ISO 14411-2:2020

Preparation of particulate reference materials — Part 2: Polydisperse spherical particles

This document describes the specifications for spherical polydisperse particulate reference materials with acceptable uncertainty in particle size distribution and describes protocols for their characterization. One potential use of these reference materials is the reliability test of the laser-diffraction instruments and other particle sizing methods. This document expresses polydispersity and the related uncertainties in size. Small variations in size can imply large variations in cumulative distribution. This document describes the requirements of particulate reference materials, which are intended to be used to test the reliability of various types of particle size measurement apparatus. The requirements for processing, homogeneity and stability assessment as well as for the preparation of certificates, which are not addressed in this document are described in ISO 17034.

Préparation des matériaux de référence à l'état particulaire — Partie 2: Particules sphériques polydispersées

General Information

• Status: Published
• Publication Date: 29-Sep-2020
• ICS: 19.120 - Particle size analysis. Sieving
• Technical Committee: ISO/TC 24/SC 4 - Particle characterization
• Drafting Committee: ISO/TC 24/SC 4/WG 11 - Sample preparation and reference materials
• Current Stage: 6060 - International Standard published
• Start Date: 30-Sep-2020
• Due Date: 27-Mar-2021
• Completion Date: 30-Sep-2020

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 14411-2
First edition
2020-09
Preparation of particulate reference
materials —
Part 2:
Polydisperse spherical particles
Préparation des matériaux de référence à l'état particulaire —
Partie 2: Particules sphériques polydispersées
Reference number
ISO 14411-2:2020(E)
©
ISO 2020

---------------------- Page: 1 ----------------------
ISO 14411-2:2020(E)

COPYRIGHT PROTECTED DOCUMENT
© ISO 2020
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
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii © ISO 2020 – All rights reserved

---------------------- Page: 2 ----------------------
ISO 14411-2:2020(E)

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions and symbols . 1
3.1 Terms and definitions . 1
3.2 Symbols . 2
4 Requirements for preparing polydisperse particles . 3
4.1 General description of a project for the production of a reference material . 3
4.2 Requirements on the general properties of the material for polydisperse particles . 4
4.3 Size distribution for polydisperse particles . 4
5 Characterization of polydisperse particles . 5
5.1 Particle size distribution . 5
5.2 Aspect ratio . 5
5.3 Apparent particle density . 5
5.4 Refractive index . 5
6 Estimation of size measurement uncertainties. 5
6.1 Uncertainty from sampling . 5
6.1.1 Uncertainty of the average value N replicate measurement . 5
6.1.2 Uncertainty of a single measurement . 6
6.2 Other uncertainty factors. 7
6.3 Expanded uncertainty of size distribution . 7
Annex A (informative) Example calculation of the uncertainty estimation of particle size
distribution determined by N replicate measurement . 8
Annex B (informative) Example calculation of the uncertainty estimation of number-based
particle size distribution determined by a single measurement .11
Annex C (informative) Example calculation of the uncertainty estimation for a volume-
based cumulative size distribution transformed from the number-based size
distribution having a log-normal size distribution .14
Bibliography .16
© ISO 2020 – All rights reserved iii

---------------------- Page: 3 ----------------------
ISO 14411-2:2020(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 24, Particle characterization including
sieving, Subcommittee SC 4, Particle characterization.
A list of all parts in the ISO 14411 series can be found on the ISO website.
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.
iv © ISO 2020 – All rights reserved

---------------------- Page: 4 ----------------------
ISO 14411-2:2020(E)

