ISO 15901-2:2006

Pore size distribution and porosity of solid materials by mercury porosimetry and gas adsorption - Part 2: Analysis of mesopores and macropores by gas adsorption

ISO 15901-2:2006 describes a method for the evaluation of porosity and pore size distribution by gas adsorption. It is a comparative, rather than an absolute test. The method is limited to the determination of the quantity of a gas adsorbed per unit mass of sample at a controlled, constant temperature. ISO 15901-2:2006 does not specify the use of a particular adsorptive gas, however nitrogen is the adsorptive gas most commonly used in such methods. Similarly, the temperature of liquid nitrogen is the analysis temperature most commonly used. Use is sometimes made of other adsorptive gases, including argon, carbon dioxide and krypton, and other analysis temperatures, including those of liquid argon and solid carbon dioxide. In the case of nitrogen adsorption at liquid nitrogen temperature, the basis of this method is to measure the quantity of nitrogen adsorbed at 77 K as a function of its relative pressure. Traditionally, nitrogen adsorption is most appropriate for pores in the approximate range of widths 0,4 nm to 50 nm. Improvements in temperature control and pressure measurement now allow larger pore widths to be evaluated. ISO 15901-2:2006 describes the calculation of mesopore size distribution between 2 nm and 50 nm, and of macropore distribution up to 100 nm. The method described in ISO 15901-2:2006 is suitable for a wide range of porous materials, even though the pore structure of certain materials is sometimes modified by pretreatment or cooling. Two groups of procedures are specified to determine the amount of gas adsorbed: those which depend on the measurement of the amount of gas removed from the gas phase (i.e. gas volumetric methods), and 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. To derive pore size distribution from the isotherm, it is necessary to apply one or more mathematical models, which entails simplifying certain basic assumptions.

Distribution des dimensions des pores et porosité des matériaux solides par porosimétrie au mercure et par adsorption de gaz — Partie 2: Analyse des mésopores et des macropores par adsorption de gaz

General Information

• Status: Withdrawn
• Publication Date: 10-Dec-2006
• 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: 9599 - Withdrawal of International Standard
• Start Date: 21-Jan-2022
• Completion Date: 13-Dec-2025

Relations

• Revised: ISO 15901-2:2022 - Pore size distribution and porosity of solid materials by mercury porosimetry and gas adsorption - Part 2: Analysis of nanopores by gas adsorption
• Effective Date: 11-Oct-2014

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 15901-2
First edition
2006-12-15
Pore size distribution and porosity of
solid materials by mercury porosimetry
and gas adsorption —
Part 2:
Analysis of mesopores and macropores
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 mésopores et des macropores par adsorption de
gaz
Reference number
©
ISO 2006
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ii © ISO 2006 – All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 2
4 Symbols . 4
5 Principles. 5
5.1 General principles. 5
5.2 Choice of method. 6
6 Verification of apparatus performance. 7
7 Calibration . 7
8 Sample preparation . 7
9 Static volumetric method. 8
9.1 Principle. 8
9.2 Apparatus and materials. 8
9.3 Typical test procedure. 9
9.4 Calculations. 11
10 Flow volumetric method . 13
10.1 Principle. 13
10.2 Apparatus and materials. 14
10.3 Typical test procedure. 14
10.4 Calculations. 14
11 Carrier gas method. 14
11.1 Principle. 14
11.2 Apparatus and materials. 15
11.3 Typical test procedure. 15
11.4 Calculations. 15
12 Gravimetric method. 16
12.1 Principle. 16
12.2 Apparatus and materials. 16
12.3 Typical test procedure. 16
12.4 Calculations. 16
13 Types of isotherms. 17
13.1 General. 17
13.2 Types of hysteresis loops. 19
14 Calculation of pore size distribution. 20
14.1 The use of reference isotherms . 20
14.2 Micropores. 21
14.3 Mesopores and macropores. 21
14.4 Representation of Pore Size Distribution. 23
15 Reporting of results. 25
Annex A (informative) Example of calculation of mesopore size distribution. 26
Bibliography . 30
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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
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.
ISO 15901-2 was prepared by Technical Committee ISO/TC 24, Sieves, sieving and other sizing methods,
Subcommittee SC 4, Sizing by methods other than sieving.
ISO 15901 consists of the following parts, under the general title Pore size distribution and porosity of solid
materials by mercury porosimetry and gas adsorption:
⎯ Part 1: Mercury porosimetry
⎯ Part 2: Analysis of mesopores and macropores by gas adsorption
⎯ Part 3: Analysis of micropores by gas adsorption
iv © ISO 2006 – All rights reserved

