1
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Physisorption Analysis of
Porous Solids
Ranjan Kumar Dash
Advisor: Prof. Yury Gogotsi
March 11, 2004
http://nano.materials.drexel.edu
Contents
Background
Background
1
1
Porosity Measurement
Porosity Measurement
3
3
Critical Comments and Conclusion
Critical Comments and Conclusion
4
4
Theory of Adsorption
Theory of Adsorption
2
2
2
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Applications of Porous Materials
Molecular
sieves
Energy
storage
Catalyst
Membranes
Application
Biomedical
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Degree of Porosity
Pore size and
its distribution
Pore volume
Surface area
Porosity
3
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Types of Pores
Dead end
(open)
Closed
Inter-connected
(open)
Passing
(open)
F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous
Solids, Academic Press, 1-25, 1999
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Shapes of Pores
Conical
Interstices
Slits
Cylindrical
Spherical or
Ink Bottle
Pore
Shapes
F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous
Solids, Academic Press, 1-25, 1999
4
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Size of Pores (IUPAC Standard)
2 nm 50 nm
Micropores
Mesopores Macropores
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Techniques for Porosity Analysis
Mercury
porosimetry
TEM
SEM
Small angle
X-ray
scattering
Small
Angle
Neutron
scattering
Gas
adsorption
Techniques
5
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Techniques for Porosity Analysis
Mercury
porosimetry
TEM
SEM
Small angle
X-ray
scattering
Small
Angle
Neutron
scattering
Gas
adsorption
Techniques
? Can measure only open pores
? Pore size : 0.4 nm – 50 nm
? Easy
? Established technique
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Techniques for Porosity Analysis
Mercury
porosimetry
TEM
SEM
Small angle
X-ray
scattering
Small
Angle
Neutron
scattering
Gas
adsorption
Techniques
? Similar to gas
adsorption
? Can measure only
open pores
? Pore size >1.5 nm
? Easy
? Established technique
6
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Techniques for Porosity Analysis
Mercury
porosimetry
TEM
SEM
Small angle
X-ray
scattering
Small
Angle
Neutron
scattering
Gas
adsorption
Techniques
? Provide information
regarding pore
connectivity
? Pore size can be
measured if the
materials contains
ordered pores
? Rarely used for pore
analysis
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Techniques for Porosity Analysis
Mercury
porosimetry
TEM
SEM
Small angle
X-ray
scattering
Small
Angle
Neutron
scattering
Gas
adsorption
Techniques
? Pore size > 5nm
? Rarely used for pore
analysis
7
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Techniques for Porosity Analysis
Mercury
porosimetry
TEM
SEM
Small angle
X-ray
scattering
Small
Angle
Neutron
scattering
Gas
adsorption
Techniques
? Any pore size
? Open + Close
porosity
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Techniques for Porosity Analysis
Mercury
porosimetry
TEM
SEM
Small angle
X-ray
scattering
Small
Angle
Neutron
scattering
Gas
adsorption
Techniques
? Any pore size
? Open & Close
porosity
? Costly
8
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Theory of Adsorption
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Adsorption Process
Adsorption is brought by the forces acting between the solid and the
molecules of the gas. These forces are of two kinds: physical
(physiosorption) and chemical (chemisorption)
Adsorbent - the solid where adsorption takes place
Adsorbate - the gas adsorbed on the
surface of solids
Adsorptive - adsorbate before being adsorbed on the surface
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MONOLAYER ADSORPTION
Langmuir Isotherm is used to model adsorption
equilibrium.
MULTILAYER ADSORPTION
BET Isotherm used to model adsorption
equilibrium.
Surface reactions may take place:- Dissociation,
reconstruction, catalysis.
No surface reactions.
Can be activated, in which case equilibrium can
be slow and increasing temperature can favour
adsorption.
Non activated with equilibrium achieved
relatively quickly. Increasing temperature
always reduces surface coverage.
?H
ads
= 50 ….. 500 kJ mol
-1
?H
ads
= 5 ….. 50 kJ mol-1
SURFACE SPECIFIC
E.g. Chemisorption of hydrogen takes place on
transition metals but not on gold or mercury.
NOT SURFACE SPECIFIC
Physisorption takes place between all
molecules on any surface providing the
temperature is low enough.
STRONG, SHORT RANGE BONDING
Chemical bonding involved.
