “smaller” (but still larger than λ ) particles contribute more to the backscattered intensity.

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ISO/TS 21357:2022(E)
5.3 Method applicability and limitations
5.3.1 General

The SMLS technique can determine the mean equivalent particle diameter of nano-objects in

concentrated dispersions as well as monitor stability of dispersions over time on the very same sample

as it is a non-destructive method. It should be noted that this technique may be used for dispersions of

solid particles in liquids (i.e. suspensions), liquid-in-liquid emulsions and bubble dispersions in liquids.

The SMLS technique does not allow for the analysis of particle size distributions. It yields a single

parameter based on the I or I measurement, which is converted into a mean equivalent particle

BS T

diameter (when the particle concentration and n are known). This limits the applicability of the

measurement technique to dynamic systems where at least one parameter (equivalent particle

diameter or volume fraction) remains constant during the measurement. For mean equivalent particle

diameter measurement, material n and volume fraction shall be known independently. The method has

been successfully applied to measurements of metal oxides, metals, ceramics, emulsions and ultrafine

bubble dispersions in water.
5.3.2 Sample concentration

The ability to analyse undiluted (as-received) samples that have not been modified by sample

preparation is one of the main strengths of the SMLS method. Another feature of the method is the

ability to measure mean equivalent particle diameter for a broad range of concentrations (from very

low to very high concentration). 5.1 describes how I and I relate to system parameters and the

T BS

equivalent particle diameter and concentration. Using the Mie theory, I and I can be calculated for a

BS T

given material (such as 100 nm diameter silica beads in water). Figure 3 shows these data.

Key
X φ [%] I
Y intensity of light [%] I

Figure 3 — Variation of I and I with particle volume fraction for silica beads (n = 1,46) in

T BS
water (n = 1,33) with D = 100 nm and λ = 880 nm
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ISO/TS 21357:2022(E)

The calculated data in Figure 3 are plotted for dispersions with volume fractions varying from 0,001 %

to 40 %. The method equally applies to very low concentration. Although there is no discrete boundary

between single scattering and multiple scattering regimes, it should be noted that phenomenologically

Formulae (3) and (4) are valid in both regimes. The effect of changing concentration is demonstrated

experimentally in Annex E for TiO dispersions in water.

The scattering by dispersed nano-objects depends heavily on several parameters, such as a material’s

n or particle size and the optical set-up of the instrument used for the evaluation. For this reason, the

lower concentration limit is sample/instrument dependent. For the purpose of this document, the lower

applicable concentration value is taken to be approximately 10 % volume fraction.

In the example given in Figure 3, the calculated data reach approximately 40 % volume fraction. Just

like for the lower concentration limit, the upper limit depends on the sample and instrument properties.

5.3.3 Mean equivalent particle diameter

Particles with diameters ranging as widely as 10 nm to 100 μm can be evaluated by SMLS. These size

limits are approximate and depend heavily on the samples. Indeed, just like for volume fraction, the

actual lower and upper size limits are determined by a number of factors, such as the particles and

continuous phase refractive indices, concentration, wavelength of light and instrument set-up.

5.3.4 Sample homogeneity and stability

SMLS is a non-destructive technique based on measurement of I and I over time to characterise

BS T

the physical evolution of a dispersion due to a destabilisation process (e.g. sedimentation, creaming,

[10]

aggregation, agglomeration or coalescence) . In all cases, the time scale of change in dispersion

parameters should be slower than the time required for a single-time-point intensity measurement in

the SMLS data sampling.

NOTE In practice a SMLS single point data acquisition interval at a given cell position is in the millisecond

range.

For the mean equivalent particle diameter measurement of nano-objects by SMLS, the sample

shall be homogeneous in terms of concentration (i.e. no sedimentation, creaming or floatation).

Spatially dependent sampling of data along the measurement cell enables one to identify these local

heterogeneities in the sample.

To identify concentration evolution due to sedimentation or creaming, the SMLS light source scans

a sample cell vertically. Repeating the scans at fixed time intervals provides information about

destabilisation kinetics (i.e. rate of change of concentration). In some systems this can be a critical

indicator of the mean equivalent particle diameter measurement quality since the local volume fraction

of measured objects in the dispersion should be uniform and stable. If local concentration change or

non-uniformity is observed, then the global volume fraction should not be used for particle sizing

measurement or homogenisation is required. In case of varying concentration with time or height, the

mean equivalent particle diameter measurement can increase its uncertainty for I and I according to

BS T
Formulae (3) and (4).
5.4 Method characteristics

Table 1 summarises the characteristics of the technique for the measurement of key dispersion

parameters.
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ISO/TS 21357:2022(E)
Table 1 — SMLS measurement characteristics
Method feature Applicability Notes

Sample preparation Generally not required Sample preparation procedure may not be required (see 7.2).

Concentration range Approximately from Dilution (ISO 14488) of the sample is not necessary; and most

0,000 1 % to 40 % vol- samples are measured in as-received form. Sample concentra-

ume fraction tion limits are discussed in 5.3.2.

Equivalent particle diameter Approximately from The lower and upper size limits are discussed in 5.3.3.

range 10 nm to 100 µm

Stability of suspension Sample should be sta- The size measurement as a function of aging time can be per-

ble during the time formed on the same sample. The allowed range of change of
required for the meas- the intensity is discussed in 5.3.4.
urement

Homogeneity Homogeneous over the The mean particle size and concentration can vary based on

whole sample height the position in the sample. This is due to non-uniform sample

mixing and processes such as sedimentation, creaming or
other instabilities.
Spatially dependent sampling of data along the measurement
cell enables one to identify these local heterogeneities in the
sample. The allowed range of homogeneity of suspension is
discussed in 5.3.4.

Sample preparation can mean any action done onto the sample including dilution, dispersion, sonication, etc. For

samples that have settled or creamed homogenisation prior to the mean equivalent particle diameter measurements is

required to have uniform concentration.
6 Apparatus

The common geometry for this kind of measurement is shown in Figure 4. Light from the source is

directed into a liquid dispersion. Two sensors (e.g. photodiodes, CCD or CMOS) allow for a simultaneous

measurement of the backscattered and transmitted light. The incident light wavelength should

be chosen in order to minimize light absorption by the dispersed particles: near-infrared light is

advantageous to utilize in the measurement of highly absorbent products. The temperature of the

sample should not vary by more than 0,5 °C during the measurement to ensure the repeatability of

the result. Temperature of the dispersion affects a number of parameters such as refractive indices,

viscosity of co
...

