Transcript Micro and Mesopore Size Determination by Gas Sorption

Quantachrome
INSTRUMENTS
Physisorption
Methods and Techniques
Pore Size by
Gas Sorption
Micro and Mesopore Size
Determination by Gas Sorption
First: Quantitative estimation of
micropore volume and area…
T-plot and DR methods.
Volume adsorbed
Multilayer adsorption
Type II, IV
After the knee,
micropores cease to
contribute to the
adsorption process.
Low slope region in middle of
isotherm indicates first few
multilayers, on external surface
including meso and macropores…
before the onset of capillary
condensation
Relative Pressure (P/Po)
Estimation of Micropores...
the t-plot method
This method uses a mathematical representation of
multi-layer adsorption. The thickness, t, of an
adsorbate layer increases with increasing pressure.
The t-curve so produced is very similar in
appearance to a type II isotherm. For every value of
P/Po, the volume adsorbed is plotted against the
corresponding value of “t”.
If the model describes the experimental data a
straight line is produced on the t-plot...
The t-plot
Statistical thickness
Resembles a type II
A statistical multilayer
A statistical monolayer
Relative Pressure (P/Po)
t-plot Method
(mesoporous only)
Slope = V/t = A
1
2
3
4
t ()
5
6
7
t-plot Method
showing a “knee”
C
X
C
X
X
X
B
B
X
X
A
A
X
1
2
3
4
5
6
7
t ()
Slope A - slope B = area contribution by micropores size C
?
?
?
Quiz
?
?
?
?
What is an s plot?

(for Ken Sing) is a comparison
s
A
plot like the t-plot but its slope
does not give area directly.
Estimation of Micropores
Dubinin-Radushkevich (DR) Theory
  T 2

P


2
W  W0 exp B  log  0 
 P 
   
W = volume of the liquid adsorbate
W0 = total volume of the micropores
B = adsorbent constant
 = adsorbate constant
A linear relationship should be found between log(W) and log2(Po/P)...
Estimation of Micropores
Log (W)
Dubinin-Radushkevich (DR) Plot
Extrapolation
yields Wo
0
Log2(Po/P)
Pore Size Determination
Requires a recognition and
understanding of different basic
isotherm types.
t-plot Method
(in the presence of micropores)
Intercept = micropore volume
1
2
3
4
t ()
5
6
7
Types of Isotherms
Type II
Volume adsorbed
Type I
Type V
Type IV
Type III
Relative Pressure (P/Po)
Volume adsorbed
Types of Isotherms
Limiting value (plateau) due to filled
pores and essentially zero external area.
Type I or
pseudo-“Langmuir”
Steep initial region due to very strong
adsorption, for example in micropores.
Relative Pressure (P/Po)
?
?
?
Quiz
?
?
?
?
Why pseudo Langmuir?
A
Langmuir applies to monolayer
limit, not volume filling limit.
Types of Isotherms
Volume adsorbed
Absence of hysteresis indicates adsorption
on and desorption from a non-porous
surface..
Type II
Low slope region in middle of
isotherm indicates first few
multilayers
Rounded knee
indicates approximate
location of monolayer
formation.
Relative Pressure (P/Po)
Types of Isotherms
Volume adsorbed
Example: krypton on polymethylmethacrylate
Type III
Lack of knee represents extremely
weak adsorbate-adsorbent interaction
BET is not applicable
Relative Pressure (P/Po)
Types of Isotherms
Volume adsorbed
Type IV
Closure at P/Po~0.4 indicates
presence of small mesopores
(hysteresis would stay open
longer but for the tensilestrength-failure of the nitrogen
meniscus.
Rounded knee
indicates approximate
location of monolayer
formation.
Hysteresis indicates capillary
condensation in meso and
macropores.
Low slope region in middle of
isotherm indicates first few
multilayers
Relative Pressure (P/Po)
Types of Isotherms
Volume adsorbed
Example: water on carbon black
Type V
Lack of knee represents extremely
weak adsorbate-adsorbent interaction
BET is not applicable
Relative Pressure (P/Po)
Types of Hysteresis
Volume adsorbed
Large pores/voids
Gel
Mesopores
MCM
Relative Pressure (P/Po)
MesoPore Size
by Gas
Sorption
(BJH)
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Quiz
?
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?
Analyzer measures volume of pores:
Yes or No?