Introduction
The measurement of particle size distribution can be accomplished by a number of techniques
which measure some characteristics of the particle and usually equate this to a circular or spherical
equivalent. Each of these techniques measures different properties of an irregular particle and thus has
particular requirements for reference materials and method standardization. Often, the methods that
are employed for particle size distribution are indirect in nature which rely on measuring some other
property and converting this to a particle size distribution by means of equations based on ideal shapes
(usually spherical) and sizes to that of the equivalent particle size distribution. Thus, these techniques
usually require or assume knowledge of some other constant in order to calculate the particle size
distribution.
Even methods that do not require size calibration require reference materials for quality control and
operation qualification. Such a reference material should be certified for its particle size distribution
and the values should be traceable to the SI unit metre. This material allows instrument manufacturers
to demonstrate proper calibration of all input factors and hence demonstrate that their instrument
results are traceable to the SI unit metre. To achieve this, the reference material should be polydisperse
and consist of spherical particles.
The heterogeneity of a particle size distribution poses statistical challenges for particle size analysis
and therefore also for the production of reference materials for particle size analysis. This document
therefore describes the production of particulate reference materials consisting of spherical particles.
© ISO 2020 – All rights reserved v

---------------------- Page: 5 ----------------------
INTERNATIONAL STANDARD ISO 14411-2:2020(E)
Preparation of particulate reference materials —
Part 2:
Polydisperse spherical particles
1 Scope
This document describes the specifications for spherical polydisperse particulate reference
materials with acceptable uncertainty in particle size distribution and describes protocols for their
characterization. One potential use of these reference materials is the reliability test of the laser-
diffraction instruments and other particle sizing methods.
This document expresses polydispersity and the related uncertainties in size. Small variations in size
can imply large variations in cumulative distribution.
This document describes the requirements of particulate reference materials, which are intended to be
used to test the reliability of various types of particle size measurement apparatus. The requirements
for processing, homogeneity and stability assessment as well as for the preparation of certificates,
which are not addressed in this document are described in ISO 17034.
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 17034, General requirements for the competence of reference material producers
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1.1
aspect ratio
ratio of minimum Feret diameter to the maximum Feret diameter of a particle
[SOURCE: ISO 26824:2013, 4.5, modified.]
3.1.2
apparent density
mass per unit volume of the material
3
Note 1 to entry: It is expressed in g/cm .
[SOURCE: ISO 5755:2012, 3.10]
© ISO 2020 – All rights reserved 1

---------------------- Page: 6 ----------------------
ISO 14411-2:2020(E)

3.1.3
reference material
RM
material, sufficiently homogeneous and stable with respect to one or more specified properties, which
has been established to be fit for its intended use in a measurement process
[SOURCE: ISO 17034:2016, 3.3, modified — Notes to entry have been deleted.]
3.1.4
certified reference material
reference material characterized by a metrological valid procedure for one or more specified
properties, accompanied by a certificate that provides the value of the specified property, its associated
uncertainty, and a statement of metrological traceability
[SOURCE: ISO 17034:2016, 3.2, modified — Notes to entry have been deleted.]
3.2 Symbols
Symbol Description Unit Derived unit
coverage factor; numerical factor used as a multiplier of the combined
k - -
standard uncertainty in order to obtain an expanded uncertainty
m total number of uncertainty contributions - -
N total number of size measurements - -
n number of particles counted - -
t
−1 −1
q (x) density distribution by number m μm
0
−1 −1
q (x) density distribution by volume m μm
3
Q (x) cumulative distribution by number - -
0
Q (x) cumulative distribution by volume - -
3
r type of quantity of distribution, r = 0: number, r = 3: volume - -
s standard deviation of Q (x) m μm
r r
s geometric standard deviation - -
g
U expanded uncertainty m μm
f
expanded uncertainty of p percentile of the cumulative distribution
U m μm
f, p, r
of r type quantity
uncertainty at p percentile of cumulative number-based size dis-
u - −
Q
tribution
p,0
u uncertainty of the between-unit homogeneity m μm
hom
u uncertainty of particle size x m μm
p, r p, r
u uncertainty of mean value due to N times of size measurement m μm
rep
u uncertainty of stability of materials m μm
stab
x minimum particle size in size range j m μm
min, j
2 © ISO 2020 – All rights reserved

