ISO/FDIS 15901-2

Pore size distribution and porosity of solid materials by mercury porosimetry and gas adsorption

Distribution des dimensions des pores et porosité des matériaux solides par porosimétrie au mercure et par adsorption de gaz

General Information

• Status: Published
• ICS: 19.120 - Particle size analysis. Sieving
• Technical Committee: ISO/TC 24/SC 4 - Particle characterization
• Drafting Committee: ISO/TC 24/SC 4/WG 3 - Pore size distribution, porosity
• Current Stage: 5020 - FDIS ballot initiated: 2 months. Proof sent to secretariat
• Start Date: 25-Aug-2021
• Completion Date: 25-Aug-2021

RELATIONS

• Revised: ISO 15901-2:2006 - Pore size distribution and porosity of solid materials by mercury porosimetry and gas adsorption
• Effective Date: 11-Oct-2014
• Revised: ISO 15901-3:2007 - Pore size distribution and porosity of solid materials by mercury porosimetry and gas adsorption
• Effective Date: 07-Aug-2021

Standards Content (sample)

FINAL
INTERNATIONAL ISO/FDIS
DRAFT
STANDARD 15901-2
ISO/TC 24/SC 4
Pore size distribution and porosity
Secretariat: BSI
of solid materials by mercury
Voting begins on:
2021-08-25 porosimetry and gas adsorption —
Voting terminates on:
Part 2:
2021-10-20
Analysis of nanopores by gas
adsorption
Distribution des dimensions des pores et porosité des matériaux
solides par porosimétrie au mercure et par adsorption de gaz —
Partie 2: Analyse des nanopores par adsorption de gaz
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 SUPPOR TING
DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
Reference number
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
ISO/FDIS 15901-2:2021(E)
LOGICAL, COMMERCIAL AND USER PURPOSES,
DRAFT INTERNATIONAL STANDARDS MAY ON
OCCASION HAVE TO BE CONSIDERED IN THE
LIGHT OF THEIR POTENTIAL TO BECOME STAN-
DARDS TO WHICH REFERENCE MAY BE MADE IN
NATIONAL REGULATIONS. ISO 2021
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ISO/FDIS 15901-2:2021(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

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Published in Switzerland
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ISO/FDIS 15901-2:2021(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

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

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 2

4 Symbols .......................................................................................................................................................................................................................... 3

5 Principles ..................................................................................................................................................................................................................... 4

5.1 General ........................................................................................................................................................................................................... 4

5.2 Methods of measurement .............................................................................................................................................................. 8

5.3 Choice of adsorptive ........................................................................................................................................................................... 9

6 Measurement procedure ...........................................................................................................................................................................10

6.1 Sampling ....................................................................................................................................................................................................10

6.2 Sample pretreatment ......................................................................................................................................................................10

6.3 Measurement .........................................................................................................................................................................................10

7 Verification of apparatus performance......................................................................................................................................10

8 Calibration ...............................................................................................................................................................................................................11

9 Pore size analysis ..............................................................................................................................................................................................11

9.1 General ........................................................................................................................................................................................................11

9.2 Classical, macroscopic, thermodynamic methods for pore size analysis ..........................................12

9.2.1 Assessment of microporosity ............................................................................................................................12

9.2.2 Assessment of meso/macroporosity ...........................................................................................................19

9.3 Advanced, microscopic approaches based on density functional theory and

molecular simulation ......................................................................................................................................................................20

9.3.1 General...................................................................................................................................................................................20

9.3.2 Application for pore size analysis: Kernel and integral adsorption equation ..........20

10 Reporting ...................................................................................................................................................................................................................21

Annex A (informative) Horvath-Kawazoe and Saito-Foley method ...................................................................................22

Annex B (informative) NLDFT method ............................................................................................................................................................25

Bibliography .............................................................................................................................................................................................................................28

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ISO/FDIS 15901-2:2021(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

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.

This second edition cancels and replaces ISO 15901-2:2006 and ISO 15901-3:2007, which have been

technically revised. It also incorporates the Technical Corrigendum ISO 15901-2:2006/Cor.1:2007.

