ISO 15901-3:2007

INTERNATIONAL ISO
STANDARD 15901-3
First edition
2007-04-15

Pore size distribution and porosity of
solid materials by mercury porosimetry
and gas adsorption —
Part 3:
Analysis of micropores by gas adsorption
Distribution des dimensions des pores et porosité des matériaux solides
par porosimétrie au mercure et par adsorption de gaz —
Partie 3: Analyse des micropores par adsorption de gaz




Reference number
ISO 15901-3:2007(E)
©
ISO 2007

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ISO 15901-3:2007(E)
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ISO 15901-3:2007(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 1
4 Symbols . 3
5 Principles. 5
5.1 General. 5
5.2 Methods of measurement . 6
6 Procedure of measurements . 6
6.1 Sampling. 6
6.2 Sample pre-treatment. 6
6.3 Measurement. 7
7 Verification of apparatus performance. 7
8 Calibration . 7
9 Evaluation of the micropore volume. 7
9.1 General. 7
9.2 Determination of the micropore volume according to Dubinin and Radushkevich . 9
9.3 Micropore analysis by comparison of isotherms. 10
9.4 Determination of micropore size distribution by the Horvath-Kawazoe (HK) and the Saito-
Foley (SF) method. 14
9.5 Determination of micropore size distribution by non-local density functional theory . 15
10 Test report . 19
Annex A (informative) Horvath-Kawazoe and Saito-Foley methods. 20
Annex B (informative) NLDFT method . 23
Bibliography . 26

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ISO 15901-3:2007(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.
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 15901-3 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
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ISO 15901-3:2007(E)
Introduction
[42]
According to the IUPAC Recommendations, 1984 , micropores are defined as pores with internal widths of
less than 2 nm. Different methods for the characterization of micropores 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. With regard to the 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. On account of the fractality of dispersed and porous
materials, the results of adsorption measurements depend on the size of the gas molecules used (effective
diameter and space required at the surface). Furthermore, micropores might not be accessible for larger
molecules and, thus, exclusion effects can be observed.
The measuring techniques of the methods described in the present standard are similar to those of
ISO 15901-2 and ISO 9277 for the measurement of gas adsorption at low temperature. From the measured
−1
isotherm, however, the very first part (i.e. relative pressures < 10 ) is evaluated and thus the evaluation
method is different.

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INTERNATIONAL STANDARD ISO 15901-3:2007(E)

