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BET Analysisfundamentals
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Surface AreaWhat is it?
Surface Area is the means through which a solid
interacts with its surroundings, especially liquids
and gases.
Surface area is created by division of particles (size
reduction) and the generation of porosity.
Surface area is destroyed by sintering (exceeding
Tg), melting and Ostwald ripening.
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How to Create Area ?
Size Reduction
Grinding,
milling,
nanoscale preparation
Make pores
Partial decomposition Leach
Gel then lyophilize
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How to Destroy Area ?
Surface area is destroyedby
melting
sintering (exceeding Tg), and
Ostwald ripening
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Adsorption Absorption
Absorptionis a phenomenonthat occurs in a volume
Adsorptionis a phenomenonthat occurs on a surface
The word sorptionencompasses both types of phenomena
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Adsorption processes
Adsorption
Physical (physisorption)
- van der Waals interactions(result in attractive forces betweenadsorbent and adsorbate molecules)
- Adsorbed molecules maintain their
identity
- Multilayers
- No activation energy
- Always reversible
Chemical (chemisorption)
- Chemical bonds between adsorbateand adsorbent formed
- Adsorbed molecules loose their
identity
- Monolayers
- Often activation energy required
- Can be irreversible
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The gas sorption process
Langmuir[1]described the kinetic behavior of theadsorption process. He postulated that atequilibrium, the rate of arrival of adsorptive
(adsorption) and the rate of evaporation ofadsorbate (desorption) were equal
Furthermore, the heat of adsorption was taken to
be constant and unchanging with the degree ofcoverage, .
[1]I. Langmuir, J. Amer. Chem. Soc., 40, 1368 (1918)
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Graduated as a metallurgical engineer from
the School of Mines at Columbia University in
1903
1903-1906 M.A. and Ph.D. in 1906 from
Gttingen.
Irving Langmuir(1881-1957)
1935-1937 With Katherine Blodgett studied thin
films.
1948-1953 With Vincent Schaefer discovered
that the introduction of dry ice and iodide into a
sufficiently moist cloud of low temperature couldinduce precipitation.
1932 The Nobel Prize in Chemistry "for his
discoveries and investigations in surface
chemistry
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Confining adsorption to a monolayer, the Langmuir equation can be
written
where V is the volume of gas adsorbed at pressure P, Vm is the
monolayer capacity (i.e. =1) expressed as the volume of gas at STP
and Kis a constant for any given gas-solid pair. Rearranging in theform of a straight line (y=ab+x) gives
KP
KP
V
V
m 1
mm V
P
KVV
P
1
Langmuirian behavior
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Suitable Methods of Determination
Gas adsorption allows probing of entire surfaceincluding irregularities and pore interiors.
The amount adsorbed is a function of temperature,pressure and the strength of attraction or interactionpotential.
Physisorption is generally weak and reversible. Thesolid must be cooled and a method used to estimate themonolayer coverage from which surface area can becalculated.
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Adsorption Process
Adsorbent
AdsorbateAdsorptive
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The Isotherm
The amount of gas adsorbed is a function of
The strength of interaction between gas and solid(intrinsic)
Temperature (fixed)
Pressure (controlled variable) expressed asrelative pressure P/Po
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Physisorption Process
4)
2
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Very Low Pressure Behavior
(micropore filling)
Relative Pressure, P/Po
AmountAdsorbed
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Low Pressure Behavior
(monolayer)
The knee
Relative Pressure, P/Po
AmountAdsorb
ed
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Medium Pressure Behavior
(multilayer)
Relative Pressure, P/Po
AmountAdsorb
ed
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High Pressure Behavior
(capillary condensation)
Relative Pressure, P/Po
AmountAdsorb
ed
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Gas Sorption: Isotherm
adsorptiveofpressuresaturated
adsorbateofpressure
where
p
p
ppf
o
oVa
Adsorption isotherm Isotherm is a measure of
the volume of gas
adsorbed at a constant
temperature as a function
of gas pressure.
Isotherms can be
grouped into six classes.
Va
Desorption isotherm
p
po
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Types of isotherms
I: microporous solids
II & III: multilayer adsorption
in non-porous solids
IV & V: capillary condensation
in mesoporous solids
VI: stepped asdorption
according to the IUPAC classification
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Types of Isotherms
Type I or
pseudo-Langmuir
Relative Pressure (P/Po)
Volumeadsorbed
Steep initial region due tovery strong adsorption, for
example in micropores.
