Surface Area, Pore Size and More:
Theory and Application of Porous Materials
Characterization Methods
• Gas Adsorption Measurements with particular
focus on Microporous Materials
• Liquid Intrusion Porosimetry with particular focus
on Meso- and Macroporous Materials
• Other Methods of Pore Size measurement Capillary Flow Porometry and Electroacoustics
• Catalyst Characterization using Chemisorption and
Temperature Programmed Analyses
• Dynamic Water Vapor Sorption - Adsorption,
Absorption, Hydrophobicity, Hydrophilicity
Inert Gas Adsorption
–
–
–
–
What can be measured using this technique?
Who would be interested in such results?
A brief overview of measurement fundamentals.
Microporous materials
• Carbons
• Zeolites
• Metal organic frameworks
– Instrument selection for these materials
– Specific features of benefit to analyzing microporous materials
– Mesoporous/nonporous materials
•
•
•
•
•
•
•
Carbon black
Ceramics
Pigments
Alumina
Silica
Metal powders
Pharmaceuticals
– Instrument selection for these materials
– Specific features of benefit to analyzing meso-/nonporous materials
Inert Gas Adsorption
– What can be measured using this technique?
• Specific Surface Area
– How low?
» Depends on instrument sensitivity and amount of
sample (more later!)
– How high?
» No limit
• Pore Size Distribution
– Min, max?
» As small as the smallest gas molecule that can be
adsorbed
– Pore Volume
» No limit
• Heats of Adsorption
» More later
Inert Gas Adsorption
– Who would be interested in such results?
– Everyone who needs to understand how pore
structure affects material performance.
• Surface Area
– affects dissolution rates.
– affects electron/ion current density at electrode interface
with electrolyte.
– affects adsorption capacity.
– represents surface free energy available for bonding in
tabletting and sintering.
Inert Gas Adsorption
– Who would be interested in such results?
– Everyone who needs to understand how pore
structure affects material performance.
• Pore Size Distribution
– affects diffusion rates.
– affects molecular sieving properties.
– affects surface area per unit volume.
Measurement Overview
• Two techniques available
• Dynamic flow (uses different concentrations
of the adsorbing gas, i.e. gas mixtures)… this
will only be covered in discussion session
• Vacuum-volumetric, better to say
“Manometric” (uses different pressures of
the adsorbing gas)… our main focus
What is a Gas Sorption Analyzer?
• Does it actually measure surface area and pore
size?
• NO!! It simply records various pressures of gas
in the sample cell due to adsorption and
desorption. The instrument then calculates the amount (as STP
volume) of gas adsorbed/desorbed. Surface area, pore size are
calculated by PC software (iQWin, NovaWin, Quadrawin).
• Pressure measurements are critical!
Adsorption/Desorption
• Adsorption is the sticking of gas molecules
onto the surface of a solid… all available
surfaces including that surface inside open
pores.
• Increasing the pressure of gas over a solid
causes increasing adsorption.
• Temperature dependent
Adsorption/Desorption
• Desorption is the removal of gas molecules
from the surface of a solid… all available
surfaces including that surface inside open
pores.
• Decreasing the pressure of gas over a solid
causes increasing desorption.
• Done at same temperature as adsorption.
Movie time!
So, How Does It Work?
• Basic Construction
– Removable sample cell
– Dosing manifold
– Pressure transducers
– Vacuum system
– Analysis gas
– Valves to move gas in and out of manifold and
sample cell
– Sample thermostat (dewar, furnace, cryostat)
So, How Does It Work?
• Basic Construction
– Removable sample cell
• A long stemmed piece of glassware that holds the
sample during degassing (preparation) and
analysis.
• Available in different stem diameters and bulb
sizes.
So, How Does It Work?
• Basic Construction
– Dosing manifold
• A chamber of known (i.e. calibrated) physical
volume from which gas is added to and removed
from the sample cell during adsorption and
desorption respectively (think burette).
So, How Does It Work?
• Basic Construction
– Pressure transducers
• Used to both quantitatively determine the amount
of gas adsorbed/desorbed and the pressures at
which the sorption is measured.
So, How Does It Work?
• Basic Construction
– Vacuum system
• Vacuum pump(s) generate sub-atmospheric
pressure conditions.