Pore size distribution and porosity of solid materials by
mercury porosimetry and gas adsorption —
Part 3:
Analysis of micropores by gas adsorption
1 Scope
This part of ISO 15901 describes methods for the evaluation of the volume of micropores (pores of internal
width less than 2 nm) and the specific surface area of microporous material by low-temperature adsorption of
[1],[2],[3],[4],[5],[6],[7]
gases . These are comparative, non-destructive tests. The methods use physisorbing gases
that can penetrate into the pores under investigation. The method is applicable to isotherms of type I, II, IV or
VI of the IUPAC classification (see ISO 15901-2:—, Figure 1, and ISO 9277).
The methods in this part of ISO 15901 are not applicable when chemisorption or absorption takes place.
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 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 9277:1995, Determination of the specific surface area of solids by gas adsorption using the BET method
ISO 15901-2:—, Pore size distribution and porosity of solid materials by mercury porosimetry and gas
adsorption — Part 2: Analysis of mesopores and macropores by gas adsorption
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
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
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ISO 15901-3:2007(E)
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
number of moles 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
number of moles of the adsorbate that form 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
macropore
pore with width greater than about 50 nm
3.11
mesopore
pore with width between approximately 2 nm and 50 nm
3.12
micropore
pore with width of about 2 nm or less
3.13
physisorption
weak bonding of the adsorbate, reversible by small changes in pressure or temperature
3.14
pore size
pore width, i.e. diameter of cylindrical pore or distance between opposite walls of slit
3.15
relative pressure
ratio of the equilibrium adsorption pressure, p, to the saturation vapour pressure, p , at analysis temperature
0
3.16
saturation vapour pressure
vapour pressure of the bulk liquefied adsorptive at the temperature of adsorption
3.17
volume absorbed
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
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ISO 15901-3:2007(E)
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 Term Unit
6
K Kirkwood-Mueller constant of adsorptive J·cm
Aa
6
K Kirkwood-Mueller constant of adsorbent J·cm
As
2 −1
a specific surface area m ·g
s
2 −1
a specific surface area of reference sample m ·g
s,ref
3
α polarizability of adsorptive cm
a
2
a molecular cross-sectional area nm
m
α normalized adsorption (see Note 1) 1
s
3
α polarizability of adsorbent cm
(s*)
β affinity coefficient 1
−1
c speed of light m·s
d diameter of an adsorptive molecule nm
a
d diameter of hard spheres nm
HS
d effective pore diameter (cylindrical pore) nm
p
d diameter of an adsorbent molecule nm
s
d d = (d + d )/2, distance between adsorptive and adsorbent molecules nm
0 0 s a
−1
E adsorption potential J⋅mol
−1
E characteristic adsorption energy J⋅mol
0
ε well depth parameter of the gas-gas Lennard Jones potential K
ff
ε well depth parameter of the gas-solid Lennard Jones potential K
sf
−23 −1
k Boltzmann constant (1,380 650 5 × 10) J K
B
l nuclei-nuclei pore width nm
m mass adsorbed g
a
m mass of an electron kg
e
m sample mass g
s
23 −1
N Avogadro's constant (6,022 1415 × 10) mol
A
−2
N number of atoms per unit area (square metre) of monolayer m
a
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ISO 15901-3:2007(E)
Symbol Term Unit
−2
N number of atoms per unit area (square metre) of adsorbent m
s
−1
n specific amount adsorbed mol·g
a
3 −1
n monolayer capacity cm ·g
m
p pressure of the adsorptive in equilibrium with the adsorbate Pa
p saturation vapour pressure of the adsorptive Pa
0
p/p relative pressure of the adsorptive 1
0
−1 −1
R ideal gas constant (8,314 472) Jmol K
−3
ρ gas density g·cm
g
−3
ρ gas density at STP (273,15 K; 101 325,02 Pa) g·cm
g,STP
−3
ρ liquid density g·cm
l

σ distance between two molecules at zero interaction energy nm
σ distance parameter of the gas-gas Lennard Jones potential nm
ff
σ distance parameter of the gas-solid Lennard Jones potential nm
sf
T temperature K
T critical temperature K
cr
t statistical layer thickness (see Note 2) nm
3 −1
V specific adsorbed liquid volume of the adsorbate cm ·g
a
3 −1
V specific adsorbed gas volume at STP (273,15 K; 101 325,02 Pa) cm ·g
g
3 −1
V micropore volume cm ·g
micro
W pore width (slit pore) nm
3

χ diamagnetic susceptibility of adsorptive cm
a
3
χ diamagnetic susceptibility of adsorbent cm
s

[43]
NOTE 1 According to ISO 31-0 , the coherent SI unit for any quantity of dimension one (at present commonly
referred to as “dimensionless”) is the unit one, symbol 1.
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 liquid-like adsorbate layer. Therefore,
all uses of the symbol t in this standard will refer to the statistical thickness and not time.
For gravimetric measurements, the mass adsorbed is measured directly (see ISO 9277:1995, Figure 6), but a
pressure-dependent buoyancy correction is necessary. Equilibrium is observed by monitoring the mass
indication. In the region between about 0,1 Pa to 100 Pa, thermal gas flow can seriously disturb the
measurements. Because the sample is not in direct contact with the thermostat, it is necessary to ensure the
correct temperature experimentally.
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ISO 15901-3:2007(E)
5 Principles
5.1 General
The methods described in this part of ISO 15901-3 are based on the measurement of the adsorption and
desorption of gases at a constant low temperature and the evaluation of the initial part of the isotherm. Gases
used are those which are bound by physisorption at the solid surface, in particular N at 77,4 K, Ar at 77,4 K
2
or 87,3 K, and CO at 195 K or 273,15 K. Because of the different size of the gas molecules, and hence,
2
different accessibility of the pores, and also because of the different measuring temperatures, different results
can be obtained. In micropores, the potential of interactions of the opposite pore walls are overlapping and,
[8]
hence, physisorption is stronger than in wide pores or at the external surface (see Figure 1). As a
consequence, micropores are filled at very low relative pressure (< 0,01). 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. Micropores are characterized by the micropore volume and the micropore distribution. Because
the pore size is similar to the molecule diameter, the choice of the gas is decisive.