WEAK, LONG RANGE BONDING
Van der Waals interactions
CHEMISORPTIONPHYSISORPTION
Physisorption vs Chemisorption
http://www.soton.ac.uk
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Adsorption Process
1. Diffusion to adsorbent surface
2. Migration into pores of adsorbent
3. Monolayer builds up of adsorbate
1 2 3
?Gas molecules admitted
under increasing pressure to
a clean, cold surface.
?Data treatment techniques
find the quantity of gas that
forms the first layer.
1 2 3
S. Lowell & J. E. Shields, Powder Surface
Area and Porosity, 3rd Ed. Chapman & Hall,
New York, 1991
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Adsorption Process
Adsorbent
Adsorbate
adsorptive of pressure saturated
adsorbate of pressure
where
:as written becan equation
above theconstant, made are I and T, W,If
adsorbent. and adsorbatebetween n interactio
re; temperatu
adsorbate; theof pressure
adsorbent; of weight
adsorbed; gas of volume
where
),,,(
=
?
?
?
?
?
?
?
?
=
=
=
=
=
=
=
p
p
p
p
f
I
T
P
W
PITWf
o
o
V
V
V
a
a
a
Equation of adsorption
isotherm
S. Lowell & J. E. Shields, Powder Surface Area and
Porosity, 3rd Ed. Chapman & Hall, New York, 1991
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Gas Sorption: Isotherm
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.
adsorptive of pressure saturated
adsorbate of pressure
where
=
?
?
?
?
?
?
?
?
=
p
p
p
p
f
o
o
V a
V
a
Desorption isotherm
p
p
o
11
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Gas Sorption: Isotherm
V
a
1
P/P
o
Type I
or
Langmuir
S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed.
Chapman & Hall, New York, 1991
?Concave to the P/P
o
axis
?Exhibited by microporous
solids ( < 2nm )
1
P/P
o
Type II
?Exhibited by nonporous or
macroporous solids ( > 50nm )
?Unrestricted monolayer-multilayer
adsorption
?Point B indicates the relative
pressure at which monolayer
coverage is complete
B
V
a
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Gas Sorption: Isotherm
V
a
1
P/P
o
Type III
?Convex to the P/P
o
axis
?Exhibited by nonporous solids
V
a
1
P/P
o
Type IV
?Exhibited 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
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Gas Sorption: Isotherm
V
a
1
P/P
o
Type V
1
P/P
o
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
V
a
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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.
1
P/P
o
Hysteresis
V
a
S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed.
Chapman & Hall, New York, 1991
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Gas Sorption: Hysteresis
V
a
1
P/P
o
Type A
Cylindrical Slits
Type B
1
P/P
o
1
P/P
o
Type C Type D
1
P/P
o
Type E
1
P/P
o
Conical
Bottle neck
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Adsorption/Desorption
Adsorption =
multilayer
formation
Desorption =
meniscus
development
14
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Adsorption Theories: Langmuir
Adsorbate
Adsorbent
Assumptions:
? homogeneous surface (all adsorption
sites energetically identical)
? monolayer adsorption (no multilayer
adsorption)
? no interaction between adsorbed
molecules
adsorbate. of pressure
and constant; empirical
monolayer; form torequired gas of volume
; pressureat adsorbed gas of volume
where
1
=
=
=
=
+=
P
b
V
PV
V
P
bVV
P
m
a
mma
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Adsorption Theories: BET
adsorbate. of pressure relative
and layer);1st of adsorption ofenergy to(relatedconstant BET C
monolayer; form torequired gas of volume
; pressureat adsorbed gas of volume
where
)1(1
)(
=
=
=
=
?
?
?
?
?
??
+=
?
o
m
a
o
mm
o
a
P
P
V
PV
P
P
CV
C
CVPPV
P
? Modification of Langmuir
isotherm
? Both monolayer and
multilayer adsorption
Adsorbate
Adsorbent
15
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Specific Surface Area Calculation
CVP
P
CV
C
PPV
P
m
o
m
o
a
1)1(
)(
+
?
?
?
?
?
??
=
?
imXY +=
im
V
m
+
=
1
P/P
o
1
V[(P
o
/P)-1]
0-1 0-2 0-3
At least three data points in the
relative pressure range 0.05 to 0.30
adsorbate ofWeight
area surface Total
csavm
ANV
=
sample ofWeight
area surface Total
area) surface (SpecificSSA =
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Single Point BET
?Single-point method offers the advantage of simplicity and
speed, often with little loss in accuracy.