The main changes compared to the previous edition are as follows:

— the analysis of nanopores by gas adsorption which combines the characterization of both micro-

and mesopores is now addressed;

— the classification of adsorption isotherms and hysteresis loops has been updated.

A list of all parts in the ISO 15901 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.
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ISO/FDIS 15901-2:2021(E)
Introduction

In general, different types of pores may be pictured as apertures, channels, or cavities within a solid

body or as the space (i.e. interstices or voids) between solid particles in a bed, compact or aggregate.

Porosity is a term which is often used to indicate the porous nature of solid material and is more

precisely defined as the ratio of the volume of accessible pores and voids to the total volume occupied

[1]

by a given amount of the solid. According to the 2015 IUPAC recommendations , nanopores are defined

as pores with internal widths of equal or less than 100 nm and are divided into several subgroups

dependent on their pore width:
— pores with width greater than about 50 nm are called macropores;
— pores of widths between 2 nm and 50 nm are called mesopores;
— pores with width of about 2 nm and less are called micropores;

Further, IUPAC suggested a subclassification of micropores into supermicropores (pore width 0,7 nm

to 2 nm), and ultramicropores (pore width < 0,7 nm). In addition to the accessible pores, a solid may

contain closed pores which are isolated from the external surface and into which fluids are not able to

penetrate. The characterization of closed pores, i.e. cavities with no access to an external surface, is not

covered in this document.

Porous materials may take the form of fine or coarse powders, compacts, extrudates, sheets or

monoliths. Their characterization usually involves the determination of the pore size distribution as

well as the total pore volume or porosity. For some purposes it is also necessary to study the pore shape

and interconnectivity, and to determine the internal and external surface area.

Porous materials have great technological importance, e.g. in the context of the following:

a) controlled drug release;
b) catalysis;
c) gas separation;
d) filtration including sterilization;
e) materials technology;
f) environmental protection and pollution control;
g) natural reservoir rocks;
h) building material properties;
i) polymer and ceramic industries.

It is well established that the performance of a porous solid (e.g. its strength, reactivity, permeability

or adsorbent power) is dependent on its pore structure. Many different methods have been developed

for the characterization of pore structure. The choice of the most appropriate method depends on the

application of the porous solid, its chemical and physical nature and the range of pore size.

Different methods for the characterization of nanopores are available, including spectroscopy, electron

and tunnel microscopy and sorption methods. In view of the complexity of most porous solids, it is not

surprising that the results obtained are not always in agreement and that no single technique can be

relied upon to provide a complete picture of the pore structure. Among these, mercury porosimetry (see

ISO 15901-1) and gas adsorption are popular ones because by combining both it is possible to assess a

wide range of pore sizes from below 0,5 nm up to 400 µm. While mercury porosimetry is the standard

technique for macropore analysis, gas adsorption techniques allow to assess pores up to approximately

100 nm. In this case, physical adsorption can be conveniently used, is not destructive, and is not that

cost intensive as compared to some of the above-mentioned methods. Particularly, with regard to the

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ISO/FDIS 15901-2:2021(E)

application of microporous material as specific sorbents, molecular sieves and carriers for catalysts

and biological active material, the field-proven methods of gas sorption are of special value.

The measuring techniques of the method described in this document are similar to those described in

ISO 9277 for the measurement of gas adsorption at low temperature. However, in order to assess the

full range of pore sizes including microporosity, adsorption experiments have to be performed over a

wide range of pressures from the ultralow pressure range (e.g. turbomolecular pump vacuum) up to

atmospheric pressure (0,1 MPa).
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FINAL DRAFT INTERNATIONAL STANDARD ISO/FDIS 15901-2:2021(E)
Pore size distribution and porosity of solid materials by
mercury porosimetry and gas adsorption —
Part 2:
Analysis of nanopores by gas adsorption
1 Scope

This document describes a method for the evaluation of porosity and pore size distribution by physical

adsorption (or physisorption). The method is limited to the determination of the quantity of a gas

[1]-[9]

adsorbed per unit mass of sample as a function of pressure at a controlled, constant temperature .