A
NO! It measures what leaves
supernatent gas phase
Pore Size Distribution
Hysteresis is indicative of the presence of
mesopores and the pore size distribution can be
calculated from the sorption isotherm.
Whilst it is possible to do so from the adsorption
branch, it is more normal to do so from the
desorption branch...
Micropore (Greek micro = small): 0 nm - 2 nm diameter
Mesopore (Greek meso = middle): 2nm - 50 nm diameter
Macropore (Greek macro = large): >50 nm diameter
Adsorption / Desorption
Adsorption =
Desorption =
multilayer formation
meniscus development
Kelvin* Equation
P 2V
ln 
cos
P0 rRT
4.15
rk ( A ) 
log( P / P0 )
* Lord Kelvin a.k.a. W.T. Thomson
Pore Size
rp  rk  t
rp = actual radius of the pore
rk = Kelvin radius of the pore
t = thickness of the adsorbed film
Statistical Thickness, t
• Halsey equation
• Generalized Halsey
• deBoer equation
• Carbon Black STSA
BJH Method
(Barrett-Joyner-Halenda)
rpore  rKelvin  t
Pore volume requires assumption
of liquid density!
Pore Size Distribution
dV/dlogD
Artifact
40
Pore Diameter (angstrom)
Amount adsorbed
~ 0.42
Relative Pressure (P/Po)
Pore Size Data
• Volume and size of pores can be expressed from
either adsorption and/or desorption data.
• The total pore volume, V, is taken from the
maximum amount of gas adsorbed at the “top” of the
isotherm and conversion of gas volume into liquid
volume.
• The mean pore diameter is calculated from simple
cylindrical geometry:
4V
d
A
where A is the BET
surface area.
Pore size analysis of MCM 41
(Templated silica) by N2 sorption
at 77 K
600
Exp. Nitrogen sorption at 77 K in MCM 41
DFT- Isotherm
Volume [cc/g]
500
400
300
200
100
0
0.2
0.4
0.6
P/P0
0.8
1
Pore size analysis of MCM 41:
Calculations compared
0.3
Dv(d) [cc/Å/g]
0.25
BJH-Pore size distribution
DFT-Pore size distribution
0.2
0.15
0.1
0.05
0
15
23
31
39
Pore Diameter [Å]
47
55
Calculation
Models
Comparisons
•
P/Po range
1x10-7 to 0.02
0.01 to 0.1
0.05 to 0.3
> 0.1
> 0.35
0.1 to 0.5
Gas Sorption Calculation Methods
Mechanism
micropore filling
sub-monolayer formation
monolayer complete
multilayer formation
capillary condensation
capillary filling
in M41S-type materials
Calculation model
DFT, GCMC, HK, SF, DA, DR
DR
BET, Langmuir
t-plot (de-Boer,FHH),
BJH, DH
DFT, BJH
Different Theories of
Physisorption
Surface area Pore volume
Pore size
BET
Total pore vol
DR ave
Langmuir
BJH
t-plot (pore vol)
DR
DH
DR (pore vol)
MP and t-plot
DA
DFT
BJH
HK
s plot
(BJH)
(DFT)
SF
(DH)
(DH)
(DFT)
HK & SF
Horvath-Kawazoe & Saito-Foley
• HK
• Direct mathematical relationship between relative
pressure (P/Po) and pore size. Relationship calculated
from modified Young-Laplace equation, and takes into
account parameters such as magnetic susceptibility.
Based on slit-shape pore geometry (e.g. activated
carbons). Calculation restricted to micropore region (
2nm width).
• SF
• Similar mathematics to HK method, but based on
cylindrical pore geometry (e.g. zeolites). Calculation
restricted to micropore region ( 2 nm diameter).
DA & DR
Dubinin-Astakov and Dubinin-Radushkevic
• DA
• Closely related to DR calculation based on pore filling mechanism.
Equation fits calculated data to experimental isotherm by varying two
parameters, E and n. E is average adsorption energy that is directly
related to average pore diameter, and n is an exponent that controls
the width of the resulting pore size distribution. The calculated pore
size distribution always has a skewed, monomodal appearance
(Weibull distribution).
• DR
• Simple log(V) vs log2(Po/P) relationship which linearizes the isotherm
based on micropore filling principles. “Best fit” is extrapolated to
log2(Po/P) (i.e. where P/Po = 1) to find micropore volume.