( )
o
am
PPVV ?= 1
i.e. V
m
= 1/slope
?A relative pressure of 0.3 gives good general agreement with the
multi-point method.
? Correction of single point “error” at P/P
0
= 0.3 by multiplying the
single point BET value by C/C-2 decreases the difference.
5.957
8.056
4.286
4.923
Multi-point
BET
(m
2
/g)
5.194
6.867
3.664
4.241
Uncorrected
single-point
(m
2
/g)
-12.8
-14.8
-14.5
-13.9
Uncorrected
difference
(%)
4
3
2
1
Sample
No.
+1.736.060
-0.568.011
-0.264.275
0.514.948
Corrected
difference
(%)
Corrected
single –
point
(m
2
/g)
16
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Pore Size Distribution
V
a
Pore diameter, d
Narrow pore size
distribution
Broad pore size
distribution
Unimodal pore size
distribution
Pore diameter, d
Multimodal pore
size distribution
The distribution of pore
volume with respect to
pore size is called a pore
size distribution.
V
a
∑
=
d
a
V volumePore
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Pore Size Distribution
?G
ads
= RT(lnP
ads
-lnP
0
)
?G
des
= RT(lnP
des
-lnP
0
)
?G
des
< ?G
ads
1
P/P
o
(P/P
o
)
des
(P/P
o
)
ads
?Adsorption or
desorption isotherm.
?The desorption
isotherm is preferred
over adsorption
isotherm.
V
a
17
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Pore Size: Kelvin Equation
?Multilayer formation
occurs in parallel to
capillary condensation.
?Capillary condensation
is described by the
Kelvin equation.
phase. condensed and solid ebetween th anglecontact
re; temperatu
constant; gas real
meniscus; liquid theof curvature of radiusmean
adsorbate; condensed of memolar volu
tension;surface liquid
;
adsorbate of pressure saturated
adsorbate of pressure
where
cos
2
ln
=
=
=
=
=
=
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
?
?
θ
γ
θ
γ
T
R
V
RT
V
r
p
p
r
p
p
k
o
k
o
θ
k
r
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Pore Size: Kelvin Equation
trr
kp
+=
Actual
radius of
the pore
Kelvin
radius of
the pore
Thickness of the
adsorbed layer
Prior to condensation, some adsorption has taken place
on the walls of the pore, r
k
does not represent the actual
pore radius.
θ
t
k
r
Adsorbed layer
18
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Methods for Calculation of Pore Size
Distribution
?BJH (Barrett, Joyner and
Halenda) method
?DH (Dollimore Heal) method
?Dubinin-Astakhov method
?HK (Horvath-Kawazoe) method
?Saito-Foley method
Mesoporous solids
Microporous solids
?NLDFT (Non Local Density
Functional Theory) and Monte
Carlo simulation method
Microporous and
Mesoporous solids
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Porosity Measurement
19
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Porosity Analyzer
Outgassing station
Analysis station
Liquid nitrogen
bath
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Steps for Measurement
3. Interpretation
2. Adsorption Analysis
1. Sample Preparation
20
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1. Sample Preparation (Outgassing)
? Surface contamination is
removed by application
of:
? Temperature
? Flowing gas (helium or
nitrogen) or vacuum
? Backfill can be done
using helium or adsorbate
gas.
? According to IUPAC
standards, materials
should be outgassed for
at least 16 hours.
Adsorbate
Helium
Vacuum
P
o
Outgassing
station
Analysis station
Sample
Cell
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2. Adsorption Analysis
? Adsorbate (nitrogen,
argon, carbon dioxide,
krypton)
? Analysis temperature
(liquid nitrogen, liquid
argon, 0
o
C)
? Quantity of sample (1
mg sample is sufficient)
? Number of points
(single point, five
points, seven points,
eleven points, full
analysis)
Adsorbate
Helium
Vacuum
P
o
Outgassing
station
Analysis station
Sample
Cell
21
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3. Interpretation
3
2
1
Volume
adsorbed
P/P
o
Points
Weight of sample
O
U
T
P
U
T
Pore shape
Specific
surface area
Pore volume
Pore size
&
distribution
Results
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Critical Comments and
Conclusion
22
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Critical Comments : Choice of
Adsorptive
? N
2(g)
in N
2(l)
is the most
commonly used
adsorbate.