Commonly used adsorptive gases for physical adsorption characterization include nitrogen, argon,

krypton at the temperatures of liquid nitrogen and argon (77 K and 87 K respectively) as well as CO (at

273 K). Traditionally, nitrogen and argon adsorption at 77 K and 87 K, respectively, allows one to assess

pores in the approximate range of widths 0,45 nm to 50 nm, although improvements in temperature

control and pressure measurement allow larger pore widths to be evaluated. CO adsorption at

273 K – 293 K can be applied for the microporous carbon materials exhibiting ultramicropores. Krypton

adsorption at 77 K and 87 K is used to determine the surface area or porosity of materials with small

surface area or for the analysis of thin porous films.

The method described is suitable for a wide range of porous materials. This document focuses on

the determination of pore size distribution from as low as 0,4 nm up to approximately 100 nm. The

determination of surface area is described in ISO 9277. The procedures which have been devised for the

determination of the amount of gas adsorbed may be divided into two groups:

— those which depend on the measurement of the amount of gas removed from the gas phase, i.e.

manometric (volumetric) methods;

— those which involve the measurement of the uptake of the gas by the adsorbent (i.e. direct

determination of increase in mass by gravimetric methods).

In practice, static or dynamic techniques can be used to determine the amount of gas adsorbed. However,

the static manometric method is generally considered the most suitable technique for undertaking

physisorption measurements with nitrogen, argon and krypton at cryogenic temperatures (i.e. 77 K

and 87 K, the boiling temperature of nitrogen and argon, respectively) with the goal of obtaining pore

volume and pore size information. This document focuses only on the application of the manometric

method.
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 3165, Sampling of chemical products for industrial use — Safety in sampling

ISO 8213, Chemical products for industrial use — Sampling techniques — Solid chemical products in the

form of particles varying from powders to coarse lumps

ISO 9277, Determination of the specific surface area of solids by gas adsorption — BET method

ISO 14488, Particulate materials — Sampling and sample splitting for the determination of particulate

properties
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ISO/FDIS 15901-2:2021(E)
3 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 https:// www .electropedia .org/
3.1
adsorbate
adsorbed gas
3.2
adsorption

enrichment of the adsorptive at the external and accessible internal surfaces of a solid

3.3
adsorptive
gas or vapour to be adsorbed
3.4
adsorbent
solid material on which adsorption occurs
3.5
adsorption isotherm

relationship between the amount of gas adsorbed and the equilibrium pressure of the gas at constant

temperature
3.6
adsorbed amount
amount of gas adsorbed at a given pressure, p, and temperature, T
3.7
equilibrium adsorption pressure
pressure of the adsorptive in equilibrium with the adsorbate
3.8
monolayer amount

amount of the adsorbate that forms a monomolecular layer over the surface of the adsorbent

3.9
monolayer capacity

volumetric equivalent of monolayer amount expressed as gas at standard conditions of temperature

and pressure (STP)
3.10
nanopore
pore with width of 100 nm or less
3.11
macropore
pore with width greater than about 50 nm
3.12
mesopore
pore with width between approximately 2 nm and 50 nm
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ISO/FDIS 15901-2:2021(E)
3.13
micropore
pore with width of about 2 nm or less
3.14
supermicropore
pore with width between approximately 0,7 nm and 2 nm
3.15
ultramicropore
pore with width of approximately < 0,7 nm
3.16
physisorption

weak bonding of the adsorbate, reversible by small changes in pressure or temperature

3.17
pore size

pore width, i.e. diameter of cylindrical pore or distance between opposite walls of slit

3.18
pore volume
volume of pores as determined by stated method
3.19
relative pressure

ratio of the equilibrium adsorption pressure, p, to the saturation vapour pressure, p , at analysis

temperature
3.20
saturation vapour pressure

vapour pressure of the bulk liquefied adsorptive at the temperature of adsorption

3.21
volume adsorbed

volumetric equivalent of the amount adsorbed, expressed as gas at standard conditions of temperature

and pressure (STP), or expressed as the adsorbed liquid volume of the adsorbate
4 Symbols

For the purposes of this document, the following symbols apply, together with their units. All specific

dimensions are related to sample mass, in grams.
Symbol Description Unit
A Kirkwood-Mueller constant of adsorptive J·cm
A Kirkwood-Mueller constant of adsorbent J·cm
2 −1
a specific surface area m ·g
2 −1
a specific surface area of reference sample m ·g
s,ref
α polarizability of adsorptive cm
α normalized adsorption 1
α polarizability of adsorbent cm
c speed of light m·s
d diameter of an adsorptive molecule nm
d diameter of hard spheres nm