• Rotary oil pumps for low vacuum applications.
• Turbo pump backed by oil-free diaphragm pump
for high vacuum applications.
So, How Does It Work?
• Basic Construction
– Analysis gas
• Nitrogen is used most often.
• Argon is recommended for micropore size
measurements.
• Krypton is used for very low surface area and thin
film applications.
• Multiple gases can be connected at one time,
though only one is actively used.
So, How Does It Work?
• Basic Construction
– Valves to move gas in and out of manifold and
of sample cell
• Automatically operated to fill the dosing manifold to
a pressure sufficient to yield a datum point at a
specified target pressure (or at target sorbed
amount)
• Magnetic latching valves… no heat generated
during pressure equilibration
So, How Does It Work?
• Basic Construction
– Sample thermostat (dewar, furnace, cryostat)
• Dewar holds cryogenic liquids (liquefied gases)
like liquid nitrogen (LN2) and liquid argon (LAr)
• Furnace: used for chemisorption measurements at
temperatures above ambient
• Cryostat: for advanced research applications,
overcomes limitations of restricted choice of
temperatures available with liquefied gases in a
dewar.
Basic Construction
Pressure transducer(s)
Analysis gas
Manifold
Sample cell
to vacuum
Basic Operation
Pressure transducer(s)
Analysis gas
Manifold
to vacuum
Manifold, transducer and
sample cell are evacuated.
Sample cell
Basic Operation
Pressure transducer(s)
Analysis gas
Manifold
to vacuum
Manifold, transducer and
sample cell are evacuated…
and cell is cooled.
Sample cell
Basic Operation
Pressure transducer(s)
Analysis gas
Manifold
to vacuum
Intermediate valve status.
Sample cell
Basic Operation
Pressure transducer(s)
Analysis gas
Manifold
to vacuum
Analysis gas is admitted to
build some pressure in the
manifold.
Sample cell
Basic Operation
Pressure transducer(s)
Analysis gas
Manifold
to vacuum
A steady pressure in the
manifold is recorded, P1.
Sample cell
Basic Operation
Pressure transducer(s)
Analysis gas
Manifold
to vacuum
Gas expands from manifold into
sample cell; pressure drops in
the manifold, rises in sample
cell.
Sample cell
Basic Operation
Pressure transducer(s)
Analysis gas
Manifold
to vacuum
Gas is adsorbed by the sample,
pressure drops further in both
volumes.
Sample cell
Basic Operation
Pressure transducer(s)
Analysis gas
Manifold
to vacuum
Eventually the pressure
equilbrates. Final pressure, P2,
is recorded.
Sample cell
Basic Operation
Pressure transducer(s)
Analysis gas
Manifold
to vacuum
Process is repeated at higher
and higher pressures.
Sample cell
Basic Operation
Pressure transducer(s)
Analysis gas
Manifold
to vacuum
Adsorption measurements are
complete... Getting ready to
desorb!
Sample cell
Basic Operation
Pressure transducer(s)
Analysis gas
Manifold
to vacuum
In desorption, some gas is
removed from the manifold
while the sample cell remains
isolated.
Sample cell
Basic Operation
Pressure transducer(s)
Analysis gas
Manifold
to vacuum
Manifold is isolated and
desorption P1 is measured.
Sample cell
Basic Operation
Pressure transducer(s)
Analysis gas
Manifold
to vacuum
Gas is expanded from sample cell
into manifold, pressure drops in
the sample cell, rises in the
manifold… P2 (desorption)
Sample cell
A More Realistic Representation
Sample Temperature Control
• As the coolant evaporates,
the level sensor signals the
dewar drive to compensate
for the change in level,
thereby maintaining a
constant and small cold
zone.
cabinet
level sensor
sample cell
90 hr dewar
drive shaft
dewar support arm
What’s Really Measured
• The pressure of gas not currently adsorbed by
the sample, just filling the void volume.
• To know quantitatively what is adsorbed, the
instrument calculates:
– The dose amounts, i.e. amount of gas moved into
(adsorption) or out of (desorption) the cell by the end
of an equilibration period.
– The amount of gas remaining unadsorbed (in the void
volume) at that time.
– The difference is what is adsorbed.