? Not completely inert.
? Dipole movement and
thus can have
localized adsorption.
? Cross-sectional area of
0.162 nm
2
is
questionable.
?S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd
Ed. Chapman & Hall, New York, 1991
?Quantachrome Autosorb-I Operational Manual
O
x
y
g
e
n
A
r
g
o
n
N
i
t
r
o
g
e
n
C
a
r
b
o
n
m
o
n
o
o
x
i
d
e
C
a
r
b
o
n
d
i
o
x
i
d
e
K
r
y
p
t
o
n
n
-
b
u
t
a
n
e
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
C
r
os
s-
sect
i
onal
ar
ea,
nm
2
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O
x
y
g
e
n
A
r
g
o
n
N
i
t
r
o
g
e
n
C
a
r
b
o
n
m
o
n
o
o
x
i
d
e
C
a
r
b
o
n
d
i
o
x
i
d
e
K
r
y
p
t
o
n
n
-
b
u
t
a
n
e
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
C
r
os
s-
sect
i
onal
ar
ea,
nm
2
Critical Comments : Choice of
Adsorptive
?S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd
Ed. Chapman & Hall, New York, 1991
?Quantachrome Autosorb-I Operational Manual
? Ar
(g)
in Ar
(l)
is preferable
but because of
unavailability of Ar
(l)
(87K),
N
2(l)
(77 K) is used.
? Ar can reach to somewhat
smaller pores than N
2
.
? Accurate measurement of
micropores is possible
using Ar.
23
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O
x
y
g
e
n
A
r
g
o
n
N
i
t
r
o
g
e
n
C
a
r
b
o
n
m
o
n
o
o
x
i
d
e
C
a
r
b
o
n
d
i
o
x
i
d
e
K
r
y
p
t
o
n
n
-
b
u
t
a
n
e
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
C
r
os
s-
sect
i
onal
ar
ea,
nm
2
Critical Comments : Choice of
Adsorptive
?S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd
Ed. Chapman & Hall, New York, 1991
?Quantachrome Autosorb-I Operational Manual
? In case of activated
carbon, CO
2
is often
the most preferred
adsorbate.
? Adsorption analysis of
CO
2
takes less time.
? Limited to micropore
analysis.
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Critical Comments : Validity of BET -
Method
? The BET method
depends on the cross-
sectional area of
adsorbate.
? Monolayer structure is
same on all the surface.
? Localized monolayer
coverage.
K. S. W. Sing, The Use of Nitrogen Adsorption for the Characterisation of Porous
Materials, Colloids and Surfaces, 187 – 188, 2001, 3 - 9
?
?
?
?
?
??
+=
?
o
mm
o
P
P
CV
C
CVPPV
P )1(1
)(
M
ALV
SSA
av
=
Adsorbate
Adsorbent
24
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Critical Comments : Validity of
Kelvin Equation
θ
γ
cos
2
ln
RT
V
r
p
p
k
o
=
?
?
?
?
?
?
?
?
?
?
? Is relation between the
meniscus curvature and the
pore size and shape valid?
? Is it applicable for micropores
and narrow mesopores?
? Does surface tension varies
with pore width?
θ
F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous
Solids, Academic Press, 203, 1999
k
r
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Critical Comments : Shape of
Microporous Materials
V
a
1
P/Po
Type I
or
Langmuir
?Type I isotherms don’t have
hysteresis.
?Pore shape cannot be
determined by isotherm.
?As various methods for pore
size calculation are based on
shape of pores, reliability of pore
size calculation is questionable.
F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous
Solids, Academic Press, 439-446, 1999
25
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2 nm
50 nm
Micropores
Mesopores Macropores
de Boer’s t-methodCylindrical or Slit shapedBrunauer MP method
?Polanyi potential
theory
?Independent of
Kelvin equation
-Dubinin-Astakhov method
AssumptionMethods
Cylindrical
Slit
Pore Shape
HK method
?Everett and Powl
method
?Independent of
Kelvin equation
Based on ..
Saito-Foley method
HK (Horvath-Kawazoe) method
Critical Comments : Choice of Method
?P. A. Webb, C. Orr, Analytical Methods in Fine Particle Technology, Micromeritics, 53 –
152, 1997
?Quantachrome Autosorb-I Operational Manual
http://nano.materials.drexel.edu
2 nm 50 nm
Micropores
Mesopores Macropores
Kelvin equationCylindrical, Slit-shapedBJH (Barrett, Joyner and
Halenda) method
t-methodCylindrical
DH (Dollimore Heal) method
AssumptionMethods
Pore Shape Based on ..
