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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
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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
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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
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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.
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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.
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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
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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!
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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
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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.
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Movie time!
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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)
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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.
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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).
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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.
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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.
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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.
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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
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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.
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Basic Construction
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
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Basic Operation
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
Manifold, transducer and sample cell are evacuated.
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Basic Operation
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
Manifold, transducer and sample cell are evacuated… and cell is cooled.
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Basic Operation
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
Intermediate valve status.
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Basic Operation
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
Analysis gas is admitted to build some pressure in the manifold.
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Basic Operation
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
A steady pressure in the manifold is recorded, P1.
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Basic Operation
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
Gas expands from manifold into sample cell; pressure drops in the manifold, rises in sample cell.
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Basic Operation
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
Gas is adsorbed by the sample, pressure drops further in both volumes.
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Basic Operation
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
Eventually the pressure equilbrates. Final pressure, P2, is recorded.
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Basic Operation
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
Process is repeated at higher and higher pressures.
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Basic Operation
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
Adsorption measurements are complete... Getting ready to desorb!
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Basic Operation
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
In desorption, some gas is removed from the manifold while the sample cell remains isolated.
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Basic Operation
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
Manifold is isolated and desorption P1 is measured.
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Basic Operation
Sample cell
Analysis gas to vacuumManifold
Pressure transducer(s)
Gas is expanded from sample cell into manifold, pressure drops in the sample cell, rises in the manifold… P2 (desorption)
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A More Realistic Representation
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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
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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.
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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
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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.
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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)
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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)
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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.
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Small Cold Zone = Sensitivity
Coolant level controlled here creates a small cold zone.
Quantachrome’s instruments
Leve
l sen
sor
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Working Equation
PV = nRT
nads = ndosed - nvoid
nads = (PV/RT)man. - (PV/RT)cell
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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.
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What Is The Result?A
mou
nt a
dsor
bed
Equilibrium pressure
It’s called an “isotherm”
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What Is The Result?A
mou
nt a
dsor
bed
Equilibrium pressure
The values on the y-axis are calculated from pressure measurements (and temperature values)
The values on the x-axis are pressure measurements.
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What Is The Result?A
mou
nt a
dsor
bed
Relative pressure
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
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Very Low Pressure Behavior (micropore filling)
Relative Pressure (P/Po)
Am
ount
Ads
orbe
d
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Low Pressure Behavior (monolayer)
The “knee”
Relative Pressure (P/Po)
Am
ount
Ads
orbe
d
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Medium Pressure Behavior (multilayer)
Relative Pressure (P/Po)
Am
ount
Ads
orbe
d
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High Pressure Behavior (capillary condensation)
Relative Pressure (P/Po)
Am
ount
Ads
orbe
d
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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
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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.
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Applications I
– Microporous materials• Carbons• Zeolites• Metal organic frameworks
– Instrument selection for these materials– Specific features of benefit to analyzing
microporous materials
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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
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Activated Carbons
– Made from a variety of materials:• Rice husk• Coconut fiber• Nut shells• Waste biomass
– plant– animal
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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.