---------------------- Page: 7 ----------------------
ISO 14411-2:2020(E)

x maximum particle size in size range j m μm
max, j
particle size at p percentile of cumulative distribution of r type
quantity, e.g. x = particle size at 90 percentile of cumulative
90,0
x m μm
p, r
number-based size distribution, x = median particle size of
50,3
cumulative volume-based size distribution
average particle size of N times of size measurement
N
x
m μm
pr, 1
= x = x
∑
pr,,pr
N
i=1
4 Requirements for preparing polydisperse particles
4.1 General description of a project for the production of a reference material
According to ISO 17034, “reference material production” is a process that covers all steps from project
planning and design to the final distribution. In particular, it consists of the following steps.
a) Production planning: In this step, the desired characteristics of the material are established.
It is decided whether a certified reference material (CRM) or a non-certified material should be
produced, which material should be used, how much should be produced, desired measurand values
and their uncertainties, required traceability and ways to achieve it as well as the planning of the
homogeneity and stability assessment, material characterization and storage and distribution.
b) Processing and production control: This is the set of physical processes that converts the (often
bulk) material into different candidate reference material units fit for distribution. Care shall be
taken to ensure sufficient homogenization, avoid contamination and ensure proper packaging
for long-term stability. Especially in the case of particulate reference materials, de-mixing during
filling shall be avoided.
c) Assessment of homogeneity and stability: The between-unit variation of the values to be certified
is assessed, usually by testing a representative number of units. Based on this assessment, an
uncertainty of homogeneity (u ) is estimated. In addition, the minimum sample intake, i.e. the
hom
minimum amount of sample that is representative for the whole unit is established.
The stability of the material under transport and storage conditions is assessed. Based on this
assessment, uncertainty contributions of stability (u ) is estimated.
stab
d) Characterization: It is the process to assess the assigned values of a CRM. Several characterization
approaches are listed in ISO 17034 and ISO Guide 35. It is crucial that an approach is chosen that
can ensure the envisaged traceability of the certified values.
e) Assignment of property values and their uncertainties: Based on the results of the characterization
and homogeneity and stability assessment, the assigned values and their uncertainty are
established.
f) Preparation of RM documents: The assigned property values and their uncertainties of CRMs are
stated on the RM certificate, together with information on the intended use, instruction for use
(which may include e.g. dispersion protocols).
g) Distribution and stability monitoring: If deemed necessary based on the material used. The
stability of the material is assessed on regular intervals to detect changes that would make the
certified values invalid.
Many of the above steps can be outsourced to third parties. However, production planning, selection
of subcontractors, assignment of property values and their uncertainties, authorization of property
values and their uncertainties and authorization of RM documents cannot be outsourced.
© ISO 2020 – All rights reserved 3

---------------------- Page: 8 ----------------------
ISO 14411-2:2020(E)