Critical Comments : Choice of Method
?P. A. Webb, C. Orr, Analytical Methods in Fine Particle Technology, Micromeritics, 53 –
152, 1997
?Quantachrome Autosorb-I Operational Manual
26
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2 nm
50 nm
Micropores
Mesopores Macropores
AssumptionMethods
Cylindrical and slit
Pore Shape
Statistical
thermodynamics
Based on ..
NLDFT (Non Local Density
Functional Theory) and Monte
Carlo simulation method
Critical Comments : Choice of Method
?P. A. Webb, C. Orr, Analytical Methods in Fine Particle Technology, Micromeritics, 53 –
152, 1997
?Quantachrome Autosorb-I Operational Manual
http://nano.materials.drexel.edu
Conclusion
?Despite limitations, physisorption is often the technique of first
choice for studying pore characteristics of solid materials.
?In spite of its artificial nature, the BET method is still the most
popular technique for determination of surface area.
?All computational procedures for pore size analysis have limitations.
The various assumptions include ideal pore shape, rigidity of structure
and oversimplified model (capillary condensation or micropore filling).
?The current IUPAC classification contain six isotherms. Apart from
these, there are many complex isotherms for which there is no
procedure available for interpretation.
?The use of single gas adsorption cannot be expected to provide more
than a semi-quantitative estimate of the micropore size distribution. It
is always advisable to compare adsorption results with two or more
gases.
27
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Questions?
Comments?
Thank you!
I love Pia.
http://nano.materials.drexel.edu
TEM of Ordered Nanoporous Carbon
R. Ryoo, S. H. Joo and S. Jun, "Synthesis of Highly Ordered Carbon Molecular Sieves via
Template-Mediated Structural Transformation", J. Phys. Chem. B 103, 7743 (1999).
28
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TEM of Amorphous Carbon
Carbon derived from boron
carbide
5 nm
http://nano.materials.drexel.edu
SEM of Porous Aluminum
http://cml.me.berkeley.edu/~jiayang/inter/english/eweb4-1.htm.
Porous aluminum with
pore-spacing about 100
nm (SEM, 70,000 X)
29
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Common Adsorbates
0.205 ? -195.8
o
C (liquid nitrogen)Kr
0.141 ? -183
o
C (liquid argon)O
2
? 0
o
C, 25
o
C
? -183
o
C (liquid argon)
? -78
o
C, -25
o
C, 0
o
C
? -183
o
C (liquid argon).
? -195.8
o
C (liquid nitrogen)
? -195.8
o
C (liquid nitrogen)
? -183
o
C (liquid argon).
Temperature
0.195CO
2
0.163CO
0.162N
2
0.142Ar
0.469
Cross sectional
area (nm
2
)
Gas
C
4
H
10
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Adsorption Analyzer
30
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Adsorption Analyzer
Adsorbate
Helium
Vacuum
P
o
Outgassing
station
Analysis station
Sample
Cell
Manifold
(known
volume)
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Adsorption Measurement
1. Adsorptive is passed through
the sample at requested
pressure.
2. Volume of gas adsorbed =
difference in pressure of
manifold.
3
2
1
Volume of
gas
adsorbed
P/P
o
Points
31
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Techniques for Porosity Analysis
?Larger pores (> 5 nm).SEM (Scanning Electron
Microscope)
?Total porosity (open + close).SAXS (Small Angle X-Ray
Scattering)
?Open porosity (pore size > 1.5 nm)Mercury Porosimetry
?Limited information regarding pore
connectivity.
?Small pores if the materials contain
ordered pores
TEM (Transmission Electron
Microscope)
?Open and closed pores.
? Open porosity (pore size: 0.4 nm -
50 nm)
Gas Adsorption
SANS (Small Angle Neutron
Scattering)
S. Lowell & J. E. Shields, Haowder Surface Area and Porosity, 3rd
Ed. Chapman & Hall, New York, 1991
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Factors Affecting Surface Area
1 m
A
i
= Initial surface area = 6 m
2
0.1 m
Number of fragments = 1000
A
f
= Final surface area = 1000 X 6 X (0.1)
2
m
2
A
f
/A
i
= 10
(Particle size)
2
α
Surface area
1