Introduction
Generally speaking, different types of pores can be pictured as apertures, channels or cavities within a solid
body, or as the space (i.e. an interstice or a void) 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 by a given
amount of the solid. In addition to the accessible pores, a solid can 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 part of ISO 15901.
Porous materials can 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 areas.
Porous materials have great technological importance, for example 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. In view of the complexity of most porous solids, it is not surprising to find
that the results obtained do not always concur, and that no single technique can be relied upon to provide a
complete picture of the 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.
Commonly used methods are as follows.
⎯ Mercury porosimetry, where the pores are filled with mercury under pressure. This method is suitable
for many materials with pores in the approximate diameter rang of 0,003 µm to 400 µm, and especially in
the range of 0,1 µm to 100 µm.
⎯ Mesopore and macropore analysis by gas adsorption, where the pores are characterized by
adsorbing a gas, such as nitrogen, at liquid nitrogen temperature. This method is used for pores in the
approximate diameter range 0,002 µm to 0,1 µm (2 nm to 100 nm), and is an extension of the surface
area estimation technique (see ISO 9277). (Discussion of other pore size distribution analysis techniques
[1]
can be found in Recommendations for the Characterization of Porous Solids .)
⎯ Micropore analysis by gas adsorption, where the pores are characterized by adsorbing a gas, such as
nitrogen, at liquid nitrogen temperature. This method is used for pores in the approximate diameter range
0,000 4 µm to 0,002 µm (0,4 nm to 2 nm).
vi © ISO 2006 – All rights reserved

INTERNATIONAL STANDARD ISO 15901-2:2006(E)

Pore size distribution and porosity of solid materials
by mercury porosimetry and gas adsorption —
Part 2:
Analysis of mesopores and macropores by gas adsorption
1 Scope
This part of ISO 15901 describes a method for the evaluation of porosity and pore size distribution by gas
adsorption. It is a comparative, rather than an absolute test. The method is limited to the determination of the
quantity of a gas adsorbed per unit mass of sample at a controlled, constant temperature.
This part of ISO 15901 does not specify the use of a particular adsorptive gas, however nitrogen is the
adsorptive gas most commonly used in such methods. Similarly, the temperature of liquid nitrogen is the
analysis temperature most commonly used. Use is sometimes made of other adsorptive gases, including
argon, carbon dioxide and krypton, and other analysis temperatures, including those of liquid argon and solid
carbon dioxide. In the case of nitrogen adsorption at liquid nitrogen temperature, the basis of this method is to
measure the quantity of nitrogen adsorbed at 77 K as a function of its relative pressure.
Traditionally, nitrogen adsorption is most appropriate for pores in the approximate range of widths 0,4 nm to
50 nm. Improvements in temperature control and pressure measurement now allow larger pore widths to be
evaluated. This part of ISO 15901 describes the calculation of mesopore size distribution between 2 nm and
50 nm, and of macropore distribution up to 100 nm.
The method described in this part of ISO 15901 is suitable for a wide range of porous materials, even though
the pore structure of certain materials is sometimes modified by pretreatment or cooling.
Two groups of procedures are specified to determine the amount of gas adsorbed:
⎯ those which depend on the measurement of the amount of gas removed from the gas phase (i.e. gas
volumetric methods), and
⎯ 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. To derive
pore size distribution from the isotherm, it is necessary to apply one or more mathematical models, which
entails simplifying certain basic assumptions.
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 8213, Chemical products for industrial use — Sampling techniques — Solid chemical products in the form
of particles varying from powders to coarse lumps
ISO 9276-1, Representation of results of particle size analysis — Part 1: Graphical representation
ISO 9277:1995, Determination of the specific surface area of solids by gas adsorption using the BET method
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
adsorbate
adsorbed gas
3.2
amount adsorbed
n
a
number of moles of gas adsorbed at a given pressure p
3.3
adsorbent
solid material on which adsorption occurs
3.4
adsorption
enrichment of the adsorptive gas at the external and accessible internal surfaces of a solid material
3.5
adsorptive
gas or vapour to be adsorbed
3.6
blind pore
dead-end pore
open pore having a single connection with an external surface
3.7
equilibrium adsorption pressure
p
pressure of the adsorptive gas in equilibrium with the adsorbate
3.8
ink bottle pore
narrow necked open pore
3.9
interconnected pore
pore which communicates with one or more other pores
3.10
isotherm
relationship between the amount of gas adsorbed and the equilibrium pressure of the gas, at constant
temperature
3.11
macropore
pore of internal width greater than 50 nm
2 © ISO 2006 – All rights reserved