What’s Measured
• To calculate the gas amounts dosed
(in/out) the instrument must know:
– P1
– P2
– Volume of the manifold
– Temperature of the manifold
What’s Measured
• To know the volume of the manifold:
– it is calibrated using a special cell and glass
cyclinder (rod).
– All instrument manifolds are factory
calibrated.
• To know the temperature of the manifold:
– it is constantly monitored by a solid state
sensor.
What’s Measured
• To calculate the gas amounts not
adsorbed the instrument must know:
– Volume of the void volume (sample cell)
– Temperature of the void volume (sample cell)
What’s Measured
• To know the volume of the sample cell the
instrument can:
– Measure it by expanding helium from the
manifold (as part of initializing the analysis)
– Use a previously measured value
– Use a stored value based on expanding
nitrogen into an empty cell, correcting for
sample volume (the so-called NOVA method)
What’s Measured
• To know the temperature of the sample
cell (in coolant) the instrument:
– is told it as an analysis parameter.
• To ensure that the volume of cell in coolant
remains constant:
– a coolant level sensor and dewar elevator
mechanism combine to maintain level of
coolant around the sample cell.
Level sensor
Small Cold Zone = Sensitivity
Coolant level controlled
here creates a small cold zone.
Quantachrome’s instruments
Working Equation
PV = nRT
nads = ndosed - nvoid
nads = (PV/RT)man. - (PV/RT)cell
Refinements
• Corrections for “non-ideality” of gas,
especially at cryogenic temperatures.
• Compensation for the slight change in
temperature of that part of the sample cell
not in coolant (“TempComp”).
• Determination of “saturation vapor
pressure” of the coolant, known as Po.
What Is The Result?
Amount adsorbed
It’s called an “isotherm”
Equilibrium pressure
What Is The Result?
Amount adsorbed
The values on the y-axis are calculated
from pressure measurements (and
temperature values)
The values on the x-axis are pressure
measurements.
Equilibrium pressure
What Is The Result?
Amount adsorbed
Desorption curve may overlay on, or
appear to left of, the adsorption curve
The values on the x-axis are in fact
expressed as relative pressure, P/Po
Relative pressure
Amount Adsorbed
Very Low Pressure Behavior
(micropore filling)
Relative Pressure (P/Po)
Amount Adsorbed
Low Pressure Behavior
(monolayer)
The “knee”
Relative Pressure (P/Po)
Amount Adsorbed
Medium Pressure Behavior
(multilayer)
Relative Pressure (P/Po)
Amount Adsorbed
High Pressure Behavior
(capillary condensation)
Relative Pressure (P/Po)
Instrument Features
• Multiple transducers
– 1000 torr
• Used for usual BET (surface area) range and mesopore
analyses
– 10 torr
• Used for krypton BET areas and shifted BET range (e.g.
zeolites)
• Used to cover intermediate pressure range between 1 torr
and 1000 torr
• Always associated with turbo pump
– 1 torr
• Used for krypton BET areas and micropore measurements
• Always associated with turbo pump
– 0.1 torr (in place of 1 torr, iQ-XR only)
• Extended range micropore
Instrument Features
• Degassing
– Is done on the degassing ports
– Is not for grossly wet samples
– Is done without a filler rod*
– Should include a “test”
– Dirty filters can reduce effectiveness
– Should be done using LN2 in cold trap
– *When using a Cell-Seal a filler rod is added first, so
degassing is done with the rod.
Applications I
– Microporous materials
• Carbons
• Zeolites
• Metal organic frameworks
– Instrument selection for these materials
– Specific features of benefit to analyzing
microporous materials
Applications I
– Microporous materials
• Activated carbons
– The small size of their pores gives them great surface area…
they can adsorb a large amount of gas directly on to their
surface. Popular support for some catalyst metals (especially
palladium and platinum). ρ~ 2g/cm3
• Zeolites
– The narrow size distribution of their pores makes them very
useful for gas separation. Also used as catalysts because of
acid sites in the pores. ρ~ 4g/cm3
• Metal organic frameworks
– Their huge surface area and pore volume makes them
potentially useful for gas sequestration/storage. ρ< 0.5g/cm3
Activated Carbons
– Made from a variety of materials:
•
•
•
•
Rice husk
Coconut fiber
Nut shells
Waste biomass
– plant
– animal
Activated Carbons
– Activation is done chemically and thermally.
