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L14 CRE II Heterogeneous Catalysis

Prof. K.K.Pant

Department of Chemical EngineeringIIT Delhi.kkpant@chemical.iitd.ac.in

mailto:kkpant@chemical.iitd.ac.inmailto:kkpant@chemical.iitd.ac.in

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Physisorption

Different Adsorbates Used in PhysisorptionStudies

Adsorbate Boiling Point (K) Am (nm2/molecule)

N2 77.3 0.162

Ar 87.4 0.142

CO2 194.5 0.17

Kr 120.8 0.152

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Determination of Surface Area

Physisorb an inert gas such as argon or

nitrogen and determine how many molecules

are needed to form a complete monolayer

For example, the N2molecule occupies 0.162

nm2at 77 K, the total surface area follows

directly.

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In addition, the molecules may condense in small

pores. The narrower the pores, the easier N2will

condense in them.

This phenomenon of capillary pore condensation,as described by the Kelvin equation

Phenomenon can be used to determine the types

of pores and their size distribution inside a system

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N2Physisorption

Adsorption and Desorption Isotherms

0

5

10

15

20

25

0 0.2 0.4 0.6 0.8 1p/p

0

nad(mmol/g)1

Adsorption

Desorption

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Pore Size and Shape

Why is it important?

it dictates the diffusion process through thematerial.

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Why is it important?

directly affect the selectivity of the catalytic

reaction.

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Pore Size and Shape

Pore Diameter

micropores (< 2 nm)

mesopores (250 nm)

macropores (> 50 nm)

Pore Shape

cylinder

slit

ink-bottle

wedge

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v

Pore Size and Shape

Measurement Techniques

1 10 100 1000 10000

Pore diameter (nm)

Micro Meso Macro

2 50

N2 capillary condensation

Hg porosimetry

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Pore volume determination ( Helium -Mercury Method)

The pore volume of the catalyst can be determined by the helium-

Mercury method.

The volume of Mercury and Helium displaced by the catalyst is used to

measured the pore volume of the catalyst.

Since mercury cannot pass through the pores of the catalyst , the

difference in the volume gives the pore volume.

Vmercury => extrenal volume of solid + pore ,

VHe =volume occupied by the solid material. density of soild (s)

Pore volume Vg = (VmercuryVHelium)/(Mass of catalyst, m)

Porosity= = mvg/ (m vg+ 1/ S )= ( 1/p - 1/s) = pVg = void volume/total

volume

p(density of porous particle) = mass of pellet /volume of mercury displaced bysam le

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Mercury Porosimetry

Pore Size Distribution r (nm)= 6300/p(atm abs.)or r (A0) = 8.75X 105 / P (psia)

Hg does not wet surfaces; pressure is needed to force intrusion

From a force balance:

(d in nm,pin bar)

Convenient method for determining pore volume versus pore

size

pd

14860p

Pressure force. (p() r = -surface tension force, (2 r)

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Dynamic method for estimating Surface Area (N2 adsorbed, He doesnot adsorbed)

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The assumptions of BET isotherm are:

Gas adsorbs on a flat, uniform surface of the solid with a uniform heat ofadsorption due to vander Waals forces between the gas and the solid.

There is no lateral interaction between the adsorbed molecules.

After the surface has become partially covered by adsorbed gas molecules,additional gas can adsorb either on the remaining free surface or on top of thealready adsorbed layer.

The adsorption of the second and subsequent layers occurs with a heat ofadsorption equal to the heat of liquefaction of the gas

0, 1, ..., n= Surface area covered (/cm2) by 0, 1, ..., n layers of adsorbed molecules

At Equilibrium 0, 1, 2must remain constant =>

Rate of Evaporation from First Layer = Rate of Condensation onto Bare Surface

k-11= k1P 0&

Rate of Condensation on the Bare Surface +Rate of Evaporation from the second layer

=

Rate of Condensation on the 1st Layer + Rate of Evaporation from the first Layer =>

k1P0+ k-22= k2P1+ k-11

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BET Isotherm

Modification of Langmuir isotherm

Both monolayer and multilayer adsorption

Layers of adsorbed molecules divided in:

