ISO 15901-2:2006
(Main)Pore size distribution and porosity of solid materials by mercury porosimetry and gas adsorption — Part 2: Analysis of mesopores and macropores by gas adsorption
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
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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 15901-2:2006(E)
©
ISO 2006
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ISO 15901-2:2006(E)
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ISO 15901-2:2006(E)
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
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ISO 15901-2:2006(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
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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
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ISO 15901-2:2006(E)
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 .)
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ISO 15901-2:2006(E)
⎯ 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).
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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
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ISO 15901-2:2006(E)
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
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ISO 15901-2:2006(E)
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
0
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)
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ISO 15901-2:2006(E)
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
3
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
0
p/p relative pressure of the adsorptive gas (see Note 1) 1
0
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
3
V sample holder volume at cryogenic bath temperature
cm
sh,b
3
V adsorptive volume of dose in sample holder
cm
d
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ISO 15901-2:2006(E)
Symbol Quantity SI Unit
3
V adsorptive volume of the ith dose placed in the sample holder cm
di
3
V free space volume with sample holder immersed in cryogenic bath cm
fs,b
3
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
3
V monolayer capacity of adsorbed gas cm
m
3
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 .
0
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.
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ISO 15901-2:2006(E)
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;
0
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.
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ISO 15901-2:2006(E)
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
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