SPÉCIFICATION ISO/TS
TECHNIQUE 21357
Première édition
2022-01
Nanotechnologies — Évaluation de la
taille moyenne des nano-objets dans
les dispersions liquides par diffusion
statique multiple de la lumière
(DSML)
Nanotechnologies — Evaluation of the mean size of nano-objects in
liquid dispersions by static multiple light scattering (SMLS)
Numéro de référence
ISO/TS 21357:2022(F)
© ISO 2022
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ISO/TS 21357:2022(F)
DOCUMENT PROTÉGÉ PAR COPYRIGHT
© ISO 2022

Tous droits réservés. Sauf prescription différente ou nécessité dans le contexte de sa mise en œuvre, aucune partie de cette

publication ne peut être reproduite ni utilisée sous quelque forme que ce soit et par aucun procédé, électronique ou mécanique,

y compris la photocopie, ou la diffusion sur l’internet ou sur un intranet, sans autorisation écrite préalable. Une autorisation peut

être demandée à l’ISO à l’adresse ci-après ou au comité membre de l’ISO dans le pays du demandeur.

ISO copyright office
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Publié en Suisse
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ISO/TS 21357:2022(F)
Sommaire Page

Avant-propos .............................................................................................................................................................................................................................iv

Introduction .................................................................................................................................................................................................................................v

1 Domaine d’application ................................................................................................................................................................................... 1

2 Références normatives ..................................................................................................................................................................................1

3 Termes et définitions ...................................................................................................................................................................................... 1

4 Symboles et abréviations ............................................................................................................................................................................2

5 Principes ....................................................................................................................................................................................................................... 3

5.1 Théorie concernée ............................................................................................................................................................................... 3

5.2 Mesurandes principaux .................................................................................................................................................................. 5

5.3 Applicabilité et limites de la méthode ............................................................................................................................... 6

5.3.1 Généralités ............................................................................................................................................................................... 6

5.3.2 Concentration de l’échantillon ............................................................................................................................... 6

5.3.3 Diamètre équivalent moyen des particules ................................... ............................................................. 7

5.3.4 Homogénéité et stabilité de l’échantillon ..................................................................................................... 8

5.4 Caractéristiques de la méthode ............................................................................................................................................... 8

6 Appareillage .............................................................................................................................................................................................................. 9

7 Mode opératoire de mesurage ........................................................................................................................................... .................10

7.1 Préparation des instruments ................................................................................................................................................. 10

7.2 Manipulation des échantillons .............................................................................................................................................. 10

7.3 Paramètres du système ............................................................................................................................................................... 11

7.3.1 Généralités ............................................................................................................................................................................ 11

7.3.2 Mode opératoire de vérification de l’homogénéité de l’échantillon ................................... 11

7.3.3 Fraction volumique ....................................................................................................................................................... 11

7.3.4 Indice de réfraction ....................................................................................................................................................... 11

8 Qualification des performances .......................................................................................................................................................11

9 Enregistrement des données ...............................................................................................................................................................12

10 Incertitude de mesure.................................................................................................................................................................................12

Annexe A (informative) I et I versus l* et l ............................................................................................................................................13

R T

Annexe B (informative) I et I en fonction de D pour des particules de dioxyde de titane et

R T

de résine mélamine ........................................................................................................................................................................................14

Annexe C (informative) Qualification de l’instrument ..................................................................................................................16

Annexe D (informative) Analyse comparative de suspensions de latex à diverses

concentrations ........................................................................................................................................... ..........................................................17

Annexe E (informative) Analyse de suspensions de dioxyde de titane à différentes

concentrations ........................................................................................................................................... ..........................................................18

Annexe F (informative) Résultats d’une étude de comparaison interlaboratoires ........................................20

Bibliographie ...........................................................................................................................................................................................................................23

iii
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ISO/TS 21357:2022(F)
Avant-propos

L’ISO (Organisation internationale de normalisation) est une fédération mondiale d’organismes

nationaux de normalisation (comités membres de l’ISO). L’élaboration des Normes internationales est

en général confiée aux comités techniques de l’ISO. Chaque comité membre intéressé par une étude

a le droit de faire partie du comité technique créé à cet effet. Les organisations internationales,

gouvernementales et non gouvernementales, en liaison avec l’ISO participent également aux travaux.

L’ISO collabore étroitement avec la Commission électrotechnique internationale (IEC) en ce qui

concerne la normalisation électrotechnique.

Les procédures utilisées pour élaborer le présent document et celles destinées à sa mise à jour sont

décrites dans les Directives ISO/IEC, Partie 1. Il convient, en particulier de prendre note des différents

critères d’approbation requis pour les différents types de documents ISO. Le présent document

a été rédigé conformément aux règles de rédaction données dans les Directives ISO/IEC, Partie 2

(voir www.iso.org/directives).

L’attention est attirée sur le fait que certains des éléments du présent document peuvent faire l’objet de

droits de propriété intellectuelle ou de droits analogues. L’ISO ne saurait être tenue pour responsable

de ne pas avoir identifié de tels droits de propriété et averti de leur existence. Les détails concernant

les références aux droits de propriété intellectuelle ou autres droits analogues identifiés lors de

l’élaboration du document sont indiqués dans l’Introduction et/ou dans la liste des déclarations de

brevets reçues par l’ISO (voir www.iso.org/brevets).

Les appellations commerciales éventuellement mentionnées dans le présent document sont données

pour information, par souci de commodité, à l’intention des utilisateurs et ne sauraient constituer un

engagement.

Pour une explication de la nature volontaire des normes, la signification des termes et expressions

spécifiques de l’ISO liés à l’évaluation de la conformité, ou pour toute information au sujet de l’adhésion

de l’ISO aux principes de l’Organisation mondiale du commerce (OMC) concernant les obstacles

techniques au commerce (OTC), voir www.iso.org/avant-propos.

Le présent document a été élaboré par le comité technique ISO/TC 229, Nanotechnologies.