BET
• The most famous gas sorption model. Extends Langmuir
model of gas sorption to multi-layer. BET equation
linearizes that part of the isotherm that contains the
“knee” , i.e. that which brackets the monolayer value.
Normally solved by graphical means, by plotting
1/(V[(Po/P)]-1) versus P/Po. Monolayer volume (Vm) is
equal to 1/(s+i) where s is the slope and i is the y-intercept.
Usually BET theory is also applied to obtain the specific
surface area of microporous materials, although from a
scientific point of view the assumptions made in the BET
theory do not take into account micropore filling. Please
note, that for such samples the linear “BET” range is
found usually at relative pressures< 0.1, in contrast to the
classical BET range, which extends over relative
pressures between 0.05 – 0.3.
Langmuir
• Adsorption model limited to the formation of a
monolayer that does not describe most real
cases. Sometimes can be successfully applied
to type I isotherms (pure micropore material) but
the reason for limiting value (plateau) is not
monolayer limit, but due to micropore filling.
Therefore type I physisorption isotherm would
be better called “pseudo-Langmuir” isotherm.
t-plot
Statistical Thickness
• Multi-layer formation is modeled mathematically to calculate
a layer “thickness, t” as a function of increasing relative
pressure (P/Po). The resulting t-curve is compared with the
experimental isotherm in the form of a t-plot. That is,
experimental volume adsorbed is plotted versus statistical
thickness for each experimental P/Po value. The linear
range lies between monolayer and capillary condensation.
The slope of the t-plot (V/t) is equal to the “external area”,
i.e. the area of those pores which are NOT micropores.
Mesopores, macropores and the outside surface is able to
form a multiplayer, whereas micropores which have already
been filled cannot contribute further to the adsorption
process.
• It is recommended to initially select P/Po range 0.2 – 0.5,
and subsequently adjust it to find the best linear plot.
BJH & DH
Barrett, Joyner, Halenda and Dollimore-Heal
• BJH
• Modified Kelvin equation. Kelvin equation predicts
pressure at which adsorptive will spontaneously condense
(and evaporate) in a cylindrical pore of a given size.
Condensation occurs in pores that already have some
multilayers on the walls. Therefore, the pore size is
calculated from the Kelvin equation and the selected
statistical thickness (t-curve) equation.
• DH
• Extremely similar calculation to BJH, which gives very
similar results. Essentially differs only in minor
mathematical details.
Other Methods
• FRACTAL DIMENSION
• The geometric topography of the surface
structure of many solids can be characterized by
the fractal dimension D, which is a kind of
roughness exponent. A “flat” surface is
considered D is 2, however for an irregular (real)
surface D may vary between 2 and 3 and
expresses so the degree of roughness of the
surface and/or porous structure. The
determination of the surface roughness can be
investigated by means of the modified FrenkelHalsey Hill method, which is applied in the
range of multilayer adsorption.
Example Data : Microporous Carbon
BET : Not strictly applicable
Example Data : Microporous Carbon
• Tag all adsorption
points
• Analyze behavior
• Note knee – transition
from micropore filling
to limited
multilayering
(plateau).
Example Data : Microporous Carbon
• Use Langmuir
(Monolayer model) /
DR for Surface Area,
Micropore Volume
• Usue Langmuir in
range of 0.05 -> 0.2
(monolayer)
Example Data : Microporous Carbon
• Langmuir Surface Area
Example Data : Microporous Carbon
• DR Method for
surface area,
micropore volume
• Choose low relative
pressure points (up
to P/P0 = 0.2)
Example Data : Microporous Carbon
• Reports micropore
surface area, and
micropore volume.
• Note Langmuir, DR
surface areas very
close (1430 m2/g vs.
1424 m2/g)
Example Data : Macroporous Sample
Little or no “knee”,
isotherm closes at
0.95
Example Data : Macroporous Sample
• BET Plot = OK
• Surface area ca. 8m2/g (low)
• Note hysteresis above P/P0 = 0.95 Pores > 35 nm
Example Data : Macroporous Sample
Intercept = (-),
no micropore
volume.
Example Data : Macroporous Sample
BJH Shows pores
> 20nm, to over
200 nm
Example Data : Mesoporous Silica
Hysteresis => mesopores
Also micropores ?? Test using tmethod
Example Data : Mesoporous Silica
BET Surface area = 112m2/g
Classic mesoporous silica !