3.12
mesopore
pore of internal width between 2 nm and 50 nm
3.13
micropore
pore of internal width less than 2 nm which is accessible for a molecule to be adsorbed
3.14
monolayer amount
n′
m
number of moles of the adsorbate that form a monomolecular layer over the surface of the adsorbent
3.15
monolayer capacity
V
m
volumetric equivalent of monolayer amount expressed as gas at standard conditions of temperature and
pressure (STP)
3.16
open pore
cavity or channel with access to an external surface
3.17
porosity
open porosity
ratio of the volume of open pores and voids to the total volume occupied by the solid
3.18
relative pressure
ratio of the equilibrium adsorption pressure, p, to the saturation vapour pressure, p
3.19
right cylindrical pore
cylindrical pore perpendicular to the surface
3.20
saturation vapour pressure
vapour pressure of the bulk liquefied adsorptive gas at the temperature of adsorption
3.21
through pore
pore which passes all the way through the sample
3.22
volume adsorbed
volumetric equivalent of adsorbed amount expressed as gas at standard conditions of temperature and
pressure (STP)
4 Symbols
Symbol Quantity SI Unit
3 -1
A slope of helium data regression from free space determination
cm ·Pa
He
2 -1
specific pore area
a′ m ·g
p
B intercept of helium data regression from free space determination
cm
He
-1
b buoyancy
g·Pa
-6 -1
C
non-ideal correction factor, equal to 0,464x10 for nitrogen at 77,35 K Pa
N
d
pore diameter nm
p
m mass of the solid sample material g
ss
m mass of gas adsorbed g
a
*
recorded mass on the balance of gas adsorbed of the ith dose g
m
ai
m correct mass of gas adsorbed at pressure p g
ai i
n amount of gas adsorbed mol
a
-1
n′ specific amount of gas adsorbed
mol·g
a
-1
n′ specific monolayer amount of gas
mol·g
m
-1
specific amount adsorbed at a particular relative pressure (x = 1, 2, 3)
n′
mol·g
a,x
p pressure of the adsorptive gas in equilibrium with the adsorbate Pa
p adsorptive pressure, used to determine free space (x = 1, 2, 3) Pa
x
p adsorptive pressure of the ith dose Pa
i
p adsorptive pressure measured in the dosing manifold Pa
man
p saturation vapour pressure Pa
p/p relative pressure of the adsorptive gas (see Note 1) 1
p standard pressure, equal to 101 325,02 Pa
std
-1 -1
R ideal gas constant, equal to 8,314 510
J·mol ·K
r Kelvin radius nm
K
t statistical thickness of the adsorbed layers of gas (see Note 2) nm
T ambient temperature K
amb
T temperature of the cryogenic bath K
b
T temperature of the dosing manifold when equilibrium of pressure has been K
eq
achieved
T temperature of the dosing manifold at time of the addition of the adsorptive K
man
dose
T standard temperature, equal to 273,15 K
std
V sample holder volume at cryogenic bath temperature
cm
sh,b
V adsorptive volume of dose in sample holder
cm
d
4 © ISO 2006 – All rights reserved