La présente version française de l'ISO/TS 21357:2022 correspond à la version anglaise publiée le 2022-

01 et corrigée le 2022-03.

Il convient que l’utilisateur adresse tout retour d’information ou toute question concernant le présent

document à l’organisme national de normalisation de son pays. Une liste exhaustive desdits organismes

se trouve à l’adresse www.iso.org/fr/members.html.
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ISO/TS 21357:2022(F)
Introduction

Les dispersions liquides de nanoparticules sont largement utilisées dans l’industrie. Les nanoparticules

dispersées dans des liquides interagissent selon diverses forces faibles ou fortes, ce qui peut entraîner

l’agrégation ou l’agglomération des objets (particules primaires, agglomérats, agrégats, etc.). Il en résulte

que l’état de dispersion et la taille moyenne des particules ainsi que la distribution granulométrique

peuvent différer de ceux qui ont été déterminés pendant la fabrication, le stockage et le traitement, en

particulier en cas d’utilisation de mesurages exigeant une dilution des échantillons ou une préparation

extensive. La préparation des échantillons peut entraîner la rupture ou la formation d’agrégats ou

d’agglomérats et peut également dans certains cas affecter la morphologie des particules primaires.

Pour des raisons de développement de produit, de contrôle qualité et de conformité règlementaire, les

industries concernées exigent des méthodes analytiques applicables aux dispersions dans leur état

natif.

Bien qu’il existe de nombreuses méthodes de caractérisation des propriétés des nanoparticules, en

particulier de leur taille et de leur distribution granulométrique, ces méthodes exigent généralement

une préparation spécifique et souvent complexe des échantillons (par exemple dilution, agitation,

cisaillement ou pompage) et par conséquent, ne fournissent pas les caractéristiques spécifiques

des dispersions en l’état. De plus, certaines expériences n’exigent pas le mesurage d’une distribution

granulométrique complète, la taille moyenne des particules étant le mesurande principal. À l’aide

du mesurage de la taille moyenne des particules, il est possible de contrôler d’autres paramètres de

dispersion du système, tels que l’état d’agglomération, d’agrégation ou de dissolution.

Les méthodes basées sur la diffusion statique multiple de la lumière (DSML) n’exigent aucune

préparation de l’échantillon, ce qui permet, dans les limites soulignées dans le présent document, un

mesurage direct du diamètre équivalent moyen des particules dans l’état de dispersion natif (en l’état).

De plus et au-delà du domaine d’application du présent document, la DSML peut dans certains cas

contrôler en temps réel l’évolution temporelle du diamètre équivalent moyen des particules due aux

processus d’agglomération ou d’agrégation.

Le présent document décrit une méthode normalisée d’évaluation du diamètre équivalent moyen des

particules dans divers types d’échantillons (dont les échantillons en l’état) présentant une large plage

de concentrations, au moyen de la méthode basée sur la DSML.
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SPÉCIFICATION TECHNIQUE ISO/TS 21357:2022(F)
Nanotechnologies — Évaluation de la taille moyenne des
nano-objets dans les dispersions liquides par diffusion
statique multiple de la lumière (DSML)
1 Domaine d’application

Le présent document présente des recommandations et des exigences pour la détermination du

diamètre équivalent moyen (sphérique) de nano-objets (particules, gouttelettes ou bulles) dispersés

dans des liquides au moyen de la technique de diffusion statique multiple de la lumière (DSML). La

technique est applicable à une large gamme de matériaux et n’exige pas la dilution des échantillons

concentrés.
2 Références normatives

Les documents suivants sont cités dans le texte de sorte qu’ils constituent, pour tout ou partie de leur

contenu, des exigences du présent document. Pour les références datées, seule l’édition citée s’applique.

Pour les références non datées, la dernière édition du document de référence s’applique (y compris les

éventuels amendements).
ISO/TS 80004-1, Nanotechnologies — Vocabulaire — Partie 1: Termes "cœur"
ISO/TS 80004-2, Nanotechnologies — Vocabulaire — Partie 2: Nano-objets

ISO/TS 80004-4, Nanotechnologies — Vocabulaire — Partie 4: Matériaux nanostructurés

ISO/TS 80004-6, Nanotechnologies — Vocabulaire — Partie 6: Caractérisation des nano-objets

3 Termes et définitions

Pour les besoins du présent document, les termes et définitions donnés dans l’ISO/TS 80004-1,

l’ISO/TS 80004-2, l’ISO/TS 80004-4, l’ISO/TS 80004-6 ainsi que les suivants s’appliquent.

L’ISO et l’IEC tiennent à jour des bases de données terminologiques destinées à être utilisées en

normalisation, consultables aux adresses suivantes:

— ISO Online browsing platform: disponible à l'adresse https:// www .iso .org/ obp

— IEC Electropedia: disponible à l'adresse https:// www .electropedia .org/
3.1
diffusion statique multiple de la lumière
DSML

technique permettant de mesurer l’intensité de la lumière transmise ou rétrodiffusée après de multiples

événements successifs de diffusion de la lumière incidente dans un milieu de diffusion aléatoire

3.2
distance moyenne de transport

distance moyenne parcourue par un photon avant que son vecteur directeur dans sa direction initiale

de déplacement soit réduit à 1/e de son amplitude initiale par diffusion élastique uniquement

[SOURCE: ISO 18115-1:2013, 4.299, modifié — «particule énergétique» a été remplacé par «photon»;

«momentum» a été remplacé par «vecteur directeur»; «valeur initiale» a été remplacé par «amplitude

initiale»; les notes à l'article ont été supprimées.]
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ISO/TS 21357:2022(F)
3.3
libre parcours moyen

distance moyenne entre des événements de diffusion de photons dans une dispersion

[SOURCE: ISO 22493:2014, 3.2.4, modifié — «électron» a été remplacé par «photon».]

3.4
fraction volumique

rapport entre le volume d’un composant spécifié et le volume total de l’échantillon

3.5
indice de réfraction

rapport entre la vitesse de la lumière (plus exactement la vitesse de phase) dans le vide et la vitesse de

cette même lumière dans un matériau

[SOURCE: ISO 18369-1:2017, 3.1.6.3, modifié — «(plus exactement la vitesse de phase)» a été ajouté; le

terme préféré alternatif «indice de réfraction» et la Note 1 à l’article ont été supprimés.]