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N2 , Ar (at 77.35 K) vs. CO2 (273.15 K) Adsorption on Activated Carbon Fiber (ACF-10) and
NLDFT-PSD Histograms
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
4 6 8 10 12 14 16 18 20
Pore Size Å
Pore
Vol
ume,
cc/
g
CO
N2
2
N2/77.35 K
CO2/273.15 K
Analysis Time: CO2 = 3 h N2 = 40 h
0
100
200
300
400
1E-06 1E-05 0.0001 0.001 0.01 0.1 1
Relative Pressure
Amou
nt A
dsor
bed,
cc(
STP)
/g
N2 (77 K)Ar (77 K)
CO2 (273 K)
CO2,
N2
Ar
Quantachrome’s Powder Technote 35
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Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF),
(M. Thommes, et al., FOA 8, 2004)
0 2.10-1 4.10-1 6.10-1 8.10-1 100
P/P0
0
100
200
300
400
500
600
700
Vol
ume
[cc/
g] S
TP
A5A5A10A10A15A15
Nitrogen, 77.35 K
Microporous Carbons: the Standard way
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5 10-6 5 10-5 5 10-4 5 10-3 5 10-2 5 10-1 5 100
P/P0
0
120
240
360
480
600
Vol
ume
[cc/
g] S
TP
A5A5A10A10A15A15
Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF), (M. Thommes, et al., FOA 8, 2004
Nitrogen, 77.35 K
Featureless Isotherms
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6 8 10 20 40 60 80 100Pore Diameter [Å]
0
0.16
0.32
0.48
0.64
0.8
NL
DF
T P
ore
Vol
ume
[cc/
g]
A5A5A10A10A15 A15
A 15
A 5
A 10
NLDFT
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
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0
100
200
300
400
500
600
700
800
0 0.2 0.4 0.6 0.8 1
A5 25CA10 25CA15 25C
A15
A10
A5
Water, 25 C
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
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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
![Page 64: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/64.jpg)
Adsorption of Nitrogen (77.35 K) and Argon (87.27 K) on a Zeolite
10-6 5 10-5 5 10-4 5 10-3 5 10-2 5 10-1 5 100
P/P0
0
70
140
210
280
350
Vol
ume
[cm
3 ]
N2/77KN2/77KAr/87 KAr/87 K
ZEOLITE | 10.5.2001
N2/77.35 K
Ar/87.27 K
Faujasite: Ar and N2 Adsorption
.
![Page 65: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/65.jpg)
Different Sized Pores Fill at Different P/Po
![Page 66: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/66.jpg)
Pore Shape is Important for Accurate Pore Size Analysis of Zeolites
(M.Thommes et al., presented at the International Zeolite Conference, Cape Town, 2004)
10-6 5 10-5 5 10-4 5 10-3 5 10-2 5 10-1 5 100
P/P0
0
60
120
180
240
300
Vol
ume
[cc/
g]
H-MordeniteH-Mordenite13X13X
NLDFT_Zeolite Fit_(spherical pore model)NLDFT_Zeolite Fit_(spherical pore model)NLDFT-Zeolite Fit (cylindrical pore model)NLDFT-Zeolite Fit (cylindrical pore model)
4 12 20 28 36 44Pore Diameter Å
0
0.14
0.28
0.42
0.56
0.7
dV[c
c/Å
/g]
MCM-41 (NLDFT_Silica_cylindrical pore model)MCM-41 (NLDFT_Silica_cylindrical pore model)Zeolite X_type (NLDFT_Zeolite spherical pore model)Zeolite X_type (NLDFT_Zeolite spherical pore model)Mordenite-type (NLDFT_Zeolite_cylindrical pore model)Mordenite-type (NLDFT_Zeolite_cylindrical pore model)
Mordenite structure(cylindrical pores)
X-Zeolite structure(spherical pores)
10-5 5 10-4 5 10-3 5 10-2 5 10-1 5 100
P/P0
0
60
120
180
240
300
Vol
ume
[cc/
g]
Zeolite X- typeZeolite X- typeDFT-Fitting : cylindrical pore modelDFT-Fitting : cylindrical pore modelDFT-Fitting : spherical pore modelDFT-Fitting : spherical pore model
![Page 67: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/67.jpg)
Metal Organic FrameworksMOFs
– Synthetic materials– Also called coordination polymers– Similar materials without metals are called
COFs… covalent coordination polymers– Still a very active research area
![Page 68: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/68.jpg)
Metal Organic FrameworksMOFs
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
![Page 69: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/69.jpg)
![Page 70: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/70.jpg)
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!).
![Page 71: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/71.jpg)
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.
![Page 72: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/72.jpg)
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
![Page 73: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/73.jpg)
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.
