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Porosity and surface area by gasphysisorption techniques

Luca Lucarelli

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2

The concept of free surface energy

Solid phase:atoms or moleculesare in equilibrium

Gaseous phase

Degassing

Gaseous phase: adsorbate

Solid phase: adsorbent

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3

Physisorption measures surface areas

Pore size is determined by gas

condensation pressure into thepores

Very low temperature(77 K), vacuum, injection of

known doses of inert gas

Surface area is measured by

counting the number ofmolecules deposed in amonolayer

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4

Montecarlo simulation of multilayeradsorption

First layer

Second layer

Third layer

Solid surface

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Adsorbed molecules in equilibrium withpressure

The dispersion forces betweenthe adsorptive molecules and thesurface atoms or ions of theadsorbing solid are described bythe Lennard-Jones potential [1]:

(r)

r

126 B r C r r

Gas molecules remain in contact with the surface for a certaintime before returning to the gaseous phase. This delay isresponsible for the phenomenon of adsorption

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Physisorption and Chemisorption

• Physisorption mainapplication fields

– Catalysts

– Active carbons – Charcoals – Pharmaceuticals – Building materials – Silica and alumina

– Metal powders – Oxides and salts – Adsorbents – Ceramics – Zeolites – Pigments – Glass

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Information provided physisorption

• Commonly used gases – Nitrogen/Argon – Krypton – Carbon dioxide

• Results on porous media – Total specific surface area – Meso-micropore size distributions – Meso-micropore total volumes

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Types of adsorption isotherms

II

B

I III

V VIIV

B

Adsorption isotherms can be classified in six types according to IUPAC[3,4]. The Type I is typical for microporous solids and chemisorptionisotherms. Type II is shown by finely divided nonporous solids. Type III andType V are typical of vapors, i.e. water on hydrophobic solids. Type IV andType V feature an hysteresis loop generated by the capillary condensationin mesopores. The rare Type VI, the steps-like isotherm, is shown e.g. withnitrogen on special carbons.

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Mechanism of adsorption on non-poroussurfaces

p/p0

n

10 p/p0

n

10

0.5481

t s

/nm

n

0 t s

/nm

n

0.5481

0

p/p0

n

10

t s

/nm

n

0.5481

0

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Adsorption on mesoporous samples:capillary condensation

p/p0

n

10 p/p0

n

10 p/p0

n

10

p/p0

n

10 p/p0

n

10 p/p0

n

10

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Why nitrogen condenses before thesaturation

At low relative pressures the surface of the pores walls adsorbs amultilayer of adsorbate. If the pressure is raised, droplets ofadsorbate occur on optimal energetic points of the pore surfacewith curvatures according to the Kelvin equation. If the dropletstouch each other, the pores will be filled with condensed

adsorbate. This will evaporate during the desorption from poresshowing core openings larger than the Kelvin radius. Theadsorption branch is pore-dimension dependant, the desorptionbranch is related to the pore openings.

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Pore size evaluation in mesoporous samples

r 2

r 1

y y+dy

x x+dx dz

q

q

r m

r k

The Kelvin equation gives directly the core radius, consideringthat the wetting angle is equal to zero. Then, the pore radius iscalculated taking into account the adsorbed film thickness onthe pore walls and a cylindrical pore geometry [5].

The Young-Laplace equation [1]describes the pressures at the interfaceof a liquid droplet and the gas phaseabove, using the surface tension:

p p r r r m

b g g

÷

1 1 2

1 2

Considerations on the surface energylead to the Kelvin equation, that put inrelation the relative pressure and thecurvature radius of the liquid meniscus:

ln p

p

V

RT r liq

m

0 2 1

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Mechanism of adsorption in micropores is complex

In micropores the potentials of both sides of the pore walls ovelap,thus enhancing the adsorption potential [7]. The smaller the porewidth the deeper the resulting potential becomes. This results inan enhanced adsorption energy and adsorption takes place atvery low pressures (see the right box figure). Micropores with thesmaller width fill firstly but adsorption on the surface of largermicropores occurs at the same time (secondary micropore filling).

-1

-2

0 +1-1

-1

-2

0 +1-1

z/r 0

-1

-2

0 +1-1

9:3 10:4

Enhancement of Potential in Micropores

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Points of remark

•

Physisorption is non-specific• Adsorption energy is very small, similar to the heat of

condensation• Physisorption is completely reversible•

Physisorption is a spontaneous phenomenon occuringat any temperature and pressure• Detectable amount of adsorbed species is achievable

by analytical instruments only at very low temperature•

Adsobates often must be chosen according to thesample nature

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Common adsorbates

Gas Temp.

K

Area per molecule

(angstron 2)

Notes

Nitrogen 77 16.2 Most of materials can beanalyzed in these conditionsexcept very low surfaces and

some micropores

Argon 87, 77 14.2 Specially used for somemicroporous zeolites thatcannot be measured by

nitrogen

Krypton 77 21(other values are also

reported)

Used for extremely lowsurfaces. Difficult analysis

due to saturation andexpensive

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Common models for adsorption interpretation Specific Surface Area

Model Assumptions

Langmuir Gases can form only one molecular layer on surfaces. Mainly used in chemisorptionanalysis or physisorption showing isotherms type 1 with almost 90 ° knee

Brunauer, Emmetand Teller (BET 2parameters)

Gases form an unlimited number of layers over surfaces. It is a generalized Langmuir.Forces active in condensation of gases are responsible of multilayers formation.