3.6
diamètre équivalent des particules

diamètre de la sphère présentant des caractéristiques définies qui se comporte, dans des conditions

définies, exactement de la même manière que la particule décrite
[SOURCE: ISO 21501-1:2009, 2.4]
3.7
absorption
réduction de l’intensité d’un faisceau lumineux qui n’est pas due à la diffusion
[SOURCE: ISO 13320:2020, 3.1.1]
4 Symboles et abréviations
I intensité lumineuse rétrodiffusée
I intensité lumineuse transmise
l* distance moyenne de transport
l libre parcours moyen
g facteur d’asymétrie
Q efficacité d’extinction
φ fraction volumique
D diamètre équivalent moyen des particules
λ longueur d’onde de la lumière incidente (dans le vide)
R demi-épaisseur de l’échantillon
n indice de réfraction
T flux lumineux transmis par la phase continue
MET microscopie électronique à transmission
DCC dispositif à couplage de charge
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ISO/TS 21357:2022(F)
CMOS semi-conducteur à oxyde de métal complémentaire
ILC comparaison interlaboratoires
MR matériau de référence
VAMAS Versailles Project on Advanced Materials and Standards
5 Principes
5.1 Théorie concernée

La technique de DSML est basée sur le principe de la diffusion élastique de la lumière par des objets

dispersés dans un liquide. La lumière incidente est diffusée de multiples fois successivement, ce qui

entraîne une perte de corrélation de la direction de la lumière incidente. La lumière I ou I dépend de

R T

la longueur d’onde de la lumière incidente, de la concentration des particules, de la taille et de la forme

des particules, des propriétés optiques (n et absorption des deux phases continue et dispersée) et de la

géométrie de mesurage.

La propagation de la lumière dans les dispersions concentrées (Figure 1) peut être caractérisée

par deux paramètres: le libre parcours moyen (Formule (1)), l et la distance moyenne de transport,

[8],[9],[11]

l* . Le libre parcours moyen caractérise les phénomènes de diffusion au niveau microscopique,

tandis que l* décrit la diffusion multiple au niveau macroscopique, comme la profondeur de pénétration

des rayonnements dans un milieu aléatoire (c’est-à-dire qu’il n’existe pas de corrélation significative

[14]

entre les diffuseurs). Les deux paramètres l et l* sont liés par la théorie de Mie dans l’hypothèse où

[11]
l > λ :
l= (1)
3ϕQ

où D est le diamètre équivalent moyen des particules, φ est la fraction volumique du matériau et Q est

l’efficacité d’extinction.
l = (2)
()1− g

NOTE 1 La diffusion anisotropique de la lumière par un objet peut être caractérisée par le facteur d’asymétrie g,

qui est la moyenne des cosinus (cos θ) des angles de diffusion pondérés par la fonction de phase ou le diagramme

de diffusion du diffuseur (par exemple g = 0 pour les diffuseurs isotropiques de Rayleigh et 0 < g < 1 pour les

[14]

diffuseurs de Mie) . Q tient compte des phénomènes de diffusion et d’absorption de la lumière.

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ISO/TS 21357:2022(F)
Légende
1 signal I élevé 2 signal I faible
T R
3 signal I faible 4 signal I élevé
T R
NOTE La dépendance de I à la fraction volumique est décrite.
Figure 1 — Représentation schématique de I , I , l et l*
R T
[8],[14]

Q et g sont tous deux décrits par la théorie de Mie et dépendent des propriétés optiques des

particules et du milieu, de la taille des particules et de la longueur d’onde de la lumière.

La théorie de Mie est ensuite utilisée pour déterminer soit le diamètre équivalent des particules soit

leur fraction volumique, à condition que l’autre soit connu, à partir de I ou de I . Cela est accompli par

T R

la comparaison des valeurs expérimentales de l ou l* avec les valeurs déterminées par la théorie de Mie.

Pour mesurer (par exemple) I à partir de la lumière incidente, il est possible de dériver une

[13]
approximation :
31ϕ()−gQ
α  
2 e
I =+βα= +β (3)
 
l  

En raison de l’influence de la géométrie expérimentale et du détecteur optique, un étalonnage de

sortie est utilisé pour convertir les valeurs brutes de I et I (par exemple signal de tension) en

R T

unité exploitable. Le gain α et le décalage β dans la Formule (3) sont déterminés avec un ensemble

d’échantillons de fraction volumique différente avec un l* connu (calculé théoriquement par la théorie

de Mie).
[15]

Le flux lumineux transmis à travers un échantillon peut être exprimé comme suit :

3RQϕ
2R  
  e
− −
 
 
l D
   
Il,RT==eeT (4)
T 0 0

NOTE 2 Les variations de I et I en fonction de l* et l respectivement sont illustrées à l’Annexe A. Les

R T

variations de I et I sur le diamètre équivalent moyen des particules D pour des nanoparticules de TiO et de

R T 2
résine mélamine sont illustrées à l’Annexe B.
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ISO/TS 21357:2022(F)
5.2 Mesurandes principaux

Le mesurande utilisé dans la DSML est un diamètre équivalent (sphérique) moyen des particules. Pour

une suspension polydispersée, un l* effectif est défini qui tient compte des contributions au signal

de particules individuelles de diverses tailles (comme décrit en 5.1). Le diamètre correspondant

au l* effectif est appelé le diamètre équivalent (sphérique) moyen des particules, voir également la

Formule (2).

Il peut être démontré que pour des particules de taille inférieure à la longueur d’onde de la lumière,

le diamètre équivalent moyen des particules mesuré est linéairement corrélé au diamètre volumique

[10],[11]

moyen, D . Dans ce cas, l’intensité lumineuse rétrodiffusée est approximativement proportionnelle

à D , ce qui signifie que des particules «plus grosses» (mais toujours inférieures à λ) contribuent plus au

signal.