Symbol Quantity SI Unit
V adsorptive volume of the ith dose placed in the sample holder cm
di
V free space volume with sample holder immersed in cryogenic bath cm
fs,b
V free space volume with sample holder at ambient temperature cm
fs,amb
th 3 -1
V′ volume of gas adsorbed on the i dose at STP (273,15 K; 101 325 Pa) cm ·g
ai
3 -1
V′ specific liquid equivalent of the volume of adsorbate condensed in pore cm ·g
l
capillaries
V monolayer capacity of adsorbed gas cm
m
V volume of the dosing manifold cm
man
3 -1
V molar volume of liquid condensate cm ·mol
m,l
α normalized adsorption (see Note 1) 1
s
-3
ρ density g·cm
δ thickness of one monolayer of adsorbate nm
a
-2
σ surface tension of the liquid condensate J·m
l
NOTE 1 According to ISO 31-0, the coherent SI unit for any quantity of dimension one (at present commonly
determined “dimensionless”) is the unit one.
NOTE 2 While the symbol t is generally used to represent time, in the normal practice of pore size distribution analysis
by gas adsorption, t is traditionally used to represent the statistical thickness of the adsorbed layers of gas, as indicated in
the list above. Therefore all uses of the symbol t in this part of ISO 15901 refer to statistical thickness, and not to time.
5 Principles
5.1 General principles
The quantity of gas adsorbed on a surface is recorded as a function of the relative pressure of the adsorptive
gas for a series of either increasing relative pressures on the adsorption portion of the isotherm, decreasing
relative pressures on the desorption portion of the isotherm, or both. The relation, at constant temperature,
between the amount adsorbed and the equilibrium relative pressure of the gas is known as the adsorption
isotherm. The minimum pore size that can be investigated is limited by the size of the adsorptive molecule.
NOTE In the case of nitrogen, the minimum investigable pore size is approximately 0,5 nm.
The maximum pore width is limited by the practical difficulty of determining the amount of gas adsorbed at
high relative pressure, p/p .
Comparative pore size distributions of less than 2 nm in width, called micropores, can be determined with
nitrogen as the adsorptive gas, although other gases (e.g. argon) may provide more reliable results. Both
nitrogen and argon have been used successfully for the determination of the mesopore size distribution.
The pore size distributions calculated respectively from the adsorption and desorption portions of the isotherm
will not necessarily be the same.
Adsorption of gas into a porous solid takes place in accordance with a number of different mechanisms. For
instance, in mesopores and macropores, multilayer adsorption onto the pore walls occurs initially. At higher
relative pressures, capillary condensation takes place with the formation of a curved liquid-like meniscus. The
computation of the mesopore size distribution is generally carried out using methods based upon the Kelvin
equation.
When nitrogen is employed as the adsorptive gas at the temperature of liquid nitrogen, 77,35 K, the Kelvin
equation may be expressed in the form:
−2σ V
−0,953
lm,l
r== (1)
K
⎛⎞ ⎛ ⎞
p p
RT ln ln
⎜⎟ ⎜ ⎟
b
p p
⎝⎠00⎝ ⎠
where
σ is the surface tension of the liquid condensate;

l
V is the molar volume of the liquid condensate;
m,l
R is the ideal gas constant;
T is the analysis temperature;
b
r is the radius of curvature of the adsorptive gas condensed in the pore;
K
p is the saturation vapour pressure of nitrogen at the temperature of the liquid nitrogen;
p is the equilibrium pressure of the nitrogen adsorptive gas.
The numeric constants evaluate to a value of 0,953 nm for nitrogen at 77 K.
Since condensation is considered to occur only after an adsorbed layer has formed on the pore walls, it is
necessary to make allowance for the thickness of this adsorbed film by means of an equation. In the case of
cylindrical pores, this equation is:
dr=+2 t (2)
( )
pK
where
d is the cylindrical pore diameter (in nm);