Applicable to isotherms type II, IV, VI.

BET 3 parameters(full equation)

Needs non-linear regression function to fit the experimental points. In addition tomonolayer volume and C value of standard BET, it gives also the number of layers N.

Applicable to all types of physisorption isotherms

t-plot and alphaplot

Introduces the concept of a standard isotherm. Adsorption data are plotted versus theaverage thickness of the adsorbed layer or referred to the amount adsorbed at a referencepressure. Reference data must be collected on a non-porous material of the same natureof sample under test

DubininRaduskevitch plot

Applicable only when pores are of molecular dimension size (microporous materials,isotherms type 1). Based on the differential molar work of adsorption (Polanyi).

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Common models for pore size calculation

Model Assumptions

Kelvin Relates the equilibrium pressure (mainly desorption) to the “core” radius of evaporatedgas inside mesopores. It is applicable whenever capillary condensation takes place(isotherms type IV, V and relevant sub-groups).

Barret, Joiner,Halenda (BJH),and other similar

methods

These models are based on the Kelvin equation correcting the Kelvin radius with thethickness of the still adsorbed gas. They differ for the way of calculating the thickness(Pr = Kr + t). Applicable to isotherms type IV, V and relevant sub-groups.

Horvath andKavazoe (HK)and relatedmodels (Saito-Foley, etc.)

It is based on the Lennard-Jones interaction between gas and solid. Potential functionof both are required. HK was developed for slit-shaped pores in microporus carbons.SF is an extension to cylindrical pores. The adsorbed phase is considered to behaveas a two-dimensional ideal gas. HK is applicable to isotherms type I on active carbons,SF to microporous zeolites or silica.

Other methods A huge number of other methods are available for surface area and pore sizecalculation. New models or variations are born every year due to the difficulty ofinterpretating the mechanisms of adsorption/desorption.

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Examples of Type I Isotherms: Activated Carbon

1.0p/p 00.0 0.2 0.4 0.6 0.8 1.0

500

V a

d s

/ c m

3 g

- 1

0

100

200

300

400

500

1

p/p 00.000001 10.00001 10.0001 10.001 10.01 10.1 1

500

V a

d s

/ c m

3 g

- 1

0

100

200

300

400

500

Example of an activatedmicroporus carbon testedusing nitrogen at 77 K• Linear plot• Logarithmic plot

Features:Gas is adsorbed at verylow relative pressuresHysteresis is almost

absentCalculation examples:BET 3, DR, HK

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Activated Carbon Surface Area by BET 3

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Activated Carbon Surface Area by DR

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Activated Carbon Pore size by HK

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Examples of Type I Isotherms: Zeolite

1.0

p/p 00.0 0.2 0.4 0.6 0.8 1.0

500

V a

d s

/ c m

3 g - 1

0

100

200

300

400

500

1

p/p 00.000001 10.00001 10.0001 10.001 10.01 10.1 1

500

V a

d s

/ c m

3 g

- 1

0

100

200

300

400

500

Example of amicroporus zeolite testedusing nitrogen at 77 K• Linear plot• Logarithmic plotFeatures:Gas is adsorbed at verylow relative pressuresHysteresis is almost

absentCalculation examples:BET 3, SF

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Zeolite Nitrogen Surface Area: BET 3

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Zeolite Nitrogen Pore Size: Saito-Foley

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Examples of Type I Isotherms: Zeolite

Example of amicroporus zeolitetested using argon at 87K• Linear plot•

Logarithmic plotFeatures:Gas is adsorbed at verylow relative pressuresHysteresis is almostabsentCalculations:SF

1.0

p/p 0

0.0 0.2 0.4 0.6 0.8 1.0

300

V a

d s

/ c m

3 g - 1

0

100

200

300

1

p/p 00.0000001 10.000001 10.00001 10.0001 10.001 10.01 10.1 1

300

V a

d s

/ c m

3 g

- 1

0

100

200

300

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Zeolite Argon Pore Size: Saito-Foley

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Comparison: two zeolites pore size (Argon)

1

p/p 00.0000001 10.000001 10.00001 10.0001 10.001 10.01 10.1 1

500

V a

d s

/ c m

3 g

- 1

0

100

200

300

400

500

10Ø / nm

0.1 101 10

0.25

V P o r e

/ c m

3 g

- 1

0.00

0.05

0.10

0.15

0.20

0.25

3

d V / d Ø / c m

3 n m

- 1 g

- 1

0

1

2

3

Isotherms Overlay: log plot

Pore Size Overlay:Saito-Foley

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Examples of Type IV Isotherms: mesoporous alumina