La dépendance de I et I au diamètre équivalent moyen des particules est représentée sur la Figure 2

R T

à titre d’exemple. Il s’agit de I et I calculés en fonction du diamètre équivalent moyen des particules

R T
dans une dispersion aqueuse de dioxyde de titane à 5 % de fraction volumique.
Légende
X D [nm] I
Y intensité de la lumière [%] I

Figure 2 — I et I calculés en fonction du diamètre des particules pour une dispersion aqueuse

R T
(n = 1,33) de dioxyde de titane (n = 2,50, φ = 5 %, λ = 880 nm)

Les signaux I et I dépendent des instruments et de l’échantillon. Ainsi, selon une règle empirique,

T R

l’estimation du diamètre équivalent moyen des particules est obtenue à partir du signal I à condition

qu’il soit non nul et du signal I lorsque I est nul.
R T

NOTE Bien que ne faisant pas partie du domaine d’application du présent document, pour les particules de

taille supérieure à λ, le diamètre équivalent moyen des particules mesuré est corrélé au diamètre de surface

[9],[10] −1

moyen D . Dans ce cas, le signal I est proportionnel à D , ce qui signifie que les particules «plus petites»

(mais toujours supérieures à λ) contribuent plus à l’intensité de la lumière rétrodiffusée.

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ISO/TS 21357:2022(F)
5.3 Applicabilité et limites de la méthode
5.3.1 Généralités

La technique de DSML permet de déterminer le diamètre équivalent moyen des particules de nano-objets

dans des dispersions concentrées, et de contrôler la stabilité des dispersions dans le temps sur le même

échantillon, puisqu’il s’agit d’une méthode non destructive. Il convient de noter que cette technique

peut être utilisée pour les dispersions de particules solides dans des liquides (des suspensions), des

émulsions de liquide dans du liquide et des dispersions de bulles dans des liquides.

La technique de DSML ne permet pas l’analyse des distributions granulométriques. Elle donne un

paramètre unique basé sur le mesurage de I ou de I , qui est converti en un diamètre équivalent moyen

R T

des particules (lorsque la concentration des particules et n sont connus). Cela limite l’applicabilité

de la technique de mesurage aux systèmes dynamiques dans lesquels au moins un paramètre

(diamètre équivalent des particules ou fraction volumique) reste constant pendant le mesurage. Pour

le mesurage du diamètre équivalent moyen des particules, le n et la fraction volumique du matériau

doivent être connus indépendamment. La méthode a été appliquée avec succès à des mesurages d’oxydes

métalliques, de métaux, de céramiques, d’émulsions et de dispersions de bulles ultrafines dans l’eau.

5.3.2 Concentration de l’échantillon

La capacité à analyser des échantillons non dilués (en l’état) qui n’ont pas été modifiés par une

préparation est l’un des atouts majeurs de la méthode de DSML. Une autre caractéristique de cette

méthode est la capacité à mesurer un diamètre équivalent moyen des particules pour une large plage

de concentrations (de très faible à très élevée). Le paragraphe 5.1 décrit comment I et I sont liés aux

T R

paramètres du système et au diamètre équivalent des particules et à leur concentration. À l’aide de la

théorie de Mie, I et I peuvent être calculés pour un matériau donné (par exemple des billes de silice de

R T
100 nm de diamètre dans de l’eau). La Figure 3 représente ces données.
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ISO/TS 21357:2022(F)
Légende
X φ [%] I
Y intensité de la lumière [%] I

Figure 3 — Variation de I et I en fonction de la fraction volumique des particules pour des

T R

billes de silice (n = 1,46) dans de l’eau (n = 1,33) avec D = 100 nm et λ = 880 nm

Les données calculées sur la Figure 3 sont tracées pour des dispersions présentant des fractions

volumiques allant de 0,001 % à 40 %. La méthode s’applique de la même façon à une concentration très

faible. Bien qu’il n’existe pas de limite discrète entre des régimes de diffusion simple et de diffusion

multiple, il convient de noter que de façon phénoménologique, les Formules (3) et (4) sont valides dans

les deux régimes. L’effet de la modification de la concentration est démontré de façon expérimentale à

l’Annexe E pour les dispersions de TiO dans l’eau.

La diffusion par des nano-objets dispersés dépend fortement de plusieurs paramètres, comme le n du

matériau ou la taille des particules et la configuration optique de l’instrument utilisé pour l’évaluation.

Pour cette raison, la limite inférieure de concentration dépend de l’échantillon ou de l’instrument. Dans

le présent document, la valeur de concentration inférieure applicable est approximativement égale à

une fraction volumique de 10 %.

Dans l’exemple donné à la Figure 3, les données calculées atteignent une fraction volumique d’environ

40 %. De même que pour la limite de concentration inférieure, la limite supérieure dépend des

propriétés de l’échantillon et de l’instrument.
5.3.3 Diamètre équivalent moyen des particules

La DSML permet d’évaluer des diamètres de particules allant de 10 nm à 100 µm. Ces limites de tailles

sont approximatives et dépendent fortement des échantillons. Comme pour la fraction volumique, les

limites réelles inférieure et supérieure de taille sont en effet déterminées par un certain nombre de

facteurs, comme les indices de réfraction des particules et de la phase continue, la concentration, la

longueur d’onde de la lumière et la configuration de l’instrument.
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ISO/TS 21357:2022(F)
5.3.4 Homogénéité et stabilité de l’échantillon

La DSML est une technique non destructive basée sur le mesurage de I et de I dans le temps afin de

R T

caractériser l’évolution physique d’une dispersion due à un processus de déstabilisation (par exemple

[10]

une sédimentation, un crémage, une agrégation, une agglomération ou une coalescence) . Dans tous

les cas, il convient que l’échelle de temps du changement des paramètres de dispersion soit plus courte

que le temps nécessaire pour un point de mesurage temporel d’intensité unique dans l’échantillonnage

des données DSML.

NOTE Dans la pratique, l’intervalle d’acquisition d’une donnée unique de DSML à une position donnée de la

cellule est de l’ordre de la milliseconde.

Pour le mesurage du diamètre équivalent moyen des particules de nano-objets par DSML, l’échantillon

doit être homogène en matière de concentration (c’est-à-dire ne pas présenter de sédimentation, de

crémage ni de flottaison). L’échantillonnage spatial des données le long de la cellule de mesurage permet

d’identifier les hétérogénéités locales dans l’échantillon.