According to ISO 80000-1, the coherent SI unit for any quantity of dimension one (at present commonly determined

“dimensionless”) is the unit one, symbol 1.
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ISO/FDIS 15901-2:2021(E)
Symbol Description Unit
d pore diameter (cylindrical pore) nm
d diameter of an adsorbent molecule nm
d d = (d + d )/2, distance between adsorptive and adsorbent molecules nm
0 0 s a
ε /k well depth parameter of gas-gas Lennard Jones potential K
ff B
ε /k well depth parameter of gas-solid Lennard Jones potential K
sf B
−23 −1
k Boltzmann constant (1,381 × 10 ) J K
l nuclei-nuclei pore width nm
m * mass adsorbed g
m mass of an electron kg
23 −1
N Avogadro's constant (6,022 × 10 ) mol
2 −2
N number of atoms per unit area (m ) of monolayer m
2 −2
N number of atoms per unit area (m ) of adsorbent m
n specific amount adsorbed mol·g
P pressure of the adsorptive in equilibrium with the adsorbate Pa
p saturation vapour pressure of the adsorptive Pa
p/p relative pressure of the adsorptive 1
−1 −1
R ideal gas constant (8,314) Jmol K
ρ gas density g·cm
ρ gas density at STP (273,15 K; 101,3 kPa) g·cm
g,STP
ρ liquid density g·cm
σ distance between two molecules at zero interaction energy nm
σ distance parameter of gas-gas Lennard Jones potential nm
σ distance parameter of gas-solid Lennard Jones potential nm
T temperature K
T critical temperature K
t statistical layer thickness nm
3 −1
V specific volume of the adsorbate cm ·g
3 −1
V specific adsorbed gas volume at STP (273,15 K; 101,3 kPa) cm ·g
3 −1
V micropore volume cm ·g
micro
W pore width (slit pore) nm
χ diamagnetic susceptibility of adsorptive cm
χ diamagnetic susceptibility of adsorbent cm

According to ISO 80000-1, the coherent SI unit for any quantity of dimension one (at present commonly determined

“dimensionless”) is the unit one, symbol 1.
5 Principles
5.1 General

Physisorption is a general phenomenon and occurs whenever an adsorbable gas (the adsorptive) is

brought into contact with the surface of a solid (the adsorbent). The forces involved are the van der

Waals forces. Physisorption in porous materials is governed by the interplay between the strength of

fluid-wall and fluid-fluid interactions as well as the effects of confined pore space on the state of fluids

in narrow pores. The effect of pore width on the interaction potential is demonstrated schematically in

[8]
Figure 1 .
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ISO/FDIS 15901-2:2021(E)
(a) (b) (c)

Figure 1 — Schematic illustration of adsorption potential, ε, on (a) planar, nonporous surface;

(b) mesopore; (c) micropore

The interplay between the strength of attractive adsorptive-adsorbent interactions and the effect

of confinement (as controlled by pore size/geometry) affect the shape of adsorption isotherm, as

[1]

demonstrated in the IUPAC classification of adsorption isotherms as shown in Figure 2.

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ISO/FDIS 15901-2:2021(E)
Key
X relative pressure
Y amount adsorbed
Figure 2 — Standard isotherm types (IUPAC 2015)

Reversible Type I isotherms are given by microporous solids having relatively small external surfaces

(e.g. some activated carbons, molecular sieve zeolites and certain porous oxides). Because the pore size

is similar to the molecule diameter, the choice of the gas is decisive, i.e. the size of the gas molecule

controls the accessibility of the pores, and hence affects the obtained porosity information. A Type I

isotherm is concave to the relative pressure (i.e. p/p axis ) and the amount adsorbed approaches a

limiting value. This limiting uptake is governed by the accessible micropore volume rather than by

the internal surface area. A steep uptake at very low p/p is due to enhanced adsorbent-adsorptive

interactions in narrow micropores (micropores of molecular dimensions), resulting in micropore

filling at very low p/p . Type I(a) isotherms are given by microporous materials having mainly narrow

micropores (of width ≤ 1 nm), which includes ultramicropores). A significant portion of the micropores

is indicated by a large and steep increase of the isotherm near its origin and subsequent bending to a

plateau. Type I(b) isotherms are found with materials having pore size distributions over a broader

range including wider micropores (including supermicropores).

