Teoria de isotermas

Physisorption

Methods 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

Relative Pressure (P/Po)

Volu

me a

dsorb

ed

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

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


Sta

tistical th

ickness

A statistical monolayer

A statistical multilayer

t-plot Method

(mesoporous only)

1 2 3 4 5 6 7

t ( )

Slope = V/t = A

t-plot Method

showing a knee

Slope A - slope B = area contribution by micropores size C

1 2 3 4 5 6 7

t ( )

X

X

X

X

XX

XC

A

B

A

C

B

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

?

? ?

? ?

?

?

Quiz

Estimation of Micropores Dubinin-Radushkevich (DR) Theory

P

Plog

TBexpWW

02

2

0

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)...

Log2(Po/P)

Log (

W)

Extrapolation

yields Wo

Estimation of Micropores Dubinin-Radushkevich (DR) Plot

0

Pore Size Determination

Requires a recognition and

understanding of different basic

isotherm types.

t-plot Method

(in the presence of micropores)

1 2 3 4 5 6 7

t ( )

Intercept = micropore volume

Types of Isotherms

Type I

Type II

Type III

Type IV


Volu

me a

dsorb

ed

Type V

Types of Isotherms

Type I or

pseudo-Langmuir


Volu

me a

dsorb

ed

Steep initial region due to very strong

adsorption, for example in micropores.

Limiting value (plateau) due to filled

pores and essentially zero external area.

Why pseudo Langmuir?

Langmuir applies to monolayer

limit, not volume filling limit. A

?

? ?

? ?

?

?

Quiz

Types of Isotherms

Type II


Volu

me a

dsorb

ed

Rounded knee

indicates approximate

location of monolayer

formation.

Absence of hysteresis indicates adsorption

on and desorption from a non-porous

surface..



multilayers

Types of Isotherms

Type III


Volu

me a

dsorb

ed

Lack of knee represents extremely

weak adsorbate-adsorbent interaction

BET is not applicable

Example: krypton on polymethylmethacrylate

Types of Isotherms

Type IV


Volu

me a

dsorb

ed

Rounded knee

indicates approximate

location of monolayer

formation.



multilayers

Hysteresis indicates capillary

condensation in meso and

macropores. Closure at P/Po~0.4 indicates

presence of small mesopores

(hysteresis would stay open

longer but for the tensile-

strength-failure of the nitrogen

meniscus.

Types of Isotherms

Type V


Volu

me a

dsorb

ed

Lack of knee represents extremely

weak adsorbate-adsorbent interaction

BET is not applicable

Example: water on carbon black

Types of Hysteresis

Large pores/voids

Gel

Mesopores

MCM

Volu

me a

dsorb

ed


MesoPore Size

by Gas

Sorption (BJH)

Analyzer measures volume of pores:

Yes or No?

NO! It measures what leaves

supernatent gas phase A

?

? ?

? ?

?

?

Quiz

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...

Mesopore (Greek meso = middle): 2nm - 50 nm diameter

Macropore (Greek macro = large): >50 nm diameter

Micropore (Greek micro = small): 0 nm - 2 nm diameter

Adsorption / Desorption

Adsorption =

multilayer formation

Desorption =

meniscus development

Kelvin* Equation

)P/Plog(

.)A(r

k

0

154

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

cos2

ln

0 rRT

V

P

P

Pore Size

trrkp

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)

trrKelvinpore

Pore volume requires assumption

of liquid density!


40 Pore Diameter (angstrom)

dV

/dlo

gD

Artifact


Am

ou

nt

ad

so

rbed

~ 0.42

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:

A

Vd

4

where A is the BET

surface area.

Pore size analysis of MCM 41

(Templated silica) by N2 sorption

at 77 K

0 0 .2 0 .4 0 .6 0 .8 1

P /P 0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0

Vo

lum

e [

cc

/g]

E x p . N itr o g en so r p tio n a t 7 7 K in M C M 4 1E x p . N itr o g en so r p tio n a t 7 7 K in M C M 4 1

D F T - I so th e r mD F T - I so th e r m

Pore size analysis of MCM 41:

Calculations compared

1 5 2 3 3 1 3 9 4 7 5 5

P o re D ia m e ter [ ]

0

0 .0 5

0 .1

0 .1 5

0 .2

0 .2 5

0 .3

Dv

(d)

[cc

//g

]

B J H -P o r e s iz e d is tr ib u t io n B J H -P o r e s iz e d is tr ib u t io n

D F T -P o r e s iz e d is tr ib u tio nD F T -P o r e s iz e d is tr ib u tio n

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

> 0.1 multilayer formation t-plot (de-Boer,FHH),

> 0.35 capillary condensation BJH, DH

0.1 to 0.5 capillary filling DFT, BJH

in M41S-type materials

Different Theories of

Physisorption

S u rfa c e a re a P o re v o lu m e P o re s iz e

B E T T o ta l p o re v o l D R a v e

L a n g m u ir t-p lo t ( p o re v o l) B J H

D R D R ( p o re v o l) D H

M P a n d t-p lo t D A D F T

s p lo t B J H H K

(B J H ) (D F T ) S F

(D H ) (D H )

(D F T )

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

Example Data : Microporous Carbon

BET : Not strictly applicable


Tag all adsorption points

Analyze behavior

Note knee transition from micropore filling to limited multilayering (plateau).