Afin d’identifier l’évolution de la concentration due à une sédimentation ou un crémage, la source de

lumière DSML balaye verticalement la cellule échantillon. La répétition des balayages à intervalles

temporels fixes donne des informations sur la cinéti
...

TECHNICAL ISO/TS
SPECIFICATION 21357
First edition
Nanotechnologies — Evaluation of the
mean size of nano-objects in liquid
dispersions by static multiple light
scattering (SMLS)
Nanotechnologies — Evaluation de la taille moyenne des nano-objets
dans les dispersions liquides par diffusion statique multiple de la
lumière (SMLS)
Member bodies are requested to consult relevant national interests in IEC/TC
113 before casting their ballot to the e-Balloting application.
PROOF/ÉPREUVE
Reference number
ISO/TS 21357:2021(E)
© ISO 2021
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ISO/TS 21357:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on

the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below

or ISO’s member body in the country of the requester.
ISO copyright office
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Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
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ISO/TS 21357:2021(E)
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 Principles ..................................................................................................................................................................................................................... 3

5.1 Relevant theory ...................................................................................................................................................................................... 3

5.2 Key measurands .................................................................................................................................................................................... 5

5.3 Method applicability and limitations ................................................................................................................................. 6

5.3.1 General ........................................................................................................................................................................................ 6

5.3.2 Sample concentration .................................................................................................................................................... 6

5.3.3 Mean equivalent particle diameter .................................................................................................................... 7

5.3.4 Sample homogeneity and stability ..................................................................................................................... 7

5.4 Method characteristics ................................................................................................................................................................... 7

6 Apparatus .................................................................................................................................................................................................................... 8

7 Measurement procedure ............................................................................................................................................................................. 9

7.1 Instrument preparation ................................................................................................................................................................. 9

7.2 Sample handling .................................................................................................................................................................................... 9

7.3 System settings ................................................................................................................................................................................... 10

7.3.1 General ..................................................................................................................................................................................... 10

7.3.2 Procedure to verify sample homogeneity ................................................................................................. 10

7.3.3 Volume fraction ................................................................................................................................................................ 10

7.3.4 Refractive index ............................................................................................................................................................... 10

8 Performance qualification .....................................................................................................................................................................11

9 Data record .............................................................................................................................................................................................................11

10 Measurement uncertainty ......................................................................................................................................................................11

Annex A (informative) I and I versus l* and l ...................................................................................................................................13

BS T

Annex B (informative) I and I as a function of D for titanium dioxide and melamine resin

BS T

particles ......... .......................... ...................................................................................................................................................................................14

Annex C (informative) Instrument qualification .................................................................................................................................16

Annex D (informative) Comparative analysis of Latex suspensions at various concentrations .......17

Annex E (informative) Analysis of titanium dioxide suspensions at different concentrations .........18

Annex F (informative) Results of an interlaboratory comparison study ..................................................................20

Bibliography .............................................................................................................................................................................................................................23

iii
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ISO/TS 21357:2021(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

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ISO/TS 21357:2021(E)
Introduction

Dispersions of nanoparticles in liquids are widely used in industry. Nanoparticles dispersed in liquids

interact via a variety of weak and strong forces, which can lead to aggregation or agglomeration of

objects (primary particles, agglomerates, aggregates, etc.). As a result, the dispersion state and the

apparent mean particle size and size distribution can differ from those determined during product

manufacturing, storage, and processing, particularly when using measurements requiring sample

dilution or extensive preparation. Sample preparation can result in breaking or formation of aggregates

or agglomerates and in some cases can also affect morphology of primary particles. Industrial

stakeholders require analytical methods that are applicable to dispersions in their native state for

reasons of product development, quality control and regulatory compliance.

While many methods exist for characterization of nanoparticle properties, in particular their size and

size distribution, these methods typically require a specific and frequently complex sample preparation

(e.g. dilution, stirring, shearing or pumping) and, therefore, do not yield characteristics specific to as-

received dispersions. In addition, some experiments do not require measurement of a full particle

size distribution with the mean particle size being the main measurand. Using the mean particle size

measurement, it is possible to monitor other dispersion parameters of the system such as the state of

agglomeration, aggregation or dissolution.

Static multiple light scattering (SMLS) based methods do not require sample preparation allowing,

within limitations outlined in this document, direct measurement of the mean equivalent particle

diameter in the native (as-received) state of dispersion. In addition, and beyond the scope of this

document, SMLS is capable in some cases of monitoring in real time the temporal evolution of mean

equivalent particle diameter due to agglomeration or aggregation processes.

This document describes a standardized method for evaluating the mean equivalent particle diameter

in various sample types (including as-received samples) having a wide range of concentrations using

the SMLS based method.
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TECHNICAL SPECIFICATION ISO/TS 21357:2021(E)
Nanotechnologies — Evaluation of the mean size of nano-
objects in liquid dispersions by static multiple light
scattering (SMLS)
1 Scope

This document provides guidance and requirements for the determination of the mean (spherical)

equivalent diameter of nano-objects (i.e. particles, droplets or bubbles) dispersed in liquids using

the static multiple light scattering (SMLS) technique. The technique is applicable to a wide range of

materials and does not require dilution of concentrated samples.
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/TS 80004-1, Nanotechnologies — Vocabulary — Part 1: Core terms
ISO/TS 80004-2, Nanotechnologies — Vocabulary — Part 2: Nano-objects
ISO/TS 80004-4, Nanotechnologies — Vocabulary — Part 4: Nanostructured materials

ISO/TS 80004-6, Nanotechnologies — Vocabulary — Part 6: Nano-object characterization

3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO/TS 80004-1, ISO/TS 80004-2,

ISO/TS 80004-4, ISO/TS 80004-6 and the following 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
static multiple light scattering
SMLS

technique in which transmitted or backscattered light intensity is measured after multiple successive

scattering events of incident light in a random scattering medium
3.2
transport mean free path

average distance that a photon travels before its direction vector in its initial direction of motion is

reduced to 1/e of its initial magnitude by elastic scattering alone

[SOURCE: ISO 18115-1:2013, 4.299, modified — "an energetic particle" has been changed to "a photon";

"momentum" has been changed to "direction vector"; "initial value" has been changed to "initial

magnitude"; notes to entry have been deleted.]
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ISO/TS 21357:2021(E)
3.3
mean free path
mean distance between photon scattering events in a dispersion

[SOURCE: ISO 22493:2014, 3.2.4, modified — "electron" has been changed to "photon".]