1.0

p/p 00.0 0.2 0.4 0.6 0.8 1.0

250

V

a d s

/ c m

3 g

- 1

0

50

100

150

200

250

Mesoporous alumina measured by nitrogen at 77 K-Presence of hysteresis depending on pore size-BET 2 parameters applicable

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Surface area on mesoporous samples: BET

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Surface area on mesoporus samples: BET 3

M i BJH

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Mesopore pore size: BJH

E mples of T pe IV Isotherms l rge mesopores

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Examples of Type IV Isotherms: large mesopores

1.0

p/p 00.0 0.2 0.4 0.6 0.8 1.0

140

V a

d s

/ c m

3 g

- 1

0

20

40

60

80

100

120

140

Capillary condensation and saturation pressure occurring almostcontemporary. Maximum limit of pore size by the gas adsorption technique

Th i li it

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The upper pore size limit

E l f T II I th l

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Examples of Type II Isotherms: non-porous sample

1.0

p/p 00.0 0.2 0.4 0.6 0.8 1.0

4

V a

d s

/ c m

3 g

- 1

0

1

2

3

4

Very small amount of gas adsorbed. No capillary condensation (macropores), No hysteresis. The only available result is the BET surface area.

For pore size it is necessary another technique (mercury porosimetry)

BET f l

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BET surface area on non-porous sample

E l f l f K d ti

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Example of very low surfaces: Kr adsorption

1.0

p/p 00.0 0.2 0.4 0.6 0.8 1.0

0.20

V a

d s

/ c m

3 g

- 1

0.00

0.05

0.10

0.15

0.20

Kr is used when surface area is extremely small therefore adsorbed nitrogenis not detectable. Kr saturation at 77 K is about 2 torr (it is not a real saturation).

Example of isotherms overlay

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Example of isotherms overlay

1.0

p/p 00.0 0.2 0.4 0.6 0.8 1.0

1200

V a

d s / c m

3 g

- 1

0

200

400

600

800

1000

1200

Example of t plot overlay of different surfaces

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Example of t-plot overlay of different surfaces

2.0

t / nm0.0 0.5 1.0 1.5 2.0

1200

V a

d s

/ c m

3 g

- 1

0

200

400

600

800

1000

1200

Two most common methods for gas adsorption

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Two most common methods for gas adsorption

The static volumetrictechnique The dynamic flowtechnique

Sorptomatic 1990 Qsurf analyzers

The static volumetric technique

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The static-volumetric technique

P P

Doser

piston

Sample

holder

Gas inlet

Measuring adsorption equilibrium pressure

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Measuring adsorption equilibrium pressure

P

time

Peq 1

Peq n

P sat

Features of static volumetric method

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Features of static volumetric method

• High vacuum required• Very accurate results• Proper and relatively fast degassing under vacuum• Dead volumes calibration required•

Pressure transducers calibration required• Analysis time is relatively long• Can measure all type of samples (in the physisorption

method range)• Can measure pore size distribution in micropores and

mesopores

The dynamic flow technique

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The dynamic flow technique

Helium

Nitrogen

Detection of adsorbed gas: single point BET

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Detection of adsorbed gas: single point BET

Time

T C D

s i g n a

l 1

2

3

4

51- Loop calibrationPeak2- Immersion in liquid

Nitrogen3- Adsorption peak

4- Exiting from liquid Nitrogen5- Desorption peak

Detection of adsorbed gas: multi point BET

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Detection of adsorbed gas: multi point BET

1 2

3

1 – 25% of Nitrogen in Helium2 – 15% of Nitrogen in Helium3 – 5 % Nitrogen in Helium

Features of dynamic method

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y

• Extremely fast and easy operations• No need of dead volume calibration• Extremely high reproducibility of results• Single point test results are less accurate but show higher

reproducibility• Multi point test results are more accurate but show a lower

reproducibility• Anyway reproducibility is comparable and often better that

static methods• Analytical method must be carefully chosen for very low or

very high surface areas• Provide surface area and total pore volume (pore size is less

reliable than static methods)• Degassing in flow requires more time than in vacuum

Recommended literature

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Literature1 S.J. Gregg, K.S.W. Sing, Adsorption, Surface Area and Porosity, Academi2 S. Brunauer, P.H. Emmet and E. Teller, J. Amer. Chem. Soc., , 309 (19383 S. Brunauer, L.S. Deming, W.S. Deming and E. Teller, J. Amer. Chem. Soc4 IUPAC Reporting physisorption data for gas/solid systems, Pure Appl. Ch

5 E.P. Barrett, L.G. Joyner and P.P. Halenda, J. Amer. Chem. Soc. , 373 (196 M.M. Dubinin, Quart. Rev. Chem. Soc. , 101 (1955)7 D.H. Everett and J.C. Powl, J. Chem. Soc., Faraday Trans. I, , 619 (1976)8 G. Horvath and K. Kawazoe, J. Chem. Eng. Jap. , 6, 470 (1983)

B.C. Lippens and J.H. de Boer, J. Catalysis , 319 (1965)

a K.S.W. Sing, Chem. & Ind. 1968, 1520

6062

57

739

7216

4t

s

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