![Page 74: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/74.jpg)
This plot actually shows THREE isotherms. One generated using just one station, and a pair generated simultaneously using both stations of the iQ2.
![Page 75: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/75.jpg)
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
correct
incorrect
![Page 76: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/76.jpg)
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
![Page 77: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/77.jpg)
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.
![Page 78: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/78.jpg)
Carbon Black
![Page 79: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/79.jpg)
Aluminas
![Page 80: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/80.jpg)
Aluminas
![Page 81: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/81.jpg)
Mesoporous Templated Carbons
![Page 82: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/82.jpg)
Mesoporous Templated Carbons
![Page 83: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/83.jpg)
Mesoporous Oxides
![Page 84: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/84.jpg)
Mesoporous Oxides (Calcination Temperature)
![Page 85: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/85.jpg)
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.
![Page 86: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/86.jpg)
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.
![Page 87: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/87.jpg)
What Does a Model Adsorbent Look Like?
TEM of MCM-41 Silica
![Page 88: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/88.jpg)
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)
![Page 89: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/89.jpg)
SEM- of Mesoporous TiO2
Pore Size Can Also be Controlled by Granulation
![Page 90: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/90.jpg)
0 0.2 0.4 0.6 0.8 1P/P0
0
30
60
90
120
150
Vol
ume
STP
[cc
/g]
Sachtopore 60Sachtopore 60Sachtopore 100Sachtopore 100Sachtopore 300Sachtopore 300Sachtopore 1000Sachtopore 1000Sachtopore 2000Sachtopore 2000
6 nm
10 nm
30 nm
100 nm
H. Kueppers, B. Hirthe, M.Thommes, G.I.T, 3 (2001) 110
Different Sized Pores Fill at Different P/Po
Nitrogen Sorption at 77 K into Mesoporous TiO2
![Page 91: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/91.jpg)
Different Sized Pores Fill at Different P/Po
0.0 0.2 0.4 0.6 0.8 1.0100
200
300
400
500
600
ads des
MCM-41A
MCM-41B
MCM-41C
VO
LU
ME
[10
-6m
3 /g]
RELATIVE PRESSURE p/p0
3.3nm
3.6 nm
4.2 nm Argon 77K/
MCM-41
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,
3.3nm 3.6 nm4.2 nm
![Page 92: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/92.jpg)
Different Temperatures Cause Same Sized Pores to Fill at Different P/Po
0.0 0.2 0.4 0.6 0.8 1.00
10
20
30
40
50
60
70
desads
87 K 77 K
Ar / 77 K and 87 K
volu
me
[10
-6m
3 /g]
relative pressure p/p0
Argon/ MCM-48 (d = 4.01nm)
87 K
77 K
M. Thommes,, R. Koehn and M. Froeba et al. J. Phys. Chem B 104, (2000), 7933
![Page 93: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/93.jpg)
Some History of Pore Size Analysis of Mesoporous Materials (a) Methods based on (modified) Kelvin Equation • e.g., - Barrett-Joyner-Halenda (BJH) (1951) - Dollimore-Heal (DH) (1964) - Broeckhoff de Boer (BdB) (1967/68) - Kruk-Jaroniec-Sayari (KJS)) (1997) - Bhatia et al (mod. BdB) (1998/2004) - D.D.Do & Ustinov (mod. BdB) (2004/2005)
![Page 94: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/94.jpg)
(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….)