p
t is the thickness of the adsorbed layer (in nm).
Various methods exist for the evaluation of t as a function of relative pressure and for calculating pore size
[3] [4]
distribution .
The Kelvin equation cannot be used for pores of less than approximately 2 nm diameter. This is because
interactions with adjacent pore walls become significant and the adsorbate can no longer be considered liquid
when it has bulk thermodynamic properties.
5.2 Choice of method
The required experimental data to establish a sorption isotherm may be obtained by volumetric or gravimetric
methods, either in measurements at stepwise varied pressure and observation of the equilibrium volume of
pressure or mass respectively, or by continuous varied pressure. Because sorption takes a long time in some
parts of the isotherm, the stepwise static method is recommended to ensure the measurement of equilibrium
values.
The volumetric method is based on calibration volumes and pressure measurements (see ISO 9277:1995,
Figure 5). The volume of adsorbate is calculated as the difference between the gas admitted and the quantity
of gas filling the dead volume (i.e. the free space in the sample container, including connections) by
application of the general gas equation. The various volumes of the apparatus should be calibrated and their
temperatures should be taken into account.
6 © ISO 2006 – All rights reserved

For gravimetric measurements, a sensitive microbalance and a pressure gauge are required (see
ISO 9277:1995, Figure 6). The mass adsorbed is measured directly, but a pressure-dependent buoyancy
correction is necessary. Equilibrium is observed by monitoring the mass indication. Because the sample is not
in direct contact with the thermostat, it is necessary to ensure the correct temperature artificially.
6 Verification of apparatus performance
1)
It is recommended that a certified reference material , selected by the user, be tested on a regular basis in
order to monitor instrument calibration and performance. In the case of specific surface area analysis, testing
may be carried out on a local reference material which is traceable to a certified reference material.
7 Calibration
Calibration of individual components should be carried out in accordance with the manufacturer’s
recommendations. Generally speaking, calibration of pressure transducers and temperature sensors is
accomplished with reference to standard pressure- and temperature-measuring devices which have
calibrations traceable to national standards. Manifold volume calibration is achieved through appropriate
pressure and temperature measures, using constant-temperature volumetric spaces or solids of known,
traceable volume. Analysis tube calibration is generally achieved by the determining of free space, as
described in 9.3.
8 Sample preparation
Sampling shall be carried out in accordance with ISO 8213. Before adsorption measurements are taken, it is
necessary to remove physisorbed material from the surface of the adsorbent by “outgassing”. In this process,
it is essential to be able to obtain reproducible adsorption data whilst avoiding irreversible changes to the
adsorbent surface. The outgassing technique should be selected in accordance with the adsorption system
being studied, and the conditions should be controlled so that these objectives are achieved.
Several outgassing techniques exist. The commonest is exposure of the surface to high vacuum, usually at an
elevated temperature. In some cases, flushing the adsorbent with an inert gas (which may be the adsorptive
gas) at an elevated temperature is sufficient. With some microporous materials, one or more cycles of flushing
with gas, followed by heating in vacuum, may be necessary before reproducible adsorption data can be
obtained. Whatever technique is used, it is sometimes possible to reduce the outgassing time, especially for
very damp materials, by a preliminary drying of the sample in an oven at a suitable temperature.
When vacuum conditions are used, outgassing to a residual pressure in the range of approximately 1,0 Pa to
0,01 Pa is usually sufficient for mesoporous materials, while a residual pressure of 0,01 Pa or lower is
recommended for microporous materials. High vacuum conditions may cause surface changes with some
adsorbents. As the rate of outgassing is heavily temperature dependent, the temperature should be the
maximum compatible with minimal outgassing, whilst avoiding changes to the adsorbent (e.g. sintering,
decomposition). Changes in the adsorbent may depend upon the heating rate used.