This document covers steps d) and e) of the above description, i.e. a part of the production planning
(requirement of material characteristics) and characterization and property value assignment. All other
steps shall be performed in accordance with ISO 17034. Guidance on the implementation of ISO 17034
is given in ISO Guide 35.
4.2 Requirements on the general properties of the material for polydisperse particles
The material shall be stable and appropriate for its intended use.
The requirements for the materials are as follows:
a) The aspect ratio or the ellipse ratio of the particles shall be characterized by image analysis. The
mean aspect ratio or the mean ellipse ratio shall be 0,90 or above in the size range between x
10,3
and x of the material.
90,3
b) When dispersed in liquid, bleeding of colour or absorption should not occur. The material should be
chemically and physically homogeneous and non-soluble in the dispersant medium.
c) The particle surface should be smooth with a minimum of contaminations or adhesions.
d) The apparent density of the material shall exceed the density of the dispersing liquid for the
particles not to float in wet applications.
e) The number of fragmented particles contained in the material should be as small as possible and
suitable for the intended use. The amount of fragmented or non-spherical particles, as well as the
number of coarse outliers, shall be characterized by image analysis.
f) The material should be easily dispersible in the chosen liquid. No particle agglomerates or
flocculation should be detectable after dispersion. It is acceptable to support the particle dispersion
using dispersing agents or ultrasound.
g) The particles should not break due to ultrasound pressure used for dispersion in liquid dispersant
media. The mechanical strength should be as high as possible since the material should be able to
withstand a typical dry dispersion procedure without getting crushed. It is not possible to define
a concrete value since there are several different dry dispersion procedures not allowing for a
reliable theoretical calculation of stress parameters.
h) The material should provide a shelf life of at least two years after production without appreciably
changing its physical properties. All-important storage conditions should be known, e.g. necessary
UV-/light-protection.
i) The swelling of the material suspended in pure dispersant media should be as low as possible.
Swelling shall not exceed a value of 0,8 % with reference to the particle size in dry conditions. The
swelling behaviour shall be specified in the sample preparation procedure.
j) The size of the particle-liquid interface in dispersion should be negligible compared to the
particle size.
4.3 Size distribution for polydisperse particles
The size distribution for polydisperse particles shall be monomodal.
More than 90 percentile of cumulative volume-based size distribution should be within one decade.
The particle size distribution should be approximately represented by a log-normal distribution, at
least in the region of 0,2 < Q (x) < 0,8.
3
4 © ISO 2020 – All rights reserved

---------------------- Page: 9 ----------------------
ISO 14411-2:2020(E)

5 Characterization of polydisperse particles
5.1 Particle size distribution
The particle size distribution is determined by a method that provides t
...

DRAFT INTERNATIONAL STANDARD
ISO/DIS 14411-2
ISO/TC 24/SC 4 Secretariat: BSI
Voting begins on: Voting terminates on:
2019-01-07 2019-04-01
Preparation of particulate reference materials —
Part 2:
Polydisperse spherical particles
Préparation des matériaux de référence à l'état particulaire —
Partie 2: Particules sphériques polydispersées
ICS: 19.120
THIS DOCUMENT IS A DRAFT CIRCULATED
FOR COMMENT AND APPROVAL. IT IS
THEREFORE SUBJECT TO CHANGE AND MAY
NOT BE REFERRED TO AS AN INTERNATIONAL
STANDARD UNTIL PUBLISHED AS SUCH.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL,
This document is circulated as received from the committee secretariat.
TECHNOLOGICAL, COMMERCIAL AND
USER PURPOSES, DRAFT INTERNATIONAL
STANDARDS MAY ON OCCASION HAVE TO
BE CONSIDERED IN THE LIGHT OF THEIR
POTENTIAL TO BECOME STANDARDS TO
WHICH REFERENCE MAY BE MADE IN
Reference number
NATIONAL REGULATIONS.
ISO/DIS 14411-2:2019(E)
RECIPIENTS OF THIS DRAFT ARE INVITED
TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
RIGHTS OF WHICH THEY ARE AWARE AND TO
©
PROVIDE SUPPORTING DOCUMENTATION. ISO 2019

---------------------- Page: 1 ----------------------
ISO/DIS 14411-2:2019(E)

COPYRIGHT PROTECTED DOCUMENT
© ISO 2019
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
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Fax: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved

---------------------- Page: 2 ----------------------
ISO/DIS 14411-2:2019(E)

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions and symbols . 1
3.1 Terms and definitions . 1
3.2 Symbols (and abbreviated terms) . 2
4 Requirements for preparing polydisperse . 3
4.1 General description . 3
4.2 Requirements on the general properties of the material for polydisperse particles . 3
4.3 Requirements on size distribution for polydisperse particles . 4
5 Characterization of polydisperse particles . 4
5.1 Particle size distribution . 4
5.2 Aspect ratio . 4
5.3 Particle density . 4
5.4 Refractive index . 5
6 Estimation of size measurement uncertainties. 5
6.1 Uncertainty from sampling . 5
6.1.1 Uncertainty of the average value N replicate measurement . 5
6.1.2 Uncertainty of a single measurement . 5
6.2 Other uncertainty factors. 6
6.3 Expanded uncertainty of size distribution . 6
Annex A (informative) Uncertainty estimation of average value based on N replicate
measurement . 8
Annex B (informative) Uncertainty estimation of particle size based on a single measurement .10
Annex C (informative) Example of uncertainty estimation for a volume-based cumulative
size distribution transformed from the number-based size distribution .12
Annex D (informative) Uncertainty of mass-based size distribution .17
Bibliography .18
© ISO 2019 – All rights reserved iii

