BET Analysis Fundamentals - Sathish

8/10/2019 BET Analysis Fundamentals - Sathish

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BET Analysisfundamentals


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Surface AreaWhat is it?

Surface Area is the means through which a solid

interacts with its surroundings, especially liquids

and gases.

Surface area is created by division of particles (size

reduction) and the generation of porosity.

Surface area is destroyed by sintering (exceeding

Tg), melting and Ostwald ripening.


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How to Create Area ?

Size Reduction

Grinding,

milling,

nanoscale preparation

Make pores

Partial decomposition Leach

Gel then lyophilize


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How to Destroy Area ?

Surface area is destroyedby

melting

sintering (exceeding Tg), and

Ostwald ripening


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Adsorption Absorption

Absorptionis a phenomenonthat occurs in a volume

Adsorptionis a phenomenonthat occurs on a surface

The word sorptionencompasses both types of phenomena


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Adsorption processes

Adsorption

Physical (physisorption)

- van der Waals interactions(result in attractive forces betweenadsorbent and adsorbate molecules)

- Adsorbed molecules maintain their

identity

- Multilayers

- No activation energy

- Always reversible

Chemical (chemisorption)

- Chemical bonds between adsorbateand adsorbent formed

- Adsorbed molecules loose their

identity

- Monolayers

- Often activation energy required

- Can be irreversible


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The gas sorption process

Langmuir[1]described the kinetic behavior of theadsorption process. He postulated that atequilibrium, the rate of arrival of adsorptive

(adsorption) and the rate of evaporation ofadsorbate (desorption) were equal

Furthermore, the heat of adsorption was taken to

be constant and unchanging with the degree ofcoverage, .

[1]I. Langmuir, J. Amer. Chem. Soc., 40, 1368 (1918)


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Graduated as a metallurgical engineer from

the School of Mines at Columbia University in

1903

1903-1906 M.A. and Ph.D. in 1906 from

Gttingen.

Irving Langmuir(1881-1957)

1935-1937 With Katherine Blodgett studied thin

films.

1948-1953 With Vincent Schaefer discovered

that the introduction of dry ice and iodide into a

sufficiently moist cloud of low temperature couldinduce precipitation.

1932 The Nobel Prize in Chemistry "for his

discoveries and investigations in surface

chemistry


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Confining adsorption to a monolayer, the Langmuir equation can be

written

where V is the volume of gas adsorbed at pressure P, Vm is the

monolayer capacity (i.e. =1) expressed as the volume of gas at STP

and Kis a constant for any given gas-solid pair. Rearranging in theform of a straight line (y=ab+x) gives

KP

KP

V

V

m 1

mm V

P

KVV

P

1

Langmuirian behavior


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Suitable Methods of Determination

Gas adsorption allows probing of entire surfaceincluding irregularities and pore interiors.

The amount adsorbed is a function of temperature,pressure and the strength of attraction or interactionpotential.

Physisorption is generally weak and reversible. Thesolid must be cooled and a method used to estimate themonolayer coverage from which surface area can becalculated.


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Adsorption Process

Adsorbent

AdsorbateAdsorptive


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The Isotherm

The amount of gas adsorbed is a function of

The strength of interaction between gas and solid(intrinsic)

Temperature (fixed)

Pressure (controlled variable) expressed asrelative pressure P/Po


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Physisorption Process

4)

2


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Very Low Pressure Behavior

(micropore filling)

Relative Pressure, P/Po

AmountAdsorbed


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Low Pressure Behavior

(monolayer)

The knee


AmountAdsorb

ed


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Medium Pressure Behavior

(multilayer)


AmountAdsorb

ed


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High Pressure Behavior

(capillary condensation)


AmountAdsorb

ed


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Gas Sorption: Isotherm

adsorptiveofpressuresaturated

adsorbateofpressure

where

p

p

ppf

o

oVa

Adsorption isotherm Isotherm is a measure of

the volume of gas

adsorbed at a constant

temperature as a function

of gas pressure.

Isotherms can be

grouped into six classes.