Limiting value (plateau) due to filled
pores and essentially zero external
area.
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Types of Isotherms
Type II
Relative Pressure (P/Po)
Vol
umeadsorbed
Rounded kneeindicates approximate
location of monolayer
formation.
Absence of hysteresis indicates
adsorption on and desorption from a
non-porous surface..
Low slope region in middle of
isotherm indicates first few
multilayers
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Gas Sorption: Isotherm
Va
1P/Po
Type I
or
Langmuir
S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed.Chapman & Hall, New York, 1991
Concave to theP/Poaxis
Exhibited by microporous solids ( < 2nm )
Type II
Exhibited by nonporous or macroporous
solids ( > 50nm )
Unrestricted monolayer-multilayeradsorption
Point B indicates the relative pressure at
which monolayer coverage is complete
B
Va
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Types of Isotherms
Type III
Relative Pressure (P/Po)
Volumeadsorbed
Lack of knee represents extremelyweak adsorbate-adsorbent
interaction
BET is not applicable
Example: krypton on polymethylmethacrylate
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Types of Isotherms
Type IV
Relative Pressure (P/Po)
Vo
lumeadsorbe
d
Rounded knee
indicates approximate
location of monolayer
formation.
Low slope region in middle of
isotherm indicates first fewmultilayers
Hysteresis indicates capillary
condensation in meso and
macropores.
Closure at P/Po~0.4 indicates
presence of small mesopores(hysteresis would stay open
longer but for the tensile-
strength-failure of the nitrogen
meniscus.
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Gas Sorption: Isotherm
Va
1
Type IIIConvex to the P/Poaxis
Exhibited by nonporous solids
Va
1P/Po
Type IVExhibited by mesoporous solids
Initial part of the type IV follows
the same path as the type II
S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed.
Chapman & Hall, New York, 1991
f
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Types of Isotherms
Type V
Relative Pressure (P/Po)
Volumeadsorb
ed
Lack of knee represents extremely
weak adsorbate-adsorbent interaction
BET is not applicable
Example: water on carbon black
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Gas Sorption: Hysteresis
Hysteresis indicates the presence of mesopores.
Hysteresis gives information regarding pore shapes .
Types I, II and III isotherms are generally reversible but type I can
have a hysteresis. Types IV and V exhibit hysteresis.
1P/Po
HysteresisVa
S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed.Chapman & Hall, New York, 1991
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Gas Sorption: Isotherm
Va
1P/Po
Type V
1P/Po
Type VI
Highly uncommon
Exhibited by mesoporous solids
Exhibited by nonporous solids with
an almost completely uniform surface
S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed.
Chapman & Hall, New York, 1991
Va
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Choice of Gas and Temperature
Gases
Nitrogen
Argon
Krypton
Carbon dioxide
Others
TemperaturesLiquid Nitrogen
Liquid Argon
Dry ice/acetone
Water/ice
Others
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Choice of Gas and Temperature
Gases
Nitrogen
Argon Krypton
Carbon dioxide
Others
TemperaturesLiquid Nitrogen
Liquid ArgonDry ice/acetone
Water/ice
Others
M M h d
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Measurement Method
Manometric(Classical vacuum, volumetric.)
Requires that adsorbate be adsorbed by the
sample, at some reduced temperature, as a
function of pressure of pure adsorptive.
M t i
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Manometric
P/Po values are achieved by creating conditions
of partial vacuum
High precision and accurate pressure
transducers monitor pressure changes due to
the adsorption process
W ki E i
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Working Equation
PV = nRT
nads= ndosed- nvoid
nads= (
PV/RT)man.- (PV/RT)cell
W ki E ti
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Working Equation
nads= (PV/RT)man.- (PV/RT)cell
That is, the amount adsorbed is calculated as the difference between
a) the amount of gas dosed from the manifold to the cell and b) the
amount of gas which remains not adsorbed at the end of the
equilibration time.
Principles of BET Surface Area Measurement
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Principles of BET Surface Area Measurement
and Calculation
Determine the monolayer capacity Vm from which
the surface area of the solid can be computed.
Adsorbate most commonly used is nitrogen
Readily available in high purity
Appropriate coolant, liquid nitrogen.
Gas-solid interaction relatively strong.