---------------------- Page: 3 ----------------------
ISO/DIS 14411-2:2019(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 on 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 the following URL: www .iso .org/iso/foreword .html.
The committee responsible for this document is ISO/TC 24/SC 4 Particle characterization
ISO 14411 consists of the following parts, under the general title Preparation of particulate reference
materials:
— Part 1: Polydisperse material based on picket fence of monodisperse spherical particles
— Part 2: Polydisperse spherical particles
Part 1 is a Technical Specification.
iv © ISO 2019 – All rights reserved

---------------------- Page: 4 ----------------------
ISO/DIS 14411-2:2019(E)

Introduction
The measurement of particle size distribution can be accomplished by a number of techniques
which measure some characteristics of the particle and usually equate this to a circular or spherical
equivalent. Each of these techniques measures different properties of an irregular particle and thus has
particular requirements for reference materials and method standardization. Often, the methods that
are employed for particle size distribution are indirect in nature which rely on measuring some other
property and converting this to a particle size distribution by means of equations based on ideal shapes
(usually spherical) and sizes to that of the equivalent particle size distribution. Thus these techniques
usually require or assume knowledge of some other constant in order to calculate the particle size
distribution.
Even methods that do not require size calibration require reference materials for quality control and
operation qualification. Such a reference material should be certified for its particle size distribution
and the values should be traceable to the SI unit meter. This material allows instrument manufacturers
to demonstrate proper calibration of all input factors and hence demonstration that their instrument
results are traceable to the SI Unit meter. To achieve this, the reference material should be polydisperse
and consist of spherical particles.
The heterogeneity of a particle size distribution poses statistical challenges for particle size analysis
and therefore also for the production of reference materials for particle size analysis. This standard
therefore describes the production of particulate reference materials consisting of spherical particles.
© ISO 2019 – All rights reserved v

---------------------- Page: 5 ----------------------
DRAFT INTERNATIONAL STANDARD ISO/DIS 14411-2:2019(E)
Preparation of particulate reference materials —
Part 2:
Polydisperse spherical particles
1 Scope
This international standard describes the specifications for spherical polydisperse particulate
reference materials with acceptable uncertainty in particle size distribution and describes protocols
for their characterisation. These reference materials will be fit for the purpose for their intended use.
One potential use of these reference materials is the reliability test of the laser-diffraction and other
related methods.
This international standard expresses polydispersity and the related uncertainties in size. Users should
take notice that small variations in size may imply large variations in cumulative distribution.
This document describes the necessary requirements of particulate reference materials, which should
be used to the reliability test of various types of particle size measurement apparatus. The requirements
described in ISO 17034 should be applied for processing, homogeneity and stability assessment as well
as for the preparation of certificates, which are not addressed in this international standard.
2 Normative references
The following referenced documents are indispensable for the application 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 13322-1:2004, Particle size analysis — Image analysis methods — Part 1: Static image analysis methods
ISO 14488:2007, Particulate materials — Sampling and sample splitting for the determination of
particulate properties
ISO 14887:2000, Sample preparation — Dispersing procedures for powders in liquids
ISO 15901-3:2007, Pore size distribution and porosity of solid materials by mercury porosimetry and gas
adsorption — Part 3: Analysis of micropores by gas adsorption
ISO 17034:2016, General requirements for the competence of reference material producers
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1.1
aspect ratio
ratio of minimum Feret diameter to the maximum Feret diameter of a particle
[SOURCE: ISO 26824:2013, 4.5]
© ISO 2019 – All rights reserved 1