– It creates spaces between layers of carbon
(graphene) of non-uniform micropore size.
– It usually produces a chemically
heterogeneous surface.
• Presents a problem for accurate pore size
calculations.
400
300
0.07
N2 (77 K)
Ar (77 K)
CO2 (273 K)
N2/77.35 K
200
100
CO 2
N2
0.06
Pore Volume, cc/g
Amount Adsorbed, cc(STP)/g
N2 , Ar (at 77.35 K) vs. CO2 (273.15 K) Adsorption
on Activated Carbon Fiber (ACF-10) and
NLDFT-PSD Histograms
N2
CO2,
Ar
CO2/273.15 K
0
1E-06 1E-05 0.0001 0.001
0.05
Analysis Time:
0.04
CO2 = 3 h
N2 = 40 h
0.03
0.02
0.01
0.01
0.1
1
0
4
6
8
Relative Pressure
10
12
Pore Size Å
Quantachrome’s Powder Technote 35
14
16
18
20
Microporous Carbons:
the Standard way
700
600
Volume [cc/g] STP
Nitrogen, 77.35 K
A5
A10
A15
500
400
300
200
100
0
0
2.10-1
4.10-1
6.10-1
8.10-1
100
P/P0
Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF),
(M. Thommes, et al., FOA 8, 2004)
Featureless Isotherms
Nitrogen, 77.35 K
600
A5
A10
A15
Volume [cc/g] STP
480
360
240
120
0
5 10-6
5 10-5
5 10-4
5 10-3
P/P0
5 10-2
5 10-1
5 100
Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF),
(M. Thommes, et al., FOA 8, 2004
State of the Art Cryogenic
Differentiation
NLDFT Pore Volume [cc/g]
0.8
NLDFT
A5
A10
A15
0.64
0.48
A 15
A 10
0.32
A5
0.16
0
6
8
10
20
Pore Diameter [Å]
40
60
80
100
Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF),
(M. Thommes, et al., FOA 8, 2004
The Special Behavior of Water
800
Water, 25 C
A15
A5 25C
A10 25C
A15 25C
700
600
A10
500
400
A5
300
200
100
0
0
0.2
0.4
0.6
0.8
1
Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF),
(M. Thommes, et al., FOA 8, 2004
Zeolites
– Micropores are part of their crystal structure:
•
•
•
•
•
Most are synthetic
Alumino-silicates
Silicalite = no aluminum
Cation can be H+, Na+, Ca2+, NH4+, etc
Pore shape needs to be incorporated into pore
size calculation for accurate results
• Some adsorbates are better than others
Adsorption of Nitrogen (77.35 K) and Argon
(87.27 K) on a Zeolite
350
N2/77K
Ar/87 K
Volume [cm3]
280
Faujasite: Ar and N2 Adsorption
210
.
N2/77.35 K
140
Ar/87.27 K
70
0
10-6
ZEOLITE | 10.5.2001
5 10-5
5 10-4
5 10-3
P/P0
5 10-2
5 10-1
5 100
Different Sized Pores Fill at Different P/Po
Pore Shape is Important for
Accurate Pore Size Analysis of Zeolites
(M.Thommes et al., presented at the International Zeolite Conference, Cape Town,
2004)
300
0.7
H-Mordenite
13X
NLDFT_Zeolite Fit_(spherical pore model)
NLDFT-Zeolite Fit (cylindrical pore model)
0.56
dV[cc/Å/g]
180
120
0
0.42
0.28
0.14
60
10-6
5 10-5
5 10-4
5 10-3
P/P0
5 10-2
5 10-1
0
5 100
4
12
20
28
Pore Diameter Å
36
44
5 10-1
5 100
300
X-Zeolite structure
(spherical pores)
Mordenite structure
(cylindrical pores)
Zeolite X- type
DFT-Fitting : cylindrical pore model
DFT-Fitting : spherical pore model
240
Volume [cc/g]
Volume [cc/g]
240
MCM-41
(NLDFT_Silica_cylindrical pore model)
Zeolite X_type (NLDFT_Zeolite spherical pore model)
Mordenite-type (NLDFT_Zeolite_cylindrical pore model)
180
120
60
0
10-5
5 10-4
5 10-3
5 10-2
P/P0
Metal Organic Frameworks
MOFs
– Synthetic materials
– Also called coordination polymers
– Similar materials without metals are called
COFs… covalent coordination polymers
– Still a very active research area
Metal Organic Frameworks
MOFs
ZnO4 tetrahedra (blue) are joined by
organic linkers (O, red, C, black),
giving an extended 3D cubic
framework with inter-connected pores
of 11.2 Â aperture width and 18.5Â
pore (yellow sphere) diameter
Microporous Materials
– Instrument selection for these materials
• A micropore size distribution requires an isotherm to be
measured at low enough pressures to see the micropore
filling, and accurately enough to yield an accurate pore size
analysis.