Va

Desorption isotherm

p

po


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Types of isotherms

I: microporous solids

II & III: multilayer adsorption

in non-porous solids

IV & V: capillary condensation

in mesoporous solids

VI: stepped asdorption

according to the IUPAC classification


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Types of Isotherms

Type I or

pseudo-Langmuir

Relative Pressure (P/Po)

Volumeadsorbed

Steep initial region due tovery strong adsorption, for

example in micropores.

Limiting value (plateau) due to filled

pores and essentially zero external

area.


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Types of Isotherms

Type II


Vol

umeadsorbed

Rounded kneeindicates approximate

location of monolayer

formation.

Absence of hysteresis indicates

adsorption on and desorption from a

non-porous surface..

Low slope region in middle of

isotherm indicates first few

multilayers


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Va

1P/Po

Type I

or

Langmuir

S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed.Chapman & Hall, New York, 1991

Concave to theP/Poaxis

Exhibited by microporous solids ( < 2nm )

Type II

Exhibited by nonporous or macroporous

solids ( > 50nm )

Unrestricted monolayer-multilayeradsorption

Point B indicates the relative pressure at

which monolayer coverage is complete

B

Va


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Types of Isotherms

Type III


Volumeadsorbed

Lack of knee represents extremelyweak adsorbate-adsorbent

interaction

BET is not applicable

Example: krypton on polymethylmethacrylate


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Types of Isotherms

Type IV


Vo

lumeadsorbe

d

Rounded knee

indicates approximate

location of monolayer

formation.

Low slope region in middle of

isotherm indicates first fewmultilayers

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.


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Va

1

Type IIIConvex to the P/Poaxis

Exhibited by nonporous solids

Va

1P/Po

Type IVExhibited by mesoporous solids

Initial part of the type IV follows

the same path as the type II

S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed.

Chapman & Hall, New York, 1991

f


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Types of Isotherms

Type V


Volumeadsorb

ed

Lack of knee represents extremely

weak adsorbate-adsorbent interaction

BET is not applicable

Example: water on carbon black


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Gas Sorption: Hysteresis

Hysteresis indicates the presence of mesopores.

Hysteresis gives information regarding pore shapes .

Types I, II and III isotherms are generally reversible but type I can

have a hysteresis. Types IV and V exhibit hysteresis.

1P/Po

HysteresisVa

S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed.Chapman & Hall, New York, 1991


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Va

1P/Po

Type V

1P/Po

Type VI

Highly uncommon

Exhibited by mesoporous solids

Exhibited by nonporous solids with

an almost completely uniform surface

S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed.

Chapman & Hall, New York, 1991

Va


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Choice of Gas and Temperature

Gases

Nitrogen

Argon

Krypton

Carbon dioxide

Others

TemperaturesLiquid Nitrogen

Liquid Argon

Dry ice/acetone

Water/ice

Others


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Choice of Gas and Temperature

Gases

Nitrogen

Argon Krypton

Carbon dioxide

Others

TemperaturesLiquid Nitrogen

Liquid ArgonDry ice/acetone

Water/ice

Others

M M h d


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Measurement Method

Manometric(Classical vacuum, volumetric.)

Requires that adsorbate be adsorbed by the

sample, at some reduced temperature, as a

function of pressure of pure adsorptive.

M t i


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Manometric

P/Po values are achieved by creating conditions

of partial vacuum

High precision and accurate pressure

transducers monitor pressure changes due to

the adsorption process

W ki E i


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Working Equation

PV = nRT

nads= ndosed- nvoid

nads= (

PV/RT)man.- (PV/RT)cell

W ki E ti


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Working Equation

nads= (PV/RT)man.- (PV/RT)cell

That is, the amount adsorbed is calculated as the difference between

a) the amount of gas dosed from the manifold to the cell and b) the

amount of gas which remains not adsorbed at the end of the

equilibration time.

Principles of BET Surface Area Measurement


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Principles of BET Surface Area Measurement

and Calculation

Determine the monolayer capacity Vm from which

the surface area of the solid can be computed.