First layer with heat of adsorption Had,1 Second and subsequent layers with H

ad,2= H

cond

BET isotherm:

BET equation does not fit entire adsorption isotherm

different mechanisms play a role at low and at high p

0mm0ad11

p

p

Cn

C

Cnppn

p

RT

HHC condadexp

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Suppose there are N0sites on the surface, then thenumber of atoms adsorbed is Na

Na= N0 i i (1)i=0

Where we have the usual sum rule i

=1i=0

If we now assume that this surface at temperature Tis in equilibrium with a gas then the adsorption rate

equals the desorption rate Since the atoms/molecules are physisorbed in a

weak adsorption potential

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reality model

54

32

10

...321 210mad nni

1-nn1-n1

0

nn1-n1

0101

0

111

00

pKpkkkpk

pKpk

kkpk

d

and

na

d

ada

1stlayer

nthlayer

For every layerLangmuir model

Assume

RT

H

RT

H

RT

H

KKK

KK

condn

ads

ee

e

0,n0,nn

0,11

0

0

0m

ad

111p

pC

p

p

p

p

C

n

n RTHH

Ccondads

e

with

BET Isotherm

BET Isotherm

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BET Isotherm

At equilibrium we have IstLayer K-11= k1P 0

II layer, k1P0+ k-22=k2P1+ k-11 ==> k-22= k2P1

In general k-ii= ki P i-1 i/ i-1= ki/k-i P

Where F is the incoming flux per site F = P/[No(2mkBT)], and Eidis the desorption

energy from layer i.

Note that, due to the change in substrate from the first to the second layer, there

may be a difference between E1dand E2

d.

However, for i = 1 and higher we consider desorption essentially as sublimation

from a multilayer of gas, and hence E2d= Ei>2

dand k

1k

2= k

3= ... = k

.

(2)

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To proceed, sample of unknown area is mounted in asmall volume and cooled to low temperature (75 K if we

use N2) The equilibrium pressure (P0) for N2at 75 K is 750 mbar

The amount of gas adsorbed is then measured as a

function of the pressure, and can conveniently beexpressed in terms of the amount of gas adsorbed in

one monolayer.

00

)1(1)( pcv

pccvppv

pmm

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Physisorption

Surface area measurement

S =nmAmN

monolayer

capacity (mol/g)

specific surface area

(m2/g)

area occupied by one

molecule (m2/molecule)

Avogadros number

(molecules/mol)

BET model: SBET

t model: St

M t f S f

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Measurement of Surface area:Measuring the surface area active forchemisorption is difficult because of:

highly selective naturefraction of surfacephysical adsorption + chemisorption

presence of promoter, carrier etc.

Universally surface area of a catalyst is

measured using physical adsorptionprinciples. It is approximated that themore the area the more would be theactivity of the catalyst.

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mmmN

N

N

v

p

Kvv

p

v

v

Kp

Kp

1

1 2

2

2

1. Langmuir Isotherm:

p/v

p

Slope = 1/vm

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26

00

)1(1

)( pcv

pc

cvppv

p

mm

2. BET Isotherm:

p/[v(p0-p)]

p/p0

Slope = (c-1)/cvm

P0= vapor pressure / Satn pressure

1/cvm

vm= 1/(slope + Intercept)

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Convert vmto no. of molecules= area covered by one molecule

22400

0NvS m3/2

0

09.1

N

M

For Nitrogen:= 0.808 g/cc at -195.8 0C= 16.2x10-16 cm2= 16.2 (A0)2

mvS 41035.4 vmis in CC at STP

Specific Surface area = S/W cm2/gm

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Pore size distribution

An important property of catalysts is the

distribution of pores across the inner and outer

surfaces. The most widely used method for

determining the pore distribution in solids is

mercury porosimetry and Nitrogen

adsorption/desorption method.

