Physisorption Methods and Techniques

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PhysisorptionMethods and Techniques
Quantachrome
I N S T R U M E N T S
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Pore Size by Gas Sorption
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Micro and Mesopore Size Determination by Gas
Sorption

• First Quantitative estimation of micropore
  volume and area
• T-plot and DR methods.

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Multilayer adsorption
Type II, IV
Low slope region in middle of isotherm indicates
first few multilayers, on external surface
including meso and macropores before the onset
of capillary condensation
Volume adsorbed
After the knee, micropores cease to contribute to
the adsorption process.
Relative Pressure (P/Po)
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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...
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The t-plot
Resembles a type II
Statistical thickness
A statistical multilayer
A statistical monolayer
Relative Pressure (P/Po)
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t-plot Method (mesoporous only)
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t-plot Methodshowing a knee
Slope A - slope B area contribution by
micropores size C
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What is an ?s plot?
?s (for Ken Sing) is a comparison plot like the
t-plot but its slope does not give area directly.
A
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Estimation of MicroporesDubinin-Radushkevich
(DR) Theory
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)...
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Estimation of MicroporesDubinin-Radushkevich
(DR) Plot
Log (W)
Extrapolation yields Wo
0
Log2(Po/P)
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Pore Size Determination

• Requires a recognition and understanding of
  different basic isotherm types.

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t-plot Method(in the presence of micropores)
Intercept micropore volume
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Types of Isotherms
Type V
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Types of Isotherms
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Why pseudo Langmuir?
Langmuir applies to monolayer limit, not volume
filling limit.
A
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Types of Isotherms
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Types of Isotherms
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Types of Isotherms
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Types of Isotherms
Example water on carbon black
Type V
Volume adsorbed
Lack of knee represents extremely weak
adsorbate-adsorbent interaction
BET is not applicable
Relative Pressure (P/Po)
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Types of Hysteresis
Large pores/voids
Gel
Volume adsorbed
Mesopores
MCM
Relative Pressure (P/Po)
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MesoPore Size by Gas Sorption(BJH)
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Analyzer measures volume of pores Yes or No?
NO! It measures what leaves supernatent gas phase
A
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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...
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Adsorption / Desorption
Adsorption multilayer formation
Desorption meniscus development
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Kelvin Equation
Lord Kelvin a.k.a. W.T. Thomson
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Pore Size
rp actual radius of the pore rk Kelvin
radius of the pore t thickness of the adsorbed
film
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Statistical Thickness, t

• Halsey equation
• Generalized Halsey
• deBoer equation
• Carbon Black STSA

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BJH Method (Barrett-Joyner-Halenda)
Pore volume requires assumption of liquid density!
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Pore Size Distribution
Artifact
dV/dlogD
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Pore Diameter (angstrom)
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0.42
Amount adsorbed
Relative Pressure (P/Po)
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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

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Pore size analysis of MCM 41 (Templated silica)
by N2 sorption at 77 K
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Pore size analysis of MCM 41 Calculations
compared
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Calculation Models
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Comparisons

• Gas Sorption Calculation Methods
•  
• P/Po range Mechanism Calculation model
• 1x10-7 to 0.02 micropore filling DFT, GCMC, HK,
  SF, DA, DR
• 0.01 to 0.1 sub-monolayer formation DR
• 0.05 to 0.3 monolayer complete BET, Langmuir
• gt 0.1 multilayer formation t-plot
  (de-Boer,FHH),
• gt 0.35 capillary condensation BJH, DH
• 0.1  to 0.5 capillary filling
  DFT, BJH
• in M41S-type materials
  

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Different Theories of Physisorption
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HK SFHorvath-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).

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DA DRDubinin-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.

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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/(si) 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
  pressureslt 0.1, in contrast to the classical BET
  range, which extends over relative pressures
  between 0.05 0.3. 

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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.

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t-plotStatistical 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.

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BJH DHBarrett, 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.