Example Data : Mesoporous Silica
Intercept ~ 0
Look at tabular data
MP SA = 8m2/g (total SA = 112)
Statistical Thickness => Use de Boer for oxidic surfaces = silicas
Example Data : Mesoporous Silica
Use BJH – shows narrow pore size distribution in 14-17nm range (mesopores)
MicroPore Size
by Gas
Sorption
Available
Calculation
Models
Pore filling pressures for nitrogen in
cylindrical pores at 77 K,
(Gubbins et al. 1997)
Pore filling pressures for nitrogen in
cylindrical silica pores at 77 K
(Neimark et al., 1998)
Pore size analysis of MCM 41
by silica by N2 sorption at 77 K
0.3
600
Exp. Nitrogen sorption at 77 K in MCM 41
DFT- Isotherm
0.25
Dv(d) [cc/Å/g]
Volume [cc/g]
500
400
300
BJH-Pore size distribution
DFT-Pore size distribution
0.2
0.15
0.1
200
0.05
100
0
0.2
0.4
0.6
P/P0
0.8
1
0
15
23
31
39
Pore Diameter [Å]
47
55
Gas- and liquid density profiles
in a slit pore by GCMC
(Walton and Quirke,1989)
NLDFT / GCMC (Monte
Carlo) Kernel File
Applicable Pore
Diameter Range
Examples
NLDFT– N2 - carbon kernel at 77 K
based on a slit-pore model
0.35nm-30 nm
Carbons with slit-like pores, such as
activated carbons and others.
NLDFT– N2 – silica equilibrium
transition kernel at 77 K, based on a
cylindrical pore model
0.35nm- 100nm
Siliceous materials such as some silica
gels, porous glasses, MCM-41, SBA15, MCM-48 and other adsorbents
which show type H1 sorption
hysteresis.
NLDFT– N2 - silica adsorption branch
kernel at 77 K, based on a cylindrical
pore model
0.35nm-100nm
Siliceous materials such as some
controlled pore glasses, MCM-41,
SBA-15, MCM-48, and others. Allows
to obtain an accurate pore size
distribution even in case of type H2
sorption hysteresis
NLDFT– Ar zeolite/silica equilibrium
transition kernel at 87 K based on a
cylindrical pore model
0.35nm -100nm
Zeolites with cylindrical pore channels
such as ZSM5, Mordenite, and
mesoporous siliceous
materials (e.g., MCM-41, SBA-15,
MCM-48, some porous glasses
and silica gels which show type H1
sorption hysteresis).
NLDFT / GCMC (Monte
Carlo) Kernel File
Applicable Pore
Diameter Range
Examples
NLDFT – Ar-zeolite/silica adsorption
branch kernel at 87 K based on a
cylindrical pore model
0.35nm-100nm
Zeolites with cylindrical pore channels
such as ZSM5, Mordenite etc., and
mesoporous siliceous materials such as
MCM-41, SBA-15, MCM-48, porous
glasses some silica gels etc). Allows to
obtain an accurate pore size distribution
even in case of H2 sorption hysteresis.
NLDFT – Ar-zeolite / silica
equilibrium transition kernel based on a
spherical pore model (pore diameter < 2
nm) and cylindrical pore model (pore
diameter > 2 nm)
0.35nm-100nm
Zeolites with cage-like structures such
as Faujasite, 13X etc. , and mesoporous
silica materials (e.g., MCM-41, SBA15, porous glasses, some silica gels
which show H1 sorption hysteresis).
NLDFT – Ar-zeolite / silica adsorption
branch kernel at 87 K based on a
spherical pore model (pore diameter < 2
nm) and cylindrical pore model (pore
diameter > 2 nm)
0.35nm-100nm
Zeolites with cage-like structures such
as Faujasite, 13X, and mesoporous
silica materials (e.g., MCM-41, SBA15, controlled-pore glasses and others).
Allows to obtain an accurate pore size
distribution even in case of H2 sorption
hysteresis.
NLDFT / GCMC (Monte
Carlo) Kernel File
Applicable Pore
Diameter Range
Examples
NLDFT – Ar - carbon kernel at
77 K based on a slit-pore model
0.35 nm - 7 nm
Carbons with slit-like pores,
such as activated carbons etc.