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N2Physisorption versus Hg

Porosimetry Hg cannot penetrate small (micro)pores, N2

can

Uncertainty of contact angle and surfacetension values

Cracking or deforming of samples

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Mercury Porosimetry

Pressure force. (p() r = -surface tension force, (2 r)

Surface tension (Hg)= 450-475 dyne/cmPore Size Distribution r (nm)= 6300/p( atm abs.)

or r (A0) = 8.75X 105 / P (psia)

Hg does not wet surfaces; pressure is needed to force intrusion

From a force balance:

(d in nm,pin bar)

Convenient method for determining pore volume versus poresize

pd

14860p

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Mercury Porosimetry:

The pore size distribution is determined bymeasuring the volume of mercury thatenters the pores under pressure.

Pressures of 0.1 to 200 MPa allow pore

sizes in the range 207500 nm to bedetermined.

sp rp

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Gas Adsorption Method:

The gas adsorption method ofestimating pore volume and diameter is

based upon the fact that gas condenses

to liquid in narrow pores at pressure

less than the saturated vapour pressure

of the adsorbate .

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P 2Vcosln( )= -

P rRT0

By relating the relative pressure and the poreradius the pore size distribution of the catalystis determined for pore size below 20nm.

The vapor pressure decreases as the capillary size

decreases as the capillary size decreases, such

condensation will occur in smaller pore. At saturation all

pores will get filled with adsorbed nitrogen.

If pressure is reduced by small increment , small amount ofnitrogen will evaporate from the meniscus of largest pore. (inwhich V.P of nitrogen is greater than chosen pressure.

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N2Desorption Method (Kelvin equation) :

The BET method can be used to determine the pore size distribution of

porous materials with diameters less than 200, except that high relativepressures are used for condensing N2in the catalyst pores. Capillary

condensation occurs in the pores in accordance with the Kelvin

equation:( variation of V.P WITH CURVATURE effect)

P= V.P of liquid over a curved surface, P0= V.P of liquid over a plane

surface, = surface tension of liquid adsorbate ( 8.85 dyne/cm for

nitrogen), V = molar volume of liquid adsorbate (35 cm3/mol for N2)

By relating the relative pressure and the pore radius the pore size

distribution of the catalyst is determined for pore size below 20nm.

0

2 cosln( )

P V

P rRT

Kelvin Equation

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Pore Size Distribution

Kelvin Equation

Cylindrical pore

Ink-bottle pore

Pore with shape of intersticebetween close-packed particles

Adsorbed layertdpdm

r (pore radius) =t + 2 VCos/(RT (ln p/p0))

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Kelvin Equationt-Method

BET

only valid in small pressure interval

interpretation not very easy

thickness (t) of adsorbed layer can be calculated

plot of tversus pfor non-porous materials is the same (has been

checked experimentally)

t-plot helps in interpretation

0.354 nm

0

2 cosln( )

P V

P rRT

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Kelvin EquationPore filling Model

Cylindrical Pore Channel

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Pore Size Distribution

Kelvin Equation

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Kelvin EquationPore Size Distribution

g-alumina

0.0

0.1

0.2

0.3

0.4

0.5

1 10 100 1000

dp(nm)

dV/dd(ml/g/nm

)

r = t + 2VCos/(RT (ln p/p0))

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N2Adsorption Isotherms & Pore Volume Distributions

0

5

10

15

20

25

0 0.2 0.4 0.6 0.8 1p/p

0

nad(mmol/g)1

wide-pore silica g-alumina

0

5

10

15

20

25

0 0.2 0.4 0.6 0.8 1p/p

0

nad(mmol/g)1

0.00

0.02

0.04

0.06

0.08

0.10

1 10 100 1000dpore(nm)

dV/dd(ml/

g/nm

0.0

0.1

0.2

0.3

0.4

0.5

1 10 100 1000dpore (nm)

dV/dd(ml/

g/nm)

N2Adsorption Isotherms & Pore Volume Distributions

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Pore Size Distributiont-Method

nm354.0

m

ad

n

nt

nad

t

Proportional to St

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Experiment:

The amount of N2adsorbed at equilibriumat the normal boiling point temp (-195.80C) is measured over a wide range of N2

partial pressures below 1 atm.

Identify the amount required to cover theentire surface by a mono-layer

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p/p0< 0.1Mono layer

0.1 < p/p0< 0.4Multi layer0.4 < p/p0< 1.0Capillary condensation