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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 Frenkel-Halsey Hill method, which is
  applied in the range of multilayer adsorption.

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Example Data Microporous Carbon
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BET Not strictly applicable
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Example Data Microporous Carbon

• Tag all adsorption points
• Analyze behavior
• Note knee transition from micropore filling to
  limited multilayering (plateau).

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Example Data Microporous Carbon

• Use Langmuir (Monolayer model) / DR for Surface
  Area, Micropore Volume
• Usue Langmuir in range of 0.05 -gt 0.2 (monolayer)

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Example Data Microporous Carbon

• Langmuir Surface Area

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Example Data Microporous Carbon

• DR Method for surface area, micropore volume
• Choose low relative pressure points (up to P/P0
  0.2)

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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)

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Example Data Macroporous Sample
Little or no knee, isotherm closes at 0.95
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Example Data Macroporous Sample

• BET Plot OK
• Surface area ca. 8m2/g (low)
• Note hysteresis above P/P0 0.95 ?Pores gt 35 nm

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Example Data Macroporous Sample
Intercept (-), no micropore volume.
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Example Data Macroporous Sample
BJH Shows pores gt 20nm, to over 200 nm
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Example Data Mesoporous Silica
Hysteresis gt mesopores Also micropores ?? Test
using t-method
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Example Data Mesoporous Silica
BET Surface area 112m2/g Classic mesoporous
silica !
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Example Data Mesoporous Silica
Intercept 0 Look at tabular data MP SA 8m2/g
(total SA 112)
Statistical Thickness gt Use de Boer for oxidic
surfaces silicas
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Example Data Mesoporous Silica
Use BJH shows narrow pore size distribution in
14-17nm range (mesopores)
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MicroPore Size by Gas Sorption
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Available Calculation Models
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Pore filling pressures for nitrogen in
cylindrical pores at 77 K, (Gubbins et al. 1997)
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Pore filling pressures for nitrogen in
cylindrical silica pores at 77 K (Neimark et al.,
1998)
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Pore size analysis of MCM 41 by silica by N2
sorption at 77 K
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Gas- and liquid density profiles in a slit pore
by GCMC (Walton and Quirke,1989)
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RECENT ADVANCES IN THE PORE SIZE ANALYSIS OF
MICRO- AND MESOPOROUS MOLECULAR SIEVES BY ARGON
GAS ADSORPTION
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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.

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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.

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Advantages of Higher Temperature Pressure

• Accelerated diffusion.
• Accelerated equilibration processes.
• Reduction in analysis time.

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Argon Adsorption at 87.3 K versus Nitrogen
Adsorption at 77.4 K
The different pore filling ranges for argon
adsorption at 87.3K and nitrogen adsorption at
77.4K in faujasite-type zeolite are illustrated
above.
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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)
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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 micro-mesopore
  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
76
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
  MCM-41/MCM-48).

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Results
Argon adsorption isotherms at 87 K on MCM-41,
ZSM-5 and their 50-50 mixture.
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Results
79
ZSM
80
MCM
81
Evaluation of DFT Algorithm
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Pore Size Distribution
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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

84
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 .

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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 lt 10 nm.

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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.

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Acknowledgements

• Special thanks go to Alex Neimark and Peter
  Ravikovitch at TRI Princeton, New Jersey, USA.

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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)

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Rapid Micropore Size Analysis by CO2 Adsorption
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CO2 Adsorption at 0oCon Carbon
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RAPID MICROPORE ANALYSIS

• The advantages of micropore analysis with
  Quantachromes 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).

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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.

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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.

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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.

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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.

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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.

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N2 Adsorption _at_ 77K 40 hours
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CO2 adsorption at 273K 2.75 hours
99
CO2 Adsorption at 0oC
Density Functional Theory Micropore Distribution
100
CO2 Adsorption at 0oC
Monte Carlo Simulation Micropore Distribution
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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.

102
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)