Key
X distance between pore walls
Y potential energy
Figure 1 — Three examples of the enhancement of interaction potential between a fluid and the
[8]
surface in infinitely long, slit-like micropores as a function of the pore width (after Everett and Powl )
The pore size and volume analysis of microporous materials, such as zeolites, carbon molecular sieves, etc.,
−7 −5
is difficult, because the filling of pores of dimension 0,5 nm to 1 nm occurs at relative pressures of 10 to 10
where the rate of diffusion and adsorption equilibration is very slow. Argon at 87,3 K fills micropores of
dimension 0,5 nm to 1 nm at appreciably higher relative pressures compared to nitrogen (at 77,4 K). Both the
higher pore-filling pressure and higher temperature help to accelerate diffusion and equilibration processes
compared to nitrogen adsorption. Hence, it is of advantage to analyse microporous materials by using argon
as the adsorptive at liquid-argon temperature (87,3 K). However, as in the case of nitrogen adsorption at
77,4 K, the absolute pressures required to fill the most narrow micropores with argon are still very low.
Associated with the low pressures required, is (as indicated above) the well known problem of diffusion
restrictions, which prevent nitrogen molecules and also argon molecules from entering the narrowest
micropores (as present in activated-carbon fibres, carbon molecular sieves, etc.). This can lead to erroneous
adsorption isotherms, underestimated pore volumes, etc. A possibility to overcome these problems (at least
for microporous carbons) is the use of CO as the adsorptive at 273,15 K. The saturation pressure at this
2
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ISO 15901-3:2007(E)
temperature is about 3,48 MPa, i.e. in order to achieve the small relative pressures required to monitor the
micropore filling, a turbomolecular pump-level vacuum is not necessary. With CO adsorption up to
2
101 325 Pa (1 atm), one can detect pores from the narrowest micropores up to about 1,5 nm. At these
relatively high temperatures and pressures, significant diffusion limitations no longer exist, which leads to the
situation that equilibrium is achieved much faster relative to low-temperature nitrogen and argon experiments.
5.2 Methods of measurement
The experimental data required to establish an adsorption/desorption (sorption) isotherm may be obtained by
volumetric (manometric) or gravimetric methods, by measurements either at stepwise, varied pressure with
observation of the equilibrium value of pressure or mass, respectively, or at a continuously varied pressure.
Because adsorption/desorption equilibrium can take a long time, the stepwise static method is recommended
to ensure the measurement of equilibrium values.
The volumetric method is based on calibrated volumes and pressure measurements (see ISO 9277:1995,
Figure 5). The amount of adsorbate is calculated as the difference between the gas admitted and the quantity
of gas filling the dead volume (free space in the sample container including connections) by application of the
general gas equation. Equilibrium is observed by monitoring the pressure in the free space. It is necessary to
take special care in the pressure measurements for micropores as physical adsorption occurs at relative
pressures substantially lower than in the case of sorption phenomena in mesopores and can span a broad
spectrum of pressures (up to seven orders of magnitude in pressure). Consequently, more than one pressure
transducer is necessary to measure the equilibrium pressure with sufficient accuracy. In order to study the
adsorption of gases like nitrogen and argon (at their boiling temperatures) within a relative pressure range of
−7
10 u p/p u 1 with sufficiently high accuracy, it is desirable to use a combination of different transducers
0
1)
with maximum ranges of 0,133 kPa (1 Torr ), 1,33 kPa (10 Torr) and 133 kPa (1 000 Torr). In addition, one
has to assure that the sample cell and the manifold can be evacuated to pressures as low as possible, which
requires a proper high-vacuum pumping system. The desired low pressure can be achieved by using a
−5
turbomolecular pump. For gas pressures below about 13 Pa (i.e. p/p < 10 for nitrogen and argon adsorption
0
at 77 K and 87 K, respectively), it is necessary to take into account the pressure differences along the
capillary of the sample bulb on account of the Knudsen effect (i.e. the thermal transpiration correction).