![Page 95: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/95.jpg)
Theoretical Predictions of Pore Filling P/Po as Function of Pore Size
. Neimark AV, Ravikovitch P.I., Grün M., Schüth F., Unger K.K, (1998) J. Coll. Interface Sci. 207,159
N2 / 77K in cylindrical silica pores
XX
![Page 96: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/96.jpg)
BJH and NLDFT Compared
0 0.2 0.4 0.6 0.8 1RELATIVE PRESSURE p/p0
140
210
280
350
420
490
560
Vol
ume
[10-6
m3 /g
]
N2 (77 K): adsN2 (77 K): adsN2 (77 K): desN2 (77 K): des
DFT-FittingDFT-Fitting
15 23 31 39 47 55Pore Diameter [Å]
0
0.05
0.1
0.15
0.2
0.25
0.3
Dv(
d) [
cc/Å
/g]
BJH-Pore size distribution BJH-Pore size distribution DFT-Pore size distributionDFT-Pore size distribution
BJH NLDFT
NLDFT method: N2/77K cylindrical-silica pore model
X
![Page 97: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/97.jpg)
Combined Micro/Mesopore Analysis by NLDFT(can’t be done by BJH)
0
5
10
15
20
25
0.000001 0.00001 0.0001 0.001 0.01 0.1 1
P/Po
Ads
orpt
ion,
[mm
ol/g
]
MCM-41
ZSM-5
50-50
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
1 10 100 1000
D, [Å]
dV
/dD
[cm
3/g
]
0
0.1
0.2
0.3
0.4
0.5
0.6
Vcu
m [c
m3/g
]
histogram
integral
ZSM-5
MCM-41
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
Argon adsorption at 87 K on a 50:50 mixture of ZSM-5 + MCM-41:
![Page 98: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/98.jpg)
0 0.2 0.4 0.6 0.8 1RELATIVE PRESSURE P/P0
0
100
200
300
400
500
600
700
VO
LU
ME
(ST
P)
[cc/
g]
VycorVycorSBA-15 SBA-15 Controlled-Pore Glass (CPG)Controlled-Pore Glass (CPG)SE3030SE3030
Studying Pore Geometry, Connectivity and Disorder
Nitrogen Sorption at 77 K into various Mesoporous Silica Materials
![Page 99: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/99.jpg)
IUPAC Classification of Hysteresis
CylindricalPores
Cylindrical & Spherical Pores
Disordered; lamellar pore structures, slit & wedge, shape pores
Micro/Mesoporous adsorbents
Due to intrinsic fluid property
Due to pore blocking / cavitation (wide bodies, narrow necks)
![Page 100: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/100.jpg)
Why Does Type H1 Exist?
spinodal condensation
spinodal evaporationequilibrium transition
0.05
0.04
0.03
0.02
0.01
0.2 0.4 0.6 0.8 10
0
Experimental (des)
Experimental (ads)
NLDFT in 4.8nm pore
Ads
orpt
ion,
m
mol
/m2
Relative pressure, P/P0
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.
NLD
FT
ad
sorp
tion
iso
the
rm o
f ar
gon
at 8
7K in
a
cylin
dric
al p
ore
of d
iam
eter
4.8
nm
in c
omp
aris
on w
ith
the
appr
opr
iate
exp
erim
enta
l so
rptio
n is
oth
erm
on
MC
M-
41.
![Page 101: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/101.jpg)
25 45 65 85 105 125Pore Diameter [Å]
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
Dv(
d) [
cc/Å
/g]
Ads (NLDFT-spinodal condensation)Ads (NLDFT-spinodal condensation)Des (NLDFT- equilibrium transition)Des (NLDFT- equilibrium transition)
0 0.2 0.4 0.6 0.8 1Relative Pressure P/P0
0
100
200
300
400
500
600
700
Vol
ume
STP
[cc
/g]
M. Thommes, in Nanoporous Materials- Science and Engineering” (edited by Max Lu), Imperial College Press, Chapter 11 p. 317 - 364 (2004)
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
![Page 102: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/102.jpg)
Nitrogen sorption at 77 K in CPG (Controlled Pore Glass)
0 0.2 0.4 0.6 0.8 1Relative Pressure P/P0
0
70
140
210
280
350
420
Vol
ume
STP
[cc
/g]
40 90 140 190 240Pore Diameter [Å]
0
0.013
0.026
Dv(
d) [
cc/Å
/g]
Ads (NLDFT-spinodal condensation)Ads (NLDFT-spinodal condensation)Des (NLDFT- equilibrium transition)Des (NLDFT- equilibrium transition)
M. Thommes, in Nanoporous Materials- Science and Engineering” (edited by Max Lu), Imperial College Press, Chapter 11 p. 317 - 364 (2004)
Pore Size from H1 Can be Calculated from Ads and/or Des using NLDFT (but not BJH)
![Page 103: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/103.jpg)
Why Does Type H2 Exist?