3.4
volume fraction
quotient of the volume of a specified component and the total sample volume
3.5
refractive index

ratio of the speed of light (more exactly, the phase velocity) in a vacuum to the speed of that same light

in a material

[SOURCE: ISO 18369-1:2017, 3.1.6.3, modified — “(more exactly, the phase velocity)” has been added;

the alternative preferred term "index of regraction" and note 1 to enty have been deleted.]

3.6
equivalent particle diameter

diameter of the sphere with defined characteristics which behaves under defined conditions in exactly

the same way as the particle being described
[SOURCE: ISO 21501-1:2009, 2.4]
3.7
absorption
reduction of intensity of a light beam not due to scattering
[SOURCE: ISO 13320:2020, 3.1.1]
4 Symbols and abbreviated terms
I backscattered light intensity
I transmitted light intensity
transport mean free path
mean free path
asymmetry factor
Q extinction efficiency factor
volume fraction
mean equivalent particle diameter
wavelength of the incident light (in vacuum)
R sample half thickness
n refractive index
T light flux transmitted by the continuous phase
TEM transmission electron microscopy
CCD charge-coupled device
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ISO/TS 21357:2021(E)
CMOS complementary metal–oxide–semiconductor
ILC interlaboratory comparison
RM reference material
VAMAS Versailles Project on Advanced Materials and Standards
5 Principles
5.1 Relevant theory

The SMLS technique is based on the principle of elastic light scattering from dispersed objects in a

liquid. Incident light is scattered multiple times successively, which results in a loss of correlation

of the incident light direction. The I or I light depends on the incident light wavelength, particle

BS T

concentration, particle size and shape, optical properties (n and absorption of both the continuous and

dispersed phases), and the measurement geometry.

Light propagation in concentrated dispersions (Figure 1) can be characterised by two parameters: the

[8],[9],[11]

mean free path (Formula (1)), l , and the transport mean free path, l . The mean free path

characterizes scattering phenomena at the microscopic level, while l describes multiple scattering at a

macroscopic level as the penetration depth of radiation in a random medium (i.e. no significant

[14]

correlation between scattering objects). Both parameters l and l are related by the Mie theory

[11]
under the hypothesis where l>λ :
l= (1)
3ϕQ

where D is the mean equivalent particle diameter, ϕ is the volume fraction of the material and Q is the

extinction efficiency factor.
l = (2)
1− g

NOTE 1 The anisotropic scattering of light by an object can be characterized by the asymmetry factor g, which

is the average cosine (cos θ) of the scattering angles weighted by the phase function or scattering diagram of the

[14]

scatterer (e.g. g = 0 for isotropic Rayleigh scatterers and 0 < g < 1 for Mie scatterers) . Q takes into account

scattering efficiency and light absorption phenomena.
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ISO/TS 21357:2021(E)
Key
1 high I signal 2 low I signal
T BS
3 low I signal 4 high I signal
T BS
NOTE The I dependence on the volume fraction is depicted.
Figure 1 — Schematic representation of the I , I , l and l
BS T
[8],[14]

Both Q and g are described by the Mie theory and depend on optical properties of the particles

and the medium, particle size and wavelength of light.

The Mie theory is then used to determine either equivalent particle diameter or volume fraction,

provided that the other is known, from I or I . This is accomplished by comparing the experimental

T BS
values of l or l with the values determined from the Mie theory.
[13]

For measuring (for instance) I from the incident light, it is possible to derive an approximate :

31ϕ()−gQ
α  
2 e
I =+βα= +β (3)
 
l  

Due to the influence of experimental geometry and the optical detector, an output calibration to convert

the raw I and the raw I (e.g. voltage signal) into an exploitable unit is used. The gain α and offset β

BS T

in Formula (3) are determined with a set of samples of different volume fraction with known l

(calculated theoretically with the Mie theory).
[15]
The light-flux transmitted through a sample can be expressed as :
3RQϕ
 
  e
 
 
   
Il(),RT==eeT (4)
T 0 0

NOTE 2 Variations of I and I as a function of l and l respectively are illustrated in Annex A. Variations of

BS T

I and I on mean equivalent particle diameter D for TiO and melamine resin nanoparticles are illustrated in

BS T 2
Annex B.
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5.2 Key measurands

The measurand used in SMLS is a volume weighted mean equivalent (spherical) particle diameter. For a

polydisperse suspension case, an effective l is defined that takes into account contributions to the

signal from individual particles of various sizes (as described in 5.1). The diameter corresponding to

the effective l is called the mean equivalent (spherical) particle diameter, also see Formula (2).

It can be shown that for particles smaller than the wavelength of light, the measured mean equivalent

10],[11

particle diameter linearly correlates with the mean volume diameter, D[ ]. In this case,

backscattered light intensity scales approximately as D , meaning that “larger” (but still smaller than

λ ) particles contribute more to the signal.

The dependence of I and I on the mean equivalent particle diameter is shown in Figure 2 by way

BS T

of example. It is the calculated I and I as a function of mean equivalent particle diameter in a 5 %

BS T
volume fraction titanium dioxide aqueous dispersion.
Key
X D [nm] I
Y intensity of light [%] I

Figure 2 — Calculated I and I as a function of particle diameter for an aqueous dispersion

BS T
(n = 1,33) of titanium dioxide (n = 2,50, φ = 5 %, λ = 880 nm)

The I and I signals are instrument and sample dependent. Thus, as a rule of thumb, mean equivalent

T BS

particle diameter estimation is obtained from I signal provided that it is not null and I signal when

T BS
I is null.

NOTE Although outside the scope of the document, for particles larger than λ , the measured mean

9],[10

equivalent particle diameter correlates with the mean surface diameter D[ ]. In this case, the I signal scales

as D , meaning that “smaller” (but still larger than λ ) particles contribute more to the backscattered intensity.