For gravimetric measurements, the mass adsorbed is measured directly (see ISO 9277:1995, Figure 6), but a
pressure-dependent buoyancy correction is necessary. Equilibrium is observed by monitoring the mass
indication. In the region between about 0,1 Pa and 100 Pa, thermal gas flow can seriously disturb the
measurements. Because the sample is not in direct contact with the thermostat, it is necessary to ensure the
correct temperature experimentally.
6 Procedure of measurements
6.1 Sampling
Sampling shall be performed in accordance with ISO 3165 and ISO 8213. The sample for test shall be
representative of the bulk material and should be of an appropriate quantity. Repeated measurements using a
second sample are recommended.
6.2 Sample pretreatment
The sample should be degassed in vacuum better than 1 Pa at elevated temperature to remove physisorbed
material. During this process, irreversible changes of the surface structure (revealed, for example, by a colour
change) should be avoided. The highest temperature that can be applied is favourably determined by means
of thermogravimetry (see ISO 9277:1995, Figure 3). Otherwise, repeated measurements should be carried out
by variying the time and the temperature (see ISO 9277:1995, Figure 4). Also, the temperatures at which
materials are evolved from the sample can be determined by means of differential scanning calorimetry and
the gas can be analysed.

1) Torr is a deprecated unit.
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ISO 15901-3:2007(E)
Alternatively, the sample is degassed at an elevated temperature by flushing with a high-quality inert gas, e.g.
helium or nitrogen. Complete degassing is indicated by a constant mass or constant pressure, respectively,
for a period of 15 min to 30 min. The mass of the dry sample should be determined.
6.3 Measurement
Adsorption measurements shall be carried out as described in ISO 9277 or ISO 15901-2.
7 Verification of apparatus performance
It is recommended that a certified reference material or a local reference material, selected by the user, be
tested on a regular basis to monitor instrument calibration and performance. The local reference material shall
be traceable to a certified reference material. Certified reference materials are offered by a number of national
2) 3)
standards bodies and are currently available from BAM , in Germany, and NIST , in the USA.
8 Calibration
The calibration of individual components should be carried out according to the manufacturer’s
recommendations. Typically, calibration of pressure transducers and temperature sensors is accomplished
with reference to standard pressure- and temperature-measuring devices that have calibrations traceable to
national standards. Manifold-volume calibration is achieved through appropriate pressure and temperature
measurements, using constant-temperature volumetric spaces or solids of known, traceable volume. Analysis
tube calibration is generally accomplished through determination of free space described in ISO 15901-2:—, 9.3.
9 Evaluation of the micropore volume
9.1 General
The isotherm V = f(p/p ) or m = f(p/p ) can be plotted on a linear scale (see Figure 2) or, preferably, on a
g 0 a 0 T
logarithmic scale (see Figure 3) of relative pressure.