Type II isotherms are typically produced by solids which are non-porous or macroporous. Point B is

often taken as indicative of the completion of the monolayer capacity.

Type III isotherms are distinguished by a convexity towards the relative pressure axis. These isotherms

are found when weak gas-solid interactions occur on non-porous or macroporous solids (e.g. water

adsorption on carbon surfaces).

Type IV isotherms are found for mesoporous solids. Type IV isotherms are given by mesoporous

adsorbents (e.g. many oxide gels, industrial adsorbents and mesoporous molecular sieves). The

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ISO/FDIS 15901-2:2021(E)

adsorption behaviour in mesopores is determined by the adsorbent-adsorptive interactions and by

the interactions between the molecules in the condensed state. In this case, the initial monolayer-

multilayer adsorption on the mesopore walls, which takes the same path as the corresponding part of

a Type II isotherm, is followed by pore condensation. Pore condensation is the phenomenon whereby a

gas condenses to a liquid-like phase in a pore at a pressure p less than the saturation pressure p of the

bulk liquid. This leads to the appearance of a Type IV adsorption isotherm. A typical feature of Type IV

isotherms is a final saturation plateau, of variable length (sometimes reduced to a mere inflexion point).

In the case of a Type IV(a) isotherm, capillary condensation is accompanied by hysteresis. This occurs

when the pore width exceeds a certain critical width, which is dependent on the adsorption system and

temperature (e.g. for nitrogen and argon adsorption in cylindrical pores at 77 K and 87 K, respectively,

hysteresis starts to occur for pores wider than ~ 4 nm). With adsorbents having mesopores of smaller

width, completely reversible Type IV(b) isotherms are observed. In principle, Type IV(b) isotherms are

also given by conical and cylindrical mesopores that are closed at the tapered end.

Type V isotherms are characterized by a convexity to the relative pressure axis. Unlike Type III

isotherms there occurs a point of inflection at higher relative pressures. Type V isotherms result from

weak gas-solid interactions on microporous and mesoporous solids (e.g. water adsorption on micro-or

mesoporous carbons).

Type VI isotherms are notable for the step-like nature of the sorption process. The steps result from

sequential multilayer adsorption or uniform non-porous surfaces. Amongst the best examples of Type

VI isotherms are those obtained with argon or krypton at low temperature on graphitized carbon

blacks.

There are various phenomena which contribute to the occurrence of hysteresis, and this is also reflected

[1]
in the IUPAC classification of hysteresis loops shown in Figure 3.

Type H1 hysteresis loops are observed for mesoporous materials with relatively narrow pore size

distributions as for instance in ordered mesoporous silicas (e.g. MCM-41, MCM-48, SBA-15), some

controlled pore glasses and ordered, mesoporous carbons, and materials with mesoporous cylindrical

pores and for agglomerates of spheroidal particles of uniform size. Usually, network effects are minimal

and occurrence of Type H1 hysteresis is often a clear sign that hysteresis is entirely caused by delayed

condensation, i.e. a metastable adsorption branch.

Hysteresis loops of Type H2 are given by more complex pore structures in which network effects are

[10]

important . The very steep desorption branch, which is a characteristic feature of H2(a) loops, can

be attributed either to pore-blocking/percolation in a narrow range of pore necks or to cavitation-

induced evaporation, as well as for some 2-dimensional materials with slit-shaped pores. H2(a) loops

are for instance given by many silica gels, some porous glasses (e.g. vycor) as well as some ordered

mesoporous materials (e.g. SBA-16 and KIT-5 silicas). The Type H2(b) loop is also associated with pore

blocking, but the size distribution of neck widths is now much larger. Examples of this type of hysteresis

loops have been observed with mesocellular silica foams and certain mesoporous ordered silicas after

hydrothermal treatment.

A distinctive feature of Type H3 is that the lower limit of the desorption branch is normally located at

the
...