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ISO/TS 21357:2021(E)
5.3 Method applicability and limitations
5.3.1 General

The SMLS technique can determine the mean equivalent particle diameter of nano-objects in

concentrated dispersions as well as monitor stability of dispersions over time on the very same sample

as it is a non-destructive method. It should be noted that this technique may be used for dispersions of

solid particles in liquids (i.e. suspensions), liquid-in-liquid emulsions and bubble dispersions in liquids.

The SMLS technique does not allow for the analysis of particle size distributions. It yields a single

parameter based on the I or I measurement, which is converted into a mean equivalent particle

BS T

diameter (when the particle concentration and n are known). This limits the applicability of the

measurement technique to dynamic systems where at least one parameter (equivalent particle

diameter or volume fraction) remains constant during the measurement. For mean equivalent particle

diameter measurement, material n and volume fraction shall be known independently. The method has

been successfully applied to measurements of metal oxides, metals, ceramics, emulsions and ultrafine

bubble dispersions in water.
5.3.2 Sample concentration

The ability to analyse undiluted (as-received) samples that have not been modified by sample

preparation is one of the main strengths of the SMLS method. Another feature of the method is the

ability to measure mean equivalent particle diameter for a broad range of concentrations (from very

low to very high concentration). 5.1 describes how I and I relate to system parameters and the

T BS

equivalent particle diameter and concentration. Using the Mie theory, I and I can be calculated for a

BS T

given material (such as 100 nm diameter silica beads in water). Figure 3 shows these data.

Key
X φ [%] I
Y intensity of light [%] I

Figure 3 — Variation of I and I with particle volume fraction for silica beads (n = 1,46) in

T BS
water (n = 1,33) with D = 100 nm and λ = 880 nm
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ISO/TS 21357:2021(E)

The calculated data in Figure 3 are plotted for dispersions with volume fractions varying from 0,001 %

to 40 %. The method equally applies to very low concentration. Although there is no discrete boundary

between single scattering and multiple scattering regimes, it should be noted that phenomenologically

Formulae (3) and (4) are valid in both regimes. The effect of changing concentration is demonstrated

experimentally in Annex E for TiO dispersions in water.

The scattering by dispersed nano-objects depends heavily on several parameters, such as a material’s

n or particle size and the optical set-up of the instrument used for the evaluation. For this reason, the

lower concentration limit is sample/instrument dependent. For the purpose of this document, the lower

applicable concentration value is taken to be approximately 10 % volume fraction.

In the example given in Figure 3, the calculated data reach approximately 40 % volume fraction. Just

like for the lower concentration limit, the upper limit depends on the sample and instrument properties.

5.3.3 Mean equivalent particle diameter

Particles with diameters ranging as widely as 10 nm to 100 μm can be evaluated by SMLS. These size

limits are approximate and depend heavily on the samples. Indeed, just like for volume fraction, the

actual lower and upper size limits are determined by a number of factors, such as the particles and

continuous phase refractive indices, concentration, wavelength of light and instrument set-up.

5.3.4 Sample homogeneity and stability

SMLS is a non-destructive technique based on measurement of I and I over time to characterise

BS T

the physical evolution of a dispersion due to a destabilisation process (e.g. sedimentation, creaming,

[10]

aggregation, agglomeration or coalescence) . In all cases, the time scale of change in dispersion

parameters should be slower than the time required for a single-time-point intensity measurement in

the SMLS data sampling.

NOTE In practice a SMLS single point data acquisition interval at a given cell position is in the millisecond

range.

For the mean equivalent particle diameter measurement of nano-objects by SMLS, the sample

shall be homogeneous in terms of concentration (i.e. no sedimentation, creaming or floatation).

Spatially dependent sampling of data along the measurement cell enables one to identify these local

heterogeneities in the sample.

To identify concentration evolution due to sedimentation or creaming, the SMLS light source scans

a sample cell vertically. Repeating the scans at fixed time intervals provides information about

destabilisation kinetics (i.e. rate of change of concentration). In some systems this can be a critical

indicator of the mean equivalent particle diameter measurement quality since the local volume fraction

of measured objects in the dispersion should be uniform and stable. If local concentration change or

non-uniformity is observed, then the global volume fraction should not be used for particle sizing

measurement or homogenisation is required. In case of varying concentration with time or height, the

mean equivalent particle diameter measurement can increase its uncertainty for I and I according to

BS T
Formulae (3) and (4).
5.4 Method characteristics

Table 1 summarises the characteristics of the technique for the measurement of key dispersion

parameters.
Table 1 — SMLS measurement characteristics.
Method feature Applicability Notes

Sample preparation Generally not required Sample preparation procedure may not be required (see 7.2).

Sample preparation can mean any action done onto the sample including dilution, dispersion, sonication, etc. For

samples that have settled or creamed homogenisation prior to the mean equivalent particle diameter measurements is

required to have uniform concentration.
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Table 1 (continued)
Method feature Applicability Notes

Concentration range Approximately from Dilution (ISO 14488) of the sample is not necessary; and most

0,000 1 % to 40 % vol- samples are measured in as-received form. Sample concentra-

ume fraction tion limits are discussed in 5.3.2.

Equivalent particle diameter Approximately from The lower and upper size limits are discussed in 5.3.3.

range 10 nm to 100 µm

Stability of suspension Sample should be sta- The size measurement as a function of aging time can be per-

ble during the time formed on the same sample. The allowed range of change of
required for the meas- the intensity is discussed in 5.3.4.
urement

Homogeneity Homogeneous over the The mean particle size and concentration can vary based on

whole sample height the position in the sample. This is due to non-uniform sample

mixing and processes such as sedimentation, creaming or
other instabilities.
Spatially dependent sampling of data along the measurement
cell enables one to identify these local heterogeneities in the
sample. The allowed range of homogeneity of suspension is
discussed in 5.3.4.

Sample preparation can mean any action done onto the sample including dilution, dispersion, sonication, etc. For

samples that have settled or creamed homogenisation prior to the mean equivalent particle diameter measurements is

required to have uniform concentration.
6 Apparatus

The common geometry for this kind of measurement is shown in Figure 4. Light from the source is

directed into a liquid dispersion. Two sensors (e.g. photodiodes, CCD or CMOS) allow for a simultaneous

measurement of the backscattered and transmitted
...

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