NLDFT - CO2 - carbon kernel at
273 K based on a slit-pore model
0.35nm-1.5 nm
Carbons with slit-like pores,
such as activated carbons etc.
GCMC – CO2 - carbon kernel at
273 K based on a slit-pore model
0.35nm-1.5 nm
Carbons with slit-like pores,
such as activated carbons etc.
RECENT ADVANCES IN THE
PORE SIZE ANALYSIS OF
MICRO- AND MESOPOROUS
MOLECULAR SIEVES BY ARGON
GAS ADSORPTION
Micropore Size Characterization
• Physical adsorption in micropores, e.g.
zeolites occurs at relative pressures
substantially lower than in case of
adsorption in mesopores.
• Adsorption measurements using nitrogen at
77.4 K is difficult, because the filling of
0.5 - 1 nm pores occurs at P/Po of 10-7 to
10-5, where the rate of diffusion and
adsorption equilibration is very slow.
Advantages of Using Argon
• Advantage to analyze such narrow
micropores by using argon at liquid argon
temperature (87.3 K).
• Argon fills these micropores (0.5 – 1nm) at
much higher relative pressures (i.e., at
relative pressures 10-5 to 10-3) compared to
nitrogen.
Advantages of Higher
Temperature & Pressure
• Accelerated diffusion.
• Accelerated equilibration processes.
• Reduction in analysis time.
Argon Adsorption at 87.3 K versus
Nitrogen Adsorption at 77.4 K
350
N2/77K
Ar/87 K
Volume [cm3]
280
210
140
70
0
10-6
ZEOLITE | 10.5.2001
5 10-5
5 10-4
5 10-3
5 10-2
5 10-1
5 100
P/P0
The different pore filling ranges for argon adsorption at 87.3K and nitrogen
adsorption at 77.4K in faujasite-type zeolite are illustrated above.
Micropore Size Calculation
• Difficulties are associated with regard to the analysis of
micropore adsorption data.
• Classical, macroscopic, theories [1] like DR and
semiempirical treatments such those of HK and SF do
not give a realistic description of micropore filling
• This leads to an underestimation of pore sizes for
micropores and even smaller mesopores [2].
[1] F. Rouquerol, J. Rouquerol & K. Sing, Adsorption by Powders & Porous Solids, Academic Press, 1999
[ 2 ] P. I Ravikovitch, G.L. Haller, A.V. Neimark, Advcances in Colloid and Interface Science 76-77 , 203 (1998)
New Calculation
• To overcome the above mentioned problems we
introduce a new method for micropore analysis
based on a Non-local Density Functional Theory
(NLDFT) model by Neimark and Co-workers [3-5].
• The new DFT-method is designed for micromesopore size characterization of zeolitic
materials ranging in size from 0.44 to 20 nm using
high-resolution low-pressure argon adsorption
isotherms at 87.3 K.
[3] P.I. Ravikovitch, G.L. Haller, A.V. Neimark, Advances in Colloid and Interface Science, 76 – 77 (1998), 203 -207
[4] A.V. Neimark, P.I Ravikovitch, M. Gruen, F. Schueth, and K.K. Unger, J. Coll. Interface Sci., 207, (1998) 159
[5] A.V. Neimark, P.I. Ravikovitch, Microporous and Mesoporous Materials (2001) 44-45, 697
Systematic, Experimental Study
• To evaluate the application of argon sorption for
micro- and mesopore size analysis of zeolites and
mesoporous silica materials including novel
mesoporous molecular sieves of type MCM-41
and MCM-48.
• The sorption isotherms were determined using a
static volumetric technique
• Samples were outgassed for 12 h under vacuum
(turbomolecular pump) at elevated temperatures
(573 K for the zeolites and 393 K for MCM41/MCM-48).
Results
25
Argon adsorption
isotherms at 87 K
on MCM-41,
ZSM-5 and their
50-50 mixture.