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
Type H2 Hysteresis
![Page 104: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/104.jpg)
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)
25 50 75 100 125 150Pore Diameter [Å]
0
0.008
0.016
0.024
0.032
0.04
Dv(
d) [
cc/Å
/g]
Ads (NLDFT- spinodal condensation)Ads (NLDFT- spinodal condensation)Des (NLDFT- equilibrium transition)Des (NLDFT- equilibrium transition)
VYCOR(PSD) | 12.11.20020 0.2 0.4 0.6 0.8 1Relative Pressure p/p0
0
30
60
90
120
150
Vol
ume
STP
[cm
3 /g]
M. Thommes, in Nanoporous Materials- Science and Engineering” (edited by Max Lu), Imperial College Press, Chapter 11 p. 317 - 364 (2004)
Body Pore Size from H2 Calculated from Ads and Neck Size from Des using NLDFT
(but not BJH)
![Page 105: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/105.jpg)
H3 Hysteresis
0 0.2 0.4 0.6 0.8 1Relative Pressure P/P0
30
60
90
120
150
180
210
240
Vol
ume
STP
[cc
/g]
AdsorptionAdsorptionDesorptionDesorption
10 50 100 500 1000Pore Diameter [Å]
0
0.2
0.4
0.6
0.8
1
Dv(
log
d) [
cc/g
]
AdsorptionAdsorptionDesorptionDesorption
BJH-PSD
Artifact
N2/77K sorption on disordered alumina catalyst
M. Thommes, In Nanoporous Materials Science and Engineering, (Max Lu and X Zhao, eds.), World Scientific, in press (2004)
![Page 106: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/106.jpg)
0 0.2 0.4 0.6 0.8 1P/P0
0
100
200
300
400
500
Vol
ume
STP
[cc
/g]
Nitrogen (77 K)Nitrogen (77 K)
H4 Hysteresis
Nitrogen adsorption at 77.4 K in activated carbon
![Page 107: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/107.jpg)
H2 versus “H2”/H3/H4
M. Thommes, B. Smarsly, P.I. Ravokovitch, A.V. Neimark et al.. Langmuir, 22, 765 (2006)
Neck size
Pore body size
NO size information
Pore body size
NO size information; Cavitation is a property of the liquid
![Page 108: Surface Area, Pore Size and More :](https://reader033.vdocuments.mx/reader033/viewer/2022061605/56814986550346895db6ce67/html5/thumbnails/108.jpg)
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
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Product Selector 1ONE SAMPLE Quantachrome
Model Nova1 iQ Nova2
Stations 1 1 1+1
Po ports 0 1 (1)
Full ads y y y
Full des y y y
Degas stn 2(vac /
flow)
2(vacuum)
2(vac /
flow)
Xducer (s) specification
0.11% f.s.
0.11% f.s.
0.11% f.s.
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Product Selector 2-3TWO-THREE
SAMPLESQuantachrome Quantachrome
Model 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
Degas stn 2(vac /
flow)
- 2 (vacuum)
4(vac /
flow)
- 4(vac /
flow)
Xducer (s) specification
0.11% f.s.
0.11% f.s.
0.11% f.s. 0.11% f.s.
0.11% f.s.
0.11% f.s.
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Product Selector 4+
FOUR or MORE SAMPLES
Quantachrome Q’chrome
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.
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Workshop topics
• Selecting sample cells
• Degassing conditions
• BET points
• Mesopore points
• Micropore points