– Why?:
• Best high vacuum performance = lowest starting
pressure.
• Best (i.e. lowest) leak rate = data quality.
• Lowest pressure measurement possible (0.1 torr xducer)
= greatest confidence at smallest pore filling pressure.
• Largest dewar = Longest unattended analysis time =
even the slowest measurements are possible.
• Optional second station = no sharing transducers =
significantly increased throughput (almost double!).
Microporous Materials
– Instrument selection for these materials
• No high vacuum available? = no micropore size
distribution except when using CO2 at 0degC
on carbons.
• Can still measure total BET surface area
including contribution from micropores.
• Can determine micropore area and micropore
volume using t-plot method.
The Autosorb-iQ
• Basic specs
– Transducers: (optional 0.1 torr), 1 torr, 10 torr, 1000 torr
– Vacuum system: turbo pump (dry pump is standard)
– Multiple gas inputs
– Large dewar (90 hour)
– Two degas ports each with own mantle
– Programmable degassing
– Po port
– Dosing algorithms
etc
The Autosorb-iQ
• Advanced specs
– Metal seals and very low leak rate allow us to
measure very low pressure isotherms even when
using helium void volume mode. No need to
disconnect helium and all other gases from the unit
when measuring micropore isotherm!
– Two stations data quality are the same as one station
(see next slide). No transducer or dosing manifold
sharing.
– Dedicated Po transducer. Sample station(s) NOT
interrupted to re-measure.
This plot actually shows THREE isotherms. One generated using just one
station, and a pair generated simultaneously using both stations of the iQ2.
Accurate pore size calculations
• Accurate pore size calculations
– QSDFT for activated carbons…accounts for
surface heterogeneity.
– Argon NLDFT models for different pore
shapes (zeolites and MOFs)
• Full and proper equilibration
incorrect
correct
Applications II
– Mesoporous/nonporous materials
• Carbon black
• Ceramics
Pigments
• Alumina
• Silica
• Metal powders
• Pharmaceuticals
– Instrument selection for these materials
– Specific features of benefit to analyzing meso/nonporous materials
Applications II
– Mesoporous/nonporous materials
• Carbon black
– Essential for tires and other rubber applications. BET (NSA) and t-plot
(STSA) are important.
• Ceramics
– Particle size affects surface area, surface area remains after particle size is
history. Pore size affects wicking of liquids.
• Pigments
– Surface area and porosity “immobilize” liquids and alter rheology.
• Alumina
– Surface area and pore size are the dominant quality control parameter.
Often used as a catalyst support.
• Silica
– Surface area and pore size are the dominant quality control parameter.
• Metal powders
– Surface area supports particle size data especially fines.
• Pharmaceuticals
– Surface area is lost during tabletting (however pore size affects wicking of
liquids) but after ingestion (and dissolution of excipient) s.s.a. of active
controls release rate.
Carbon Black
Aluminas
Aluminas
Mesoporous Templated Carbons
Mesoporous Templated Carbons
Mesoporous Oxides
Mesoporous Oxides
(Calcination Temperature)
Applications II
– Mesoporous/nonporous materials
• Materials Research
– Templated silicas
» MCM41 is the most famous example. Pore size
by gas adsorption is an essential part of
characterization.
– Templated carbons
– Thin films
» For low-k (dielectric) applications. Difficulty is
associated with very small amount of porous
material.