1) Certified reference materials are offered by a number of national standard bodies and are currently available from the
following addresses:
Bundesanstalt für Materialforschung und -prüfung (BAM)
Division I. 1 Inorganic Chemical Analysis; Reference Materials
Branch Adlershof, Richard-Willstätter-Straße 11, D-12489 Berlin
Standard Reference Materials Program
National Institute of Standards and Technology (NIST)
100 Bureau Drive, Stop 2322
Gaithersburg, MD 20899-2322
This information is given for the convenience of users of this part of ISO 15901 and does not constitute an endorsement
by ISO of the product named. Equivalent products may be used if they can be shown to lead to the same results.
In order to optimize pretreatment, it is advisable to study the thermal behaviour of the material, e.g. by
thermogravimetric analysis and differential scanning calorimetry, in order to determine the temperatures at
which materials are evolved from the sample, together with any phase changes which could affect the history
of the sample.
If this information is not available, temperature selection should be based on prior experience and general
knowledge of the properties of the adsorbent, and trials should be conducted if necessary.
The progress of outgassing should be followed by a suitable monitoring variable. This may be the pressure in
the system (commonly used for the vacuum technique), or the mass of the adsorbent (applicable to the
gravimetric method). When the observed variable has reached a steady value, which may take 0,25 h or many
more, depending on the sample, the completeness of outgassing should be checked, e.g. with vacuum
techniques; which can be done by isolating the heated sample and checking that the pressure over the
sample does not rise significantly over a period of a few minutes. A sample outgas rate of less than
0,7 Pa/min at ambient temperature is generally sufficient where nitrogen is to be used as the adsorptive gas.
In all cases, the outgassing conditions (e.g. temperatures, heating rates, duration, residual pressure) should
be recorded.
9 Static volumetric method
9.1 Principle
In the static volumetric method, a known amount of gas is admitted to a sample bulb thermostatted at the
adsorption temperature. Adsorption of the gas onto the sample occurs, and the pressure in the confined
volume continues to fall until the adsorbate and the adsorptive gas are in equilibrium. The amount of
adsorbate at the equilibrium pressure is the difference between the amount of gas admitted and the amount of
adsorptive gas remaining in the gas phase. The pressure is measured, together with the temperatures and
volumes of the system. The volumes are most easily determined by gas expansion of an inert gas such as
helium.
9.2 Apparatus and materials
9.2.1 General
A static volumetric apparatus generally consists of a metal or glass manifold, which interconnects the sample
tube, a saturation pressure probe, a pressure-measuring device, a vacuum source, and nitrogen and helium
supplies. The volume of the manifold shall be calibrated. A means of recording the temperature of the
manifold should be provided. Current commercial instrumentation offers two levels of vacuum systems and
pressure resolution, both of which are suitable for the analyses discussed in this part of ISO 15901. The upper
pore size limit of the technique is limited by the ability to measure adsorptive saturation pressure.
3 3
Sample tubes of various sizes may be used. Typical volumes range from 10 cm to 20 cm . To minimize
errors, the free space above the sample should be kept as small as possible and can, for example, be
reduced by placing a glass rod in the neck of the sample tube.
9.2.2 Apparatus
9.2.2.1 Dewar flasks, of various sizes, and storage facilities for liquid nitrogen. A 20 litre to 40 litre
storage vessel will generally be required.
9.2.2.2 Constant level device, to maintain the liquid nitrogen level around the sample tube at a minimum
of 15 mm above the sample, and constant to within 1 mm. Minimizing volumes exposed to level change
serves to minimize errors due to change.
9.2.2.3 Small electric heating mantle or furnace, to fit around the sample tube during outgassing. A
maximum temperature of 350 °C is generally adequate.
8 © ISO 2006 – All rights reserved