Adsorbate most commonly used is nitrogen

Readily available in high purity

Appropriate coolant, liquid nitrogen.

Gas-solid interaction relatively strong.

Widely accepted cross sectional area.

Multilayer adsorption


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y p

the BET equation (1938)

Stephen Brunauer

Paul Emmett

Edward Teller

B E tt & T ll


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Brunauer, Emmett & Teller

Model of adsorption extended to multilayers.

S. Brunauer, P.H. Emmett and E. Teller, J. Amer. Chem. Soc., 60, 309 (1938)

)(1)(1(

)(

000

0

PPCPPPP

PPC

V

V

m

Brunauer Emmett & Teller


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Brunauer, Emmett & Teller

BET C constant varies from solid to solid.

Low values represent weak gas adsorption

typical of low surface area solids, organicsand metals in particular.

00

11

]1)[(

1

P

P

CV

C

CVPPV mm

Or, in its familiar linearizedform

Measurement


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Measurement

Obtain at least three data points in the relative pressure

range

0.025 to 0.30

Plot 1/[VSTP(Po/P)-1] versusP/Po. It should yield a

straight line if the BET model holds true.

On all surfaces the BET model fails to accurately predict

the multilayer adsorption behavior above P/Po = 0.5 (the

onset of capillary condensationwhich fills pores with

liquid adsorbate)

Calculation of Surface Area by


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y

the BET method

relative pressure, P/Po

1

X[(Po/P)-1

]

0

negativeintercepts are unacceptable


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Calculation


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Calculation

isVm

1

v

mavmt

M

ALVS

Solving for Vm

Total surface area, St, is calculated thus

Lav= 6.022 x 1023

Am= 0.162 nm2

Mv= 22 414 mL

nm2to m2, x 10-18

Adsorbate cross sectional area

(0.162 nm2 for Nitrogen

Multi-Point BET Plot (Interpretation)


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Multi Point BET Plot (Interpretation)

Never use data points too low in relative pressure (P/Po).

Never use data points too high in (P/Po).

Multi-Point BET Plot (Interpretation)


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Multi Point BET Plot (Interpretation)

Discard under-equilibrated points (at low P/Po)

Never use less than three, preferably five data points.

Porosity


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Porosity

Pore VolumeTotal pore volume is derived from the amountof vapour adsorbed at a relative temperatureclose to unity (assuming pores are filled withliquid adsorbate).

Vads= volume of gas adsorbed

Vliq= volume of liquid N2in pores

Vm= molar vol. of liquid adsorbate (N2=34.7cm3/mol)Pa= ambient pressure

T = ambient temperature

Concept of Porosity: Open vs.


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Closed Pores

Dead end

(open)

ClosedInter-connected

(open)

Passing

(open)

F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 1-25, 1999

Open pores are accessible

whereas closed pores areinaccessible pores.

Open pores can be inter-

connected, passing or dead

end.

Size of Pores (IUPAC Standard)


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Size of Pores (IUPAC Standard)

2 nm 50 nm

Micropores Mesopores Macropores

Zeolite,

Activated

carbon,Metal organic

framework

Mesoporous silica,

Activated carbonSintered metals

and ceramics

Porous material are classified according to the size of pores: material

with pores less than 2 nm are called micropores, materials with poresbetween 2 and 50 nm are called mesopores, and material with pores

greater than 50 nm are macrospores

Sing, K. S. W. et al. Reporting Physisorption Data for Gas/Solid Systems. Pure & Appl. Chem. 57, 603-619 (1985).


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Techniques for Porosity Analysis


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Gas Sorption: Hysteresis


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Va

1P/Po

Type A

Cylindrical Slits

Type B

1P/Po 1P/Po

Type C Type D

1P/Po

Type E

1P/Po

Conical Bottle neck

Pore Radius


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The average pore size can be estimated from the porevolume.

Assuming cylindrical pore geometry (type A hysteresis)average pore radius (rp) can be expressed as:

Other pore geometry models may require furtherinformation on the isotherm hysteresis before applyingappropriate model.

BET Analysis Fundamentals - Sathish

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