Mesopore Analysis
Significant progress in the pore size analysis of
porous materials made in the last few years,
mainly because of the following reasons:
• (i) The discovery of novel ordered mesoporous
molecular sieves which were used as model adsorbents to test
theories of gas adsorption
•
(ii) The development of microscopic methods,
such as Non-Local-Density Functional Theory (NLDFT) and Quenched Solid
Density Functional Theory (QSDFT)
• (iii) Carefully performed adsorption
experiments… something at which Quantachrome excels.
What Does a Model Adsorbent
Look Like?
TEM of MCM-41 Silica
Sorption, Pore Condensation and Hysteresis Behavior of a
Fluid in a Single Cylindrical Mesopore
From: M Thommes, “ Physical adsorption characterization of ordered and amorphous mesoporous materials”,
Nanoporous Materials- Science and Engineering” (edited by Max Lu, X.S Zhao), Imperial College Press, Chapter 11,
317-364 (2004)
Pore Size Can Also be
Controlled by Granulation
SEM- of Mesoporous TiO2
Different Sized Pores Fill at Different P/Po
Nitrogen Sorption at 77 K into Mesoporous TiO2
150
Sachtopore 60
Sachtopore 100
Sachtopore 300
Sachtopore 1000
Sachtopore 2000
Volume STP [cc/g]
120
6 nm
10 nm
90
30 nm
60
30
100 nm
0
0
0.2
0.4
0.6
P/P0
H. Kueppers, B. Hirthe, M.Thommes, G.I.T, 3 (2001) 110
0.8
1
Different Sized Pores Fill at Different P/Po
3.6 nm
500
-6
3
VOLUME [10 m /g]
600
3.3nm
400
4.2 nm
Argon 77K/
MCM-41
300
ads
des
MCM-41A 3.3nm
MCM-41B 3.6 nm
MCM-41C 4.2 nm
200
100
0.0
0.2
0.4
0.6
0.8
1.0
RELATIVE PRESSURE p/p0
In : S. Lowell, J. Shields, M. Thomas, M. Thommes, Characterization of porous solids and Powders: Surface Area, Pore Size and Density, Kluwer
Academic Publ, 2004,
Different Temperatures Cause Same Sized
Pores to Fill at Different P/Po
Ar / 77 K and 87 K
70
77 K
50
87 K
-6
3
volume [10 m /g]
60
40
ads
30
des
20
77 K
87 K
10
Argon/ MCM-48 (d = 4.01nm)
0
0.0
0.2
0.4
0.6
0.8
1.0
relative pressure p/p0
M. Thommes,, R. Koehn and M. Froeba et al. J. Phys. Chem B 104, (2000), 7933
Some History of Pore Size
Analysis of Mesoporous Materials
(a) Methods based on (modified) Kelvin Equation
• e.g., - Barrett-Joyner-Halenda (BJH)
- Dollimore-Heal (DH)
- Broeckhoff de Boer (BdB)
- Kruk-Jaroniec-Sayari (KJS))
- Bhatia et al (mod. BdB)
- D.D.Do & Ustinov (mod. BdB)
(1951)
(1964)
(1967/68)
(1997)
(1998/2004)
(2004/2005)
(b) Density Functional Theory (DFT / NLDFT):
e.g.- Evans and Tarazona (1985/86)
- Seaton (1989),
- Lastoskie and Gubbins (1993)
- Sombathley and Olivier (1994)
- Neimark and Ravikovitch (1995 ……)
(c) Quenched Solid DFT (QSDFT):
- Neimark and Ravikovitch (1995 ……)
(d) Monte Carlo (MC) and Molecular dynamics (MD),
e.g. - Gubbins et. al. (1986…. )
- Walton and Quirke (1989…)
- Gelb (1999- ….)
- Neimark and Ravikovitch (1995….)