Widely accepted cross sectional area.
Multilayer adsorption
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y p
the BET equation (1938)
Stephen Brunauer
Paul Emmett
Edward Teller
B E tt & T ll
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Brunauer, Emmett & Teller
Model of adsorption extended to multilayers.
S. Brunauer, P.H. Emmett and E. Teller, J. Amer. Chem. Soc., 60, 309 (1938)
)(1)(1(
)(
000
0
PPCPPPP
PPC
V
V
m
Brunauer Emmett & Teller
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Brunauer, Emmett & Teller
BET C constant varies from solid to solid.
Low values represent weak gas adsorption
typical of low surface area solids, organicsand metals in particular.
00
11
]1)[(
1
P
P
CV
C
CVPPV mm
Or, in its familiar linearizedform
Measurement
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Measurement
Obtain at least three data points in the relative pressure
range
0.025 to 0.30
Plot 1/[VSTP(Po/P)-1] versusP/Po. It should yield a
straight line if the BET model holds true.
On all surfaces the BET model fails to accurately predict
the multilayer adsorption behavior above P/Po = 0.5 (the
onset of capillary condensationwhich fills pores with
liquid adsorbate)
Calculation of Surface Area by
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y
the BET method
relative pressure, P/Po
1
X[(Po/P)-1
]
0
negativeintercepts are unacceptable
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Calculation
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Calculation
isVm
1
v
mavmt
M
ALVS
Solving for Vm
Total surface area, St, is calculated thus
Lav= 6.022 x 1023
Am= 0.162 nm2
Mv= 22 414 mL
nm2to m2, x 10-18
Adsorbate cross sectional area
(0.162 nm2 for Nitrogen
Multi-Point BET Plot (Interpretation)
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Multi Point BET Plot (Interpretation)
Never use data points too low in relative pressure (P/Po).
Never use data points too high in (P/Po).
Multi-Point BET Plot (Interpretation)
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Multi Point BET Plot (Interpretation)
Discard under-equilibrated points (at low P/Po)
Never use less than three, preferably five data points.
Porosity
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Porosity
Pore VolumeTotal pore volume is derived from the amountof vapour adsorbed at a relative temperatureclose to unity (assuming pores are filled withliquid adsorbate).
Vads= volume of gas adsorbed
Vliq= volume of liquid N2in pores
Vm= molar vol. of liquid adsorbate (N2=34.7cm3/mol)Pa= ambient pressure
T = ambient temperature
Concept of Porosity: Open vs.
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Closed Pores
Dead end
(open)
ClosedInter-connected
(open)
Passing
(open)
F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 1-25, 1999
Open pores are accessible
whereas closed pores areinaccessible pores.
Open pores can be inter-
connected, passing or dead
end.
Size of Pores (IUPAC Standard)
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Size of Pores (IUPAC Standard)
2 nm 50 nm
Micropores Mesopores Macropores
Zeolite,
Activated
carbon,Metal organic
framework
Mesoporous silica,
Activated carbonSintered metals
and ceramics
Porous material are classified according to the size of pores: material
with pores less than 2 nm are called micropores, materials with poresbetween 2 and 50 nm are called mesopores, and material with pores
greater than 50 nm are macrospores
Sing, K. S. W. et al. Reporting Physisorption Data for Gas/Solid Systems. Pure & Appl. Chem. 57, 603-619 (1985).
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Techniques for Porosity Analysis
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Techniques for Porosity Analysis
Techniques for Porosity Analysis
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Techniques for Porosity Analysis
Techniques for Porosity Analysis
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Techniques for Porosity Analysis
Techniques for Porosity Analysis
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Techniques for Porosity Analysis
Techniques for Porosity Analysis
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Techniques for Porosity Analysis
Techniques for Porosity Analysis
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Techniques for Porosity Analysis
Techniques for Porosity Analysis
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Gas Sorption: Hysteresis
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Va
1P/Po
Type A
Cylindrical Slits
Type B
1P/Po 1P/Po
Type C Type D
1P/Po
Type E
1P/Po
Conical Bottle neck
Pore Radius
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The average pore size can be estimated from the porevolume.
Assuming cylindrical pore geometry (type A hysteresis)average pore radius (rp) can be expressed as:
Other pore geometry models may require furtherinformation on the isotherm hysteresis before applyingappropriate model.