Adsorption, [mmol/g]
20
15
10
MCM-41
5
ZSM-5
50-50
0
0
0.2
0.4
0.6
P/Po
0.8
1
Results
25
Adsorption, [mmol/g]
20
15
MCM-41
10
ZSM-5
50-50
5
0
0.000001
0.00001
0.0001
0.001
P/Po
0.01
0.1
1
ZSM
0.12
0.4
0.35
0.1
0.3
0.25
0.2
0.06
0.15
histogram
0.04
0.1
integral
0.05
0.02
0
0
-0.05
1
10
100
D, [Å]
1000
Vcum, [cm3/g]
dV/dD [cm3/g
0.08
MCM
0.2
0.7
0.18
0.6
0.16
dV/dD [cm3/g]
/g]
0.12
0.4
0.1
0.08
0.06
histogram
0.3
integral
0.2
0.04
0.1
0.02
0
0
1
10
100
D, [Å]
1000
Vcum, [cm3/g]
0.5
0.14
Evaluation of DFT Algorithm
20
18
Adsorption, [mmol/g]
16
14
12
experimental
10
NLDFT fit
8
6
4
2
0
0.000001
0.00001
0.0001
0.001
P/Po
0.01
0.1
1
Pore Size Distribution
0.1
0.6
0.09
0.5
0.08
0.07
dV/dD [cm3/g]
0.06
0.05
0.3
histogram
0.04
0.2
0.03
integral
0.02
0.1
0.01
0
0
1
10
100
D, [Å]
1000
Vcum [cm3/g]
0.4
Discussion
• Argon sorption at 77 K is limited to pore
diameters smaller than 12 nm.
i.e. no pore filling/pore condensation can be observed at this
temperature for silica materials containing larger pores.
• This lack of argon condensation for pores
larger than ca. 12 nm is associated with the
fact, that 77 K is ca. 6.8 K below the bulk
triple point [4,5] .
[4] M. Thommes, R. Koehn and M. Froeba, J. Phys. Chem. B (2000), 104, 7932
[5] M. Thommes, R. Koehn and M. Froeba, Stud. Surf. Sci. Catal., (2001), 135 17
Discussion
• These limitation do not exist for argon
sorption at its’ boiling temperature,
i.e.
ca. 87 K.
• Pore filling and pore condensation can be
observed over the complete micro- and
mesopore size range .
Discussion
• Results of classical, and semi-empirical
methods (e.g., BJH, SF etc) indicate that
these methods underestimate the pore
size considerably.
• Deviations from the DFT-results are
often in a range of ca. 20 % for pore
diameters < 10 nm.
Summary
• Our results indicate that argon sorption
data at 87 K combined with the new
NLDFT-methods provides a convenient
way to achieve an accurate and
comprehensive pore size analysis over
the complete micro-and mesopore size
range for zeolites, catalysts, and
mesoporous silica materials.
Acknowledgements
• Special thanks go to Alex Neimark and
Peter Ravikovitch at TRI Princeton, New
Jersey, USA.
References
to research work of nitrogen, argon and krypton
in MCM-48/MCM-41 materials
(1) M. Thommes, R. Koehn and M. Froeba, “ Systematic Sorption studies on surface and pore size
characteristics of different MCM-48 silica materials”, Studies in Surface Science and
Catalysis 128, 259 (2000)
(2) M. Thommes, R. Koehn and M. Froeba, “Sorption and pore condensation behavior of nitrogen,
argon and krypton in mesoporous MCM-48 silica materials” J. Phys. Chem. B 104, 7932
(2000)
(3)M. Thommes, R. Koehn and M. Froeba, “Sorption and pore condensation behavior of pure fluids
in mesoporous MCM-48 silica, MCM-41 silica and controlled pore glass, Studies in Surface
Science and Catalysis, 135, 17 (2001)
(4)M. Thommes, R. Koehn and M. Froeba, “Characterization of porous solids: Sorption and pore
condensation behavior of nitrogen, argon and krypton in ordered and disordered mesoporous
silica materials (MCM-41, MCM-48, SBA-15, controlled pore glass, silica gel) at temperatures
above and below the bulk triple point”, Proceedings of the first topical conference on
nanometer scale science and engineering” (G.U. Lee, Ed) AIChE Annual Meeting, Reno,
Nevada, November 4-9, 2001
(5)M. Thommes, R. Koehn and M. Froeba, “Sorption and pore condensation behavior of pure fluids
in mesoporous MCM-48 silica, MCM-41 silica and controlled pore glass at temperatures
above and below the bulk triple point”, submitted to Applied Surface Science, (2001)
Rapid Micropore Size
Analysis by CO2
Adsorption

o
CO2 Adsorption at 0 C
on Carbon
RAPID MICROPORE ANALYSIS
• The advantages of micropore analysis with
Quantachrome’s Density Functional Theory
(DFT) and CO2 include:
• Speed of analysis; with the higher diffusion
rate at 273.15K, analysis times are reduced
as much as 90%.