Theoretical Predictions of Pore Filling P/Po as
Function of Pore Size
N2 / 77K in cylindrical
silica pores
X
X

. Neimark AV, Ravikovitch P.I., Grün M., Schüth F., Unger K.K, (1998) J. Coll. Interface Sci. 207,159
BJH and NLDFT Compared
0.3
560
N2 (77 K): ads
N2 (77 K): des
490
0.25
BJH
420
Dv(d) [cc/Å/g]
Volume [10-6 m3/g]
DFT-Fitting
350
0.15
0.1
210
0.05
0
0.2
0.4
0.6
RELATIVE PRESSURE p/p0
0.8
1
NLDFT
0.2
280
140
BJH-Pore size distribution
DFT-Pore size distribution
0
15

X
23
31
39
Pore Diameter [Å]
NLDFT method: N2/77K cylindrical-silica pore model
47
55
Combined Micro/Mesopore Analysis by NLDFT
(can’t be done by BJH)
Argon adsorption at 87 K on a 50:50 mixture of ZSM-5 + MCM-41:
0.6
0.1
25
0.09
MCM-41
10
ZSM-5
0.4
0.06
MCM-41
0.3
0.05
ZSM-5
0.04
histogram
0.03
0.2
integral
50-50
5
3
3
15
0.07
0.02
0.1
0.01
0
0.000001
0.00001
0.0001
0.001
P/Po
0.01
0.1
1
0
0
1
10
100
Vcum [cm /g]
0.5
0.08
dV/dD [cm /g]
Adsorption, [mmol/g]
20
1000
D, [Å]
S. Lowell, J.E. Shields, M.A. Thomas and M. Thommes, Characterization of porous solids and powders:
Surface Area, Pore Size and Density, Kluwer Academic Publisher, 2004
Studying Pore Geometry, Connectivity
and Disorder
Nitrogen Sorption at 77 K into various Mesoporous Silica Materials
700
Vycor
SBA-15
Controlled-Pore Glass (CPG)
SE3030
VOLUME (STP) [cc/g]
600
500
400
300
200
100
0
0
0.2
0.4
0.6
RELATIVE PRESSURE P/P0
0.8
1
IUPAC Classification of Hysteresis
Due to intrinsic fluid property
Cylindrical
Pores
Due to pore blocking /
cavitation (wide bodies,
narrow necks)
Cylindrical &
Spherical Pores
Disordered;
lamellar pore
structures, slit &
wedge, shape
pores
Micro/Mesoporous
adsorbents
NLDFT adsorption isotherm of argon at 87K in a cylindrical
pore of diameter 4.8 nm in comparison with the
appropriate experimental sorption isotherm on MCM-41.
Why Does Type H1 Exist?
equilibrium transition
spinodal evaporation
0.05
0.04
0.03
Adsorption,
mmol/m2
spinodal condensation
0.02
Experimental (des)
0.01
Experimental (ads)
NLDFT in 4.8nm pore
0
0
0.2
0.4
0.6
Relative pressure, P/P0
0.8
1
It can be clearly seen that the experimental desorption branch is associated with the
equilibrium gas-liquid phase transition, whereas the condensation step corresponds to the
spinodal spontaneous transition (i.e. delayed until nucleation occurs).
(a)Neimark A.V., Ravikovitch P.I. and Vishnyakov A. (2000) Phys. Rev. E 62, R1493; (b)Neimark A.V. and Ravikovitch P.I. (2001)
Microporous and Mesoporous Materials 44-56, 697.
Pore Size from H1 Can be Calculated from Ads
and/or Des using NLDFT (but not BJH)
Nitrogen adsorption/desorption at 77.35 K in SBA-15 and pore size distributions
700
0.22
0.2
600
500
0.16
Dv(d) [cc/Å/g]
Volume STP [cc/g]
0.18
Ads (NLDFT-spinodal condensation)
Des (NLDFT- equilibrium transition)
400
300
200
0.14
0.12
0.1
0.08
0.06
100
0
0.04
0.02
0
0.2
0.4
0.6
Relative Pressure P/P0
0.8
1
0
25
45
65
85
Pore Diameter [Å]
105
M. Thommes, in Nanoporous Materials- Science and Engineering” (edited by Max Lu), Imperial College Press, Chapter 11 p. 317 - 364 (2004)
125
Pore Size from H1 Can be Calculated from Ads
and/or Des using NLDFT (but not BJH)
Nitrogen sorption at 77 K in CPG (Controlled Pore Glass)
420
0.026
Ads (NLDFT-spinodal condensation)
Des (NLDFT- equilibrium transition)
280
Dv(d) [cc/Å/g]
Volume STP [cc/g]
350
210
140
0.013
70
0
0
0.2
0.4
0.6
Relative Pressure P/P0
0.8
1
0
40
90
140
Pore Diameter [Å]
190
M. Thommes, in Nanoporous Materials- Science and Engineering” (edited by Max Lu), Imperial College Press, Chapter 11 p. 317 - 364 (2004)
240
Why Does Type H2 Exist?