---------------------- Page: 6 ----------------------
ISO/DIS 14411-2:2019(E)

3.1.2
pycnometry
a method wherein particle density is obtained from the measured mass of sample with a given
calibrated volume
[SOURCE: ISO 26824:2013, 2.4]
3.1.3
density
3
mass per unit volume of the material – expressed in g/cm
[SOURCE: ISO 5755:2012, 3.10]
3.1.4
reference material
material, sufficiently homogeneous and stable with respect to one or more specified properties, which
has been established to be fit for its intended use in a measurement process
[SOURCE: ISO 17034:2017, 3.3]
3.1.5
certified reference material
reference material characterized by a metrological valid procedure for one or more specified
properties, accompanied by a certificate that provides the value of the specified property, its associated
uncertainty, and a statement of metrological traceability
[SOURCE: ISO 17034:2017, 3.2]
3.2 Symbols (and abbreviated terms)
For the purposes of this technical report, the following symbols apply.
Symbol Quantity Unit derived unit
Coverage factor; numerical factor used as a multiplier of the combined
k - -
standard uncertainty in order to obtain an expanded uncertainty
m total number of uncertainty contributions - -
N Total number of size measurements - -
n number of particles counted - -
t
The minimum number of particles that should be counted for predeter-
n - -
min
mined admissible maximum uncertainty with a defined level of confidence
-1 -1
q (x) density distribution by number m μm
0
-1 -1
q (x) density distribution by volume or mass m μm
3
Q (x) cumulative distribution by number - -
0
Q (x) cumulative distribution by volume or mass - -
3
r type of quantity of distribution, r=0: number, r=3: volume or mass - -
s standard deviation m μm
s standard deviation of Q (x) m μm
r r
s geometric standard deviation - -
g
U expanded uncertainty m μm
f
expanded uncertainty of p percentile of the cumulative distribution of
U m μm
f, p, r
r type quantity
u uncertainty m μm
u uncertainty of mean value due to N times of size measurement m μm
rep
uncertainty at p percentile of cumulative number-based size distribution
u
- −
Q
p,0
2 © ISO 2019 – All rights reserved

---------------------- Page: 7 ----------------------
ISO/DIS 14411-2:2019(E)

Symbol Quantity Unit derived unit
u uncertainty of particle size x m μμ
p, 0 p, 0
x , minimum particle diameter in size range j m μm
min, j
x maximum particle diameter in size range j m μm
max, j
particle diameter at p percentile of cumulative distribution of r type
quantity, e.g. x = particle diameter at 90 percentile of cumulative
90,0
x m μm
p, r
number distribution, x = median particle size of cumulative volume
50,3
or mass distribution
N
1
x
m μm
average particle diameter of N times = x = x
pr,
∑
pr,,pr
N
i=1
4 Requirements for preparing polydisperse
4.1 General description
The material shall be stable and appropriate for its intended use.
4.2 Requirements on the general properties of the material for polydisperse particles
The requirements for the materials are as follows:
1. The aspect ratio or the ellipse ratio of the particles shall be characterized by image analysis. The
mean aspect ratio or the mean ellipse ratio shall be 0,80 or above in the size range between x
10,3
and x of the material.
90,3
2. When dispersed in liquid, bleeding of colour or absorbing material should not occur. The material
should be chemically and physically homogeneous, and be non-soluble in the dispersant medium.
3. The particle surface should be smooth with a minimum of contaminations or adhesions.
4. The apparent density of the material has to exceed the density of the dispersing liquid for the
particles not to float in wet applications.
5. The material should contain the minimum number of fragmented particles suitable for the intended
use. The amount of fragmented or non-spherical particles as well as the amount of coarse outliers
shall be characterized by image analysis.
6. The material should be easily dispersible in the chosen liquid. No particle agglomerates or
flocculation should be detectable after dispersion. It is allowed to support the particle dispersion
using dispersing agents or ultrasound.
7. The particles should not be disrupted by ultrasound pressure in dispersant media. The mechanical
strength should be as high as possible since the material should be able to withstand a typical
dry dispersion procedure without getting crushed. It is not possible to define a concrete value
since there are several different dry dispersion procedures not allowing for a reliable theoretical
calculation of stress parameters.
8. The material should provide a shelf life of at least 2 years after production without appreciably
changing its physical properties. All-important storage conditions have to be known, e.g. necessary
UV-/light-protection.
9. The swelling of the material suspended in pure dispersant media should be as low as possible.
Swelling shall not exceed a value of 0,8 % referred to the particle diameter in dry condition. The
swelling behaviour shall be specified in the sample preparation procedure
© ISO 2019 – All rights reserved 3