Use Langmuir

(Monolayer model) /

DR for Surface Area,

Micropore Volume

Usue Langmuir in

range of 0.05 -> 0.2

(monolayer)


Langmuir Surface Area


DR Method for surface area, micropore volume

Choose low relative pressure points (up to P/P0 = 0.2)


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


BET Plot = OK

Surface area ca. 8m2/g (low)

Note hysteresis above P/P0 = 0.95 Pores > 35 nm


Intercept = (-),

no micropore

volume.


BJH Shows pores

> 20nm, to over

200 nm

Example Data : Mesoporous Silica

Hysteresis => mesopores

Also micropores ?? Test using t-

method


BET Surface area = 112m2/g

Classic mesoporous silica !


Statistical Thickness => Use de Boer for oxidic surfaces = silicas

Intercept ~ 0

Look at tabular data

MP SA = 8m2/g (total SA = 112)


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 0 .2 0 .4 0 .6 0 .8 1

P /P 0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0

Vo

lum

e [

cc

/g

]

E x p . N itr o g en so r p tio n a t 7 7 K in M C M 4 1E x p . N itr o g en so r p tio n a t 7 7 K in M C M 4 1

D F T - I so th e r mD F T - I so th e r m

1 5 2 3 3 1 3 9 4 7 5 5

P o re D ia m e ter [ ]

0

0 .0 5

0 .1

0 .1 5

0 .2

0 .2 5

0 .3

Dv

(d

) [

cc

/

/g

]

B J H -P o r e s iz e d is tr ib u t io n B J H -P o r e s iz e d is tr ib u t io n

D F T -P o r e s iz e d is tr ib u tio nD F T -P o r e s iz e d is tr ib u tio n

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, SBA-

15, 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


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


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, SBA-

15, 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, SBA-

15, 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


0.35nm-1.5 nm Carbons with slit-like pores,


GCMC CO2 - carbon kernel at


0.35nm-1.5 nm Carbons with slit-like pores,


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

1 0-6

5 1 0-5

5 1 0- 4

5 1 0-3

5 1 0-2

5 1 0-1

5 1 00

P /P 0

0

7 0

1 4 0

2 1 0

2 8 0

3 5 0V

olu

me

[c

m3]

N 2 /7 7 KN 2 /7 7 K

A r/8 7 KA r/8 7 K

Z E O L IT E | 1 0 .5 .2 0 0 1

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

0

5

1 0

1 5

2 0

2 5

0 0 .2 0 .4 0 .6 0 .8 1

P /P o

Ad

so

rp

tio

n,

[mm

ol/

g]

M C M -4 1

Z S M -5

5 0 -5 0

Argon adsorption

isotherms at 87 K

on MCM-41,

ZSM-5 and their

50-50 mixture.

Results

0

5

10

15

20

25

0.000001 0.00001 0.0001 0.001 0.01 0.1 1

P/Po

Ad

so

rpti

on

, [m

mo

l/g

]

MCM-41

ZSM-5

50-50

0

0.02

0.04

0.06

0.08

0.1

0.12

1 10 100 1000

D, []

dV

/dD

[c

m3/g

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Vc

um

, [c

m3/g

]

histogram

integral

ZSM

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1 10 100 1000

D, []

dV

/dD

[c

m3/g

]

/g]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Vc

um

, [c

m3/g

]

histogram

integral

MCM

Evaluation of DFT Algorithm

0

2

4

6

8

10

12

14

16

18

20

0.000001 0.00001 0.0001 0.001 0.01 0.1 1

P/Po

Ad

sorp

tion

, [m

mo

l/g]

experimental

NLDFT fit

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

1 10 100 1000

D, []

dV

/dD

[c

m3/g

]

0

0.1

0.2

0.3

0.4

0.5

0.6

Vc

um

[c

m3/g

]

histogram

integral


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

CO2 Adsorption at 0oC

on 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 @ 77K: 40 hours

CO2 adsorption at 273K: 2.75 hours


Density Functional Theory Micropore Distribution


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. Lpez-Ramn, 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. Domhnaill, A.V. Neimark, F. Schth, K.K. Unger. Langmuir, 11, 4765 (1995)

8. A.V. Neimark, P.I. Ravikovitch, M. Grn, F. Schth, 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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