Type H2
Hysteresis
Two Problems for Pore Size Analysis:
Adsorption Branch:
metastable pore fluid  delayed pore condensation
Desorption Branch:
pore blocking,percolation  delayed evaporation
How to Solve:
 Application of novel NLDFT approaches
Body Pore Size from H2 Calculated from Ads
and Neck Size from Des using NLDFT
(but not BJH)
Nitrogen sorption at 77 K in porous Vycor Glass and pore size distributions from adsorption- (NLDFT spinodal
condensation kernel) and desorption (NLDFT equilibrium transition kernel)
150
0.04
Ads (NLDFT- spinodal condensation)
Des (NLDFT- equilibrium transition)
0.032
Dv(d) [cc/Å/g]
Volume STP [cm3/g]
120
90
60
0.024
0.016
0.008
30
0
0
25
0
0.2
0.4
0.6
0.8
1
VYCOR(PSD) | 12.11.2002
50
75
100
Pore Diameter [Å]
125
150
Relative Pressure p/p0
M. Thommes, in Nanoporous Materials- Science and Engineering” (edited by Max Lu), Imperial College Press, Chapter 11 p. 317 - 364 (2004)
H3 Hysteresis
N2/77K sorption on disordered alumina catalyst
1
240
210
0.8
BJH-PSD
180
Dv(log d) [cc/g]
Volume STP [cc/g]
Adsorption
Desorption
Adsorption
Desorption
150
120
0.6
Artifact
0.4
90
0.2
60
30
0
0.2
0.4
0.6
Relative Pressure P/P0
0.8
1
0
10
50
100
Pore Diameter [Å]
500
M. Thommes, In Nanoporous Materials Science and Engineering, (Max Lu and X Zhao, eds.), World Scientific, in press (2004)
1000
H4 Hysteresis
Nitrogen adsorption at 77.4 K in activated carbon
500
Nitrogen (77 K)
Volume STP [cc/g]
400
300
200
100
0
0
0.2
0.6
0.4
P/P0
0.8
1
H2 versus “H2”/H3/H4
NO size information
Neck size
Pore body size
NO size information;
Cavitation is a property
of the liquid
M. Thommes, B. Smarsly, P.I. Ravokovitch, A.V. Neimark et al.. Langmuir, 22, 765 (2006)
Pore body size
Product Selection
• Mesopore analysis needs:
– Regular vacuum
– 1000 torr pressure range
– 24 hour dewar
– Po station (usually)
– A simple BET does not need a long life dewar
and Po is less critical
Product Selector 1
ONE SAMPLE
Model
Quantachrome
Nova1
iQ
Nova2
Stations
1
1
1+1
Po ports
0
1
(1)
Full ads
y
y
y
Full des
y
y
y
2
(vac /
flow)
2
(vacuum)
2
(vac /
flow)
Degas stn
Xducer (s)
specification
0.11%
f.s.
0.11%
f.s.
0.11%
f.s.
Product Selector 2-3
TWO-THREE
SAMPLES
Model
Quantachrome
Quantachrome
Nova2
Quad 2
iQ2
Nova 3
Quad 3
Nova 4
Stations
1+1
2
2
2+1
3
3+1
Po ports
(1)
2
1
(1)
3
(1)
Full ads
y
y
y
y
y
y
Full des
y
y
y
y
y
y
2
(vac /
flow)
-
2
(vacuum)
4
(vac /
flow)
-
0.11%
f.s.
0.11%
f.s.
0.11% f.s.
0.11%
f.s.
0.11%
f.s.
Degas stn
Xducer (s)
specification
4
(vac /
flow)
0.11%
f.s.
Product Selector 4+
Q’chrome
FOUR or MORE
SAMPLES
Quantachrome
Model
N4
Quad
AS6B
Stations
3+1
4
6
Po ports
(1)
4
6
Full ads
y
y
y
Full des
y
y
y
Degas stn
4
(vac/flow)
-
-
Xducer (s)
specification
0.11% f.s.
0.11% f.s.
0.11% f..s.
Workshop topics
•
•
•
•
•
Selecting sample cells
Degassing conditions
BET points
Mesopore points
Micropore points