9.2.2.4 Weighing balance, with a resolution of 1 mg or better.
9.2.3 Materials
9.2.3.1 Nitrogen or other suitable adsorptive gas (e.g. argon), dry, not less than 99,99 % purity.
9.2.3.2 Helium, not less than 99,99 % purity.
9.2.3.3 Liquid nitrogen or other means of temperature control (e.g. liquid argon), not less than 99 %
purity.
9.3 Typical test procedure
9.3.1 General
The procedure described here assumes that manually-controlled apparatus is used. The use of automated
apparatus based upon the same operating principles is acceptable.
9.3.2 Measuring mass of sample
Weigh the empty sample bulb, along with any stopper and void-space filling device. Weigh a representative
test sample and place it in the sample bulb.
NOTE 1 To ensure accuracy, the sample is reweighed after analysis. If the mass is not equal to the initial mass after
outgassing and prior to analysis, the calculations are based on the mass after analysis (“outgassed sample mass”, see
9.3.8).
NOTE 2 For the measurement of nitrogen adsorption, it is preferable that the size of the sample be such that the total
2 2
surface area lies between 5 m and 200 m .
9.3.3 Outgassing
Connect the sample tube to the apparatus and outgas the sample (see Clause 7), first at room temperature
and then, if necessary, while the sample is heated at a higher temperature for a sufficient duration. Outgas the
powders carefully to avoid loss of sample. Evacuate the sample and the apparatus. Check the outgassing rate
by isolating the sample from the vacuum system. Any significant increase in pressure indicates incomplete
outgassing or a leak in the system (see ISO 9277:1995, Figure 4.).
NOTE 1 Sample outgassing can take place on another apparatus especially designed for that purpose. At the end of
the outgassing process, the sample tube is filled to approximately atmospheric pressure with a dry inert gas, generally the
adsorptive gas.
NOTE 2 For more precise measurement, helium can be introduced into the sample tube before immersion in the liquid
nitrogen, thereby helping to maintain the outgassed condition of the sample. Given that some microporous materials retain
helium strongly, it is important that, prior to analysis, all helium be evacuated completely, which can take many hours.
Rather than helium, a non-adsorbing and non-reacting gas, e.g. the adsorptive gas, is introduced into the sample holder
with the samples.
NOTE 3 When sealing valves are available, the sample can be transferred under vacuum.
9.3.4 Measuring free space
The free space shall be measured before or after the measurement of the adsorption isotherm. The calibration
is done volumetrically, using helium at the measuring temperature. It should be noted that some materials
may adsorb and/or absorb helium. In such cases, corrections can be made after measuring the sorption
isotherm. If the measurement of the free space can be separated from the adsorption measurement, the use
of helium can be avoided. The void volume of the empty sample cell is measured at ambient temperature
using nitrogen. Subsequently, a blank experiment (with the empty sample cell) is performed under the same
experimental conditions (temperature and relative pressure range) as the sorption measurements. The
required correction for the sample volume is made by entering the sample density or by pycnometric
measurement with nitrogen at ambient temperature at the start of the sorption analysis (in which case the
effects of nitrogen adsorption can be ignored). The need to determine free space may be avoided if difference
measurements are used, i.e. by means of a reference and sample tube connected by a differential transducer.
In this case, and in the case where variation in effective free space is known, a constant level device is not
needed.
9.3.5 Measuring free space with helium
9.3.5.1 If free space determination is initiated before the sample is immersed into liquid nitrogen, use the
following procedure.
4 5
Admit helium into the apparatus manifold to a pressure of between 7 × 10 Pa and 1,1 × 10 Pa. Record this
pressure, p , and then admit the helium into the sample tube. Record the new pressure, p . Record the
1 2
temperature of the manifold, T .
man
Immerse the sample bulb and saturation pressure probe in the liquid nitrogen. Record the new pressure of the
helium, p . Evacuate the sample and the apparatus. Maintain the level of liquid nitrogen at a constant level.
9.3.5.2 If free space determination is initiated after the sample is immersed into liquid nitrogen, use the
following alternative procedure.
Connect the sample tube to the apparatus and outgas the sample, evacuating the sample and the apparatus.
Determine saturation vapour pressure as described above. Ensure that the apparatus manifold is fully
evacuated.
4 4
Admit helium into the apparatus manifold to a pressure of between 1,3 × 10 Pa and 4 × 10 Pa. Allow the
helium to thermally equilibrate, then record the pressure, p . Admit helium into the sample tube. Allow the
helium to equilibrate such that a constant pressure is achieved. Record the new pressure, p , and the
apparatus manifold temperature. Close the sample and repeat the procedure, such that at least one additional
helium sample pressure point is measured. Evacuate the helium from the apparatus and sample tube.
9.3.6 Measuring saturation pressure (p )
Stop evacuation and admit nitrogen into the saturation pressure tube whilst monitoring the pressure. Continue
admitting nitrogen until the pressure is constant. Once the pressure reaches saturation, nitrogen will begin to
condense in the saturation tube. Record the saturation vapour pressure of the nitrogen, p . Close the
saturation pressure valve. Re-evacuate the apparatus manifold. It is recommended that the saturation vapour
pressure of nitrogen be recorded at least every 1 h to 2 h. An alternative way of obtaining the saturation
pressure is to measure the temperature of the liquid nitrogen bath and to calculate the corresponding
saturation pressure using a proper equation of state.
9.3.7 Measuring adsorption isotherm
To record the adsorption portion of the isotherm, the pressure of nitrogen over the sample is increased in a
series of steps. Close off the vacuum system from the manifold and admit nitrogen into the manifold. Allow
time for the nitrogen gas to thermally equilibrate with the manifold. Record the pressure in the manifold, p ,
man
and the temperature of the manifold, T . Allow nitrogen to expand into the sample tube. Allow enough time
man
for the adsorption process to equilibrate, which is indicated by a constant pressure reading. Record this stable
pressure, p (equilibrium pressure). Record the manifold temperature after equilibration, T . Repeat this
eq
sequence of operations for subsequent steps, admitting nitrogen to the sample from the manifold in a series of
doses, until the maximum required equilibrium pressure has been reached (generally at least 0,99 × 10 Pa,
i.e. a relative pressure of at least 0,99). Care should be taken not to reach the saturation pressure of nitrogen
over the sample while collecting the adsorption portion of the isotherm.
10 © ISO 2006 – All rights reserved

