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PhysisorptionMethods and Techniques

Quantachrome

I N S T R U M E N T S

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.

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)

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

Resembles a type II

Statistical thickness

A statistical multilayer

A statistical monolayer

Relative Pressure (P/Po)

t-plot Method (mesoporous only)

t-plot Methodshowing a knee

Slope A - slope B area contribution by

micropores size C

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

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)...

Estimation of MicroporesDubinin-Radushkevich

(DR) Plot

Log (W)

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

Types of Isotherms

Type V

Types of Isotherms

Why pseudo Langmuir?

Langmuir applies to monolayer limit, not volume

filling limit.

A

Types of Isotherms

Types of Isotherms

Types of Isotherms

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)

Types of Hysteresis

Large pores/voids

Gel

Volume adsorbed

Mesopores

MCM

Relative Pressure (P/Po)

MesoPore Size by Gas Sorption(BJH)

Analyzer measures volume of pores Yes or No?

NO! It measures what leaves supernatent gas phase

A

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...

Adsorption / Desorption

Adsorption multilayer formation

Desorption meniscus development

Kelvin Equation

Lord Kelvin a.k.a. W.T. Thomson

Pore Size

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)

Pore volume requires assumption of liquid density!

Pore Size Distribution

Artifact

dV/dlogD

40

Pore Diameter (angstrom)

0.42

Amount adsorbed

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

Pore size analysis of MCM 41 (Templated silica)

by N2 sorption at 77 K

Pore size analysis of MCM 41 Calculations

compared

Calculation Models

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

Different Theories of Physisorption

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).

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.

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.

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-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.

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.

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.

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 -gt 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 gt 35 nm

Example Data Macroporous Sample

Intercept (-), no micropore volume.

Example Data Macroporous Sample

BJH Shows pores gt 20nm, to over 200 nm

Example Data Mesoporous Silica

Hysteresis gt mesopores Also micropores ?? Test

using t-method

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 gt 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

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

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

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 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

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).

Results

Argon adsorption isotherms at 87 K on MCM-41,

ZSM-5 and their 50-50 mixture.

Results

ZSM

MCM

Evaluation of DFT Algorithm

Pore Size Distribution

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 lt 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

CO2 Adsorption at 0oCon Carbon

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).

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 _at_ 77K 40 hours

CO2 adsorption at 273K 2.75 hours

CO2 Adsorption at 0oC

Density Functional Theory Micropore Distribution

CO2 Adsorption at 0oC

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)

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