• Carbon dioxide at 273.15K permits probing
pores from about 2 angstroms (0.2 nm).
DFT ADVANTAGE
DFT has recently been applied to describe the
behavior of fluids that are confined in small
pores. The current popular gas sorption
models, e.g. BJH, HK, SF, DA, etc., assume
that the density of the adsorbed phase
remains constant, regardless of the size of
the pores that are being filled. Packing
considerations suggest that these models are
less than satisfactory for analyses of pores
less than 2 nm.
DFT “Fitting”
• For a given adsorbate-adsorbent
system, DFT calculates the most likely
summation of "ideal isotherms“
calculated from "ideal pores" of fixed
sizes needed to match the experimental
results.
CO2 for Speed!
• Typically, micropore analyses with nitrogen as adsorbate
will require 24 hours or more to run.
• Using carbon dioxide as adsorbate provides several
advantages.
– Carbon dioxide molecules are slightly thinner than
nitrogen molecules (2.8 angstroms radius vs. 3.0
angstroms) and will fill smaller pores than nitrogen.
– The use of carbon dioxide allows the measurements
to be made at 273.15K, typically with an ice/water
bath.
– There is no longer any need to provide and maintain or
replenish a level of liquid nitrogen during the analysis.
CO2 Benefits
• At this temperature, the diffusion rate of
molecules moving through small and tortuous
micropores is much higher than at 77.35K. This
so-called "activated adsorption" effect led to the
popularization of the use of carbon dioxide to
characterize carbonaceous material since the
early 1960s.
CO2 Benefits
• This higher diffusion rate is responsible for
reducing the analysis time to a few hours for a
complete adsorption experiment. The faster rate
also provides for the possibility of using larger
samples than with nitrogen adsorption, thus
reducing sample weighing errors.
• Pore size distributions thus obtained are
comparable to those from a 24-hour
nitrogen/77.35K analysis.
N2 Adsorption @ 77K: 40 hours
CO2 adsorption at 273K: 2.75 hours
o
CO2 Adsorption at 0 C
Density Functional Theory Micropore Distribution
o
CO2 Adsorption at 0 C
Monte Carlo Simulation Micropore Distribution
How to do it?
• Hardware requirements for this new method are
minimal:
– a wide- mouth dewar and
– a water-level sensor.
• The proprietary Quantachrome Autosorb®
software provides the DFT data reduction
capabilities to do the rest. Pore size
distributions from about 2 angstroms can be
determined from the data taken at 273.15K.
• Currently, calculation parameters are optimized for
studies on carbon surfaces.
BIBLIOGRAPHY for Rapid Micropore Size Analysis by
CO2 Adsorption
1. J. Garrido, A. Linares-Solano, J.M. Martin-Martinez, M. Molina-Sabio, F. Rodriguez-Reinoso, R.
Torregosa Langmuir, 3, 76, (1987)
2. F. Carrasco-Martin, M.V. López-Ramón, C. Moreno-Castilla. Langmuir, 9, 2758 (1993)
3. P. Tarazona. Phys.Rev.A 31, 2672 (1985)
4. N.A. Seaton, J.P.R.B. Walton, N. Quirke. Carbon, 27, 853 (1989)
5. C. Lastoskie, K.E. Gubbins, N. Quirke. J.Phys.Chem., 97, 4786 (1993)
6. J.J. Olivier. Porous Materials 2, 9 (1995)
7. P.I. Ravikovitch, S.C. Ó Domhnaill, A.V. Neimark, F. Schüth, K.K. Unger. Langmuir, 11, 4765 (1995)
8. A.V. Neimark, P.I. Ravikovitch, M. Grün, F. Schüth, K.K. Unger. COPS-IV, 1997 (in press)
9. P.I. Ravikovitch P.I., D. Wei, W.T. Chuen, G.L. Haller,A.V. Neimark. J.Phys.Chem., May 1997
10. E.J. Bottani, V. Bakaev, W.A. Steele. Chem.Eng.Sci. 49, 293 (1994)
11. M.M. Dubinin. Carbon 27, 457 (1989)