9.3.8 Measuring desorption isotherm
The desorption portion of the isotherm may then be recorded by decreasing the pressure of nitrogen over the
sample in a series of steps. The procedure is identical to that for adsorption, except that for each step, instead
of admitting nitrogen to the manifold, the pressure in the manifold should be reduced to below the pressure in
the sample tube by using the vacuum system.
The number of steps, and therefore the dose pressures required, depend on the pore volume distribution of
the sample and the number of isotherm points needed (at least 20 are recommended for each of the
adsorption and the desorption portions of the curve). Since the pore volume of the sample is unknown before
the analysis, the dose pressures are best determined on the basis of prior experience for the particular sample
type.
CAUTION — Reduce the pressure in the sample tube by means of the vacuum system before lowering
the Dewar flask of liquid nitrogen.
The outgassed sample mass should be measured either immediately after the outgassing or upon completion
of the test. Before weighing, it is recommended that the sample be backfilled to atmospheric pressure with dry
air or nitrogen, or kept under vacuum with appropriate buoyancy correction.
9.4 Calculations
9.4.1 Manifold volume
The volume of the manifold, V , should be determined when the apparatus is constructed or modified. This
man
can be carried out by attaching a calibrated volume in place of the sample tube and expanding helium into it
from the manifold, or by expanding helium into a chamber containing a known volume solid.
9.4.2 Free space
9.4.2.1 If free space determination is initiated prior to immersion of the sample into liquid nitrogen, use
the following method of calculation.
First calculate the apparent volume of the free space at ambient temperature, V , using the expression:
fs,amb
⎛⎞V
pV V
fs,amb
1 man man
=+p (3)
⎜⎟
TT T
man⎝⎠man std
where
V is the volume of the manifold;
man
T is standard temperature, 273,15 K.
std
Next calculate the apparent volume of the free space at liquid nitrogen temperature, V , using the
fs,b
expression:
⎛⎞V
pV V
fs,b
1 man man
=+p (4)
⎜⎟
TT T
man man std
⎝⎠
The total volume of gas dosed into the sample tube after the ith dose, V , is given by:
di
⎛⎞
⎛⎞
pV pV T
man man man std
VV=+⎜⎟− (5)
⎜⎟
ddii−1
⎜⎟
TT p
man eq ⎝⎠std
⎝⎠
where
V is the total volume of gas dosed into the sample tube before the ith dose (equal to zero for the

di-
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