---------------------- Page: 8 ----------------------
ISO/DIS 14411-2:2019(E)

10. The size of the particle-liquid interface in dispersion should be negligible compared to the particle
diameter.
4.3 Requirements on size distribution for polydisperse particles
The size distribution shall satisfy the following requirements:
1. Distribution shall be monomodal.
2. More than 90 percentile of cumulative mass distribution should be within one decade.
3. The particle size distribution should be approximately represented by a log-normal, at least in the
region of 0,2 < Q (x) < 0,8.
3
5 Characterization of polydisperse particles
5.1 Particle size distribution
Particle size distribution is determined by a method that provides traceable results, and satisfies the
following requirements:
1. The relative expanded uncertainty (corresponding to a confidence level of 95 %) of the most reliable
mass median diameter x * shall be not larger than 5 %.
50,3
2. The reference data for the range from Q to Q should be provided with adequate quality.
10, 3 90, 3
3. The particle size distribution should be measured by two or more types of different measurement
principles. For each measurement data, 95% reliability or 5% uncertainty should be indicated.
Using an image analysis method with an electron microscope or optical microscope should be
suitable. Other methods such as the electrical sensing zone method with focus flow system can be
used as appropriate.
The requirements for the individual methods are:
1. Results shall be traceable to the International System of Units (SI) either by using CRMs with
traceable reference values or by appropriate calibration of all relevant input parameters, in case of
no direct calibration for length.
2. The methods shall be validated in a way that allows estimation of a measurement uncertainty.
3. For each dataset, the expanded uncertainty on a 95 % confidence level should be given.
4. All results and characteristic values shall be given in terms of a volume-based particle size
distribution Q (x).
3
5. The number of particles measured shall be sufficiently high to achieve the required precision.
5.2 Aspect ratio
The aspect ratio shall be measured by a suitable image analysis method measuring at least 1 000
particles by random sampling. Fewer particles would not allow demonstrating fulfilment of the criteria
set for the aspect ratio.
5.3 Particle density
The particle density shall be measured by any suitable methods.
4 © ISO 2019 – All rights reserved

---------------------- Page: 9 ----------------------
ISO/DIS 14411-2:2019(E)

5.4 Refractive index
Refractive index of particle or bulk material shall be measured by any suitable method, e.g. by the liquid
immersion method.
6 Estimation of size measurement uncertainties
The uncertainty of each quantile shall be estimated. The following uncertainty contributions shall be
included in the combined uncertainty of the particle size distribution:
6.1 Uncertainty from sampling
6.1.1 Uncertainty of the average value N replicate measurement
At least four measurements shall be performed to obtain a sufficiently accurate value. This section
described the estimation of the uncertainty of N replicate measurements.
The average value of N measurements of the p percentile of the cumulative distribution of r type is
calculated as;
N
1
x = xi (1)
()
∑
pr,,pr
N
i=1
where xi is the particle size of p percentile of the cumulative distribution of r type quantity at the
()
pr,
i-th measurement. The uncertainty of the average value of the part
...