2) Bundesanstalt für Materialforschung und -prüfung (BAM)
Division I. 1 Inorganic Chemical Analysis; Reference Materials
Branch Adlershof, Richard-Willstätter-Straße 11, D-12489 Berlin, Germany
3) Standard Reference Materials Program
National Institute of Standards and Technology (NIST)
100 Bureau Drive, Stop 2322
Gaithersburg, MD 20899-2322, USA
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ISO 15901-3:2007(E)

Figure 2 — Linear plot of the isotherm of argon on zeolite at 87,3 K

Figure 3 — Semi-logarithmic plot of the isotherm of argon on zeolite at 87,3 K
Adsorption measurements of highly microporous materials result in a Langmuir-type isotherm (type I of the
IUPAC classification; see ISO 9277:1995, Figure 1) if the external surface and the volume of mesopores are
negligible. The plateau corresponds to the micropore volume. If macropores are present, a steep increase
near p/p @ 1 can be observed.
0
The amount adsorbed at the plateau is a measure of the adsorption capacity. To obtain the pore volume, it is
assumed that the adsorbate has the normal molar volume of the liquid at the operational temperature (liquid
density). The pore volume is then given by Equation (1):
V = m /(ρ ⋅m ) (1)
a a l s
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ISO 15901-3:2007(E)
9.2 Determination of the micropore volume according to Dubinin and Radushkevich
[9]
The method, originally developed to investigate the microporosity of activated carbons , can be used for any
[10], [11], [12], [13]
microporous material . The isotherms of the adsorption of pure gases on microporous sorbents
[14]
can be described by means of Polanyi’s potential theory . Each adsorptive/adsorbent system is
characterized by an adsorption potential, E, which is influenced by the particular chemical properties of the
adsorbent. The volume, V , filled at a given relative pressure, p/p , as a fraction of the total micropore volume,
a 0
V , is a function of the adsorption potential, E, as given in Equation (2):
micro
Vf= ()E (2)
a
According to Dubinin, the adsorption potential equals the work required to bring an adsorbed molecule into the
gas phase. Using Polanyi’s potential yields at T < T , E can be defined as given in Equation (3):
cr
p
0
ER= T ln (3)
p
Based on the Polanyi concept of a temperature-invariant “characteristic curve” (i.e. plots of V versus E) for a
a
given adsorbent, Dubinin and Radushkevich arrived at the empirical equation given as Equation (4):
2
⎧⎫
⎡⎤
⎛⎞
⎪⎪RT p
0
VV=−exp⎢⎥ln (4)
⎨⎬⎜⎟
amicro
⎜⎟
βEp
⎢⎥0
⎪⎝ ⎠ ⎪
⎣⎦
⎩⎭
The characteristic adsorption energy, E , is correlated with the pore size distribution. The affinity coefficient, β,
0
allows the scaling of the characteristic curves of different adsorptives (for a given adsorbent) to the
characteristic curve of some particular adsorbate, which has been taken as an arbitrary standard. The Dubinin
isotherm can now be written in logarithmic form to yield a straight line, as given in Equation (5):
2
⎛⎞p
0
lgVV=−lg D lg (5)
amicro ⎜⎟
p
⎝⎠
where
2
⎛⎞
RT
D = 2,303 (6)
⎜⎟
⎜⎟
β E
⎝⎠0
−4
Data for evaluation should be taken preferably from the region of relative pressure 10 < p/p < 0,1. Then plot
0
2
⎡⎤
p
0
the data on a lgV versus lg diagram; see Figure 4. The slope of the regression line gives the
⎢⎥
g
p
⎢⎥
⎣⎦
parameter D. The total micropore volume, V , can be calculated from the ordinate intercept.
micro
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ISO 15901-3:2007(E)

Key
experimental data point
experimental data point used for the Dubinin-Radushkevitch (DR) fit
DR fit line
Figure 4 — Dubinin-Radushkevitch plot of an adsorption isotherm of N at 77,4 K on activated carbon
2
9.3 Micropore analysis by comparison of isotherms
9.3.1 General
In this method of analysis, gas adsorption isotherms on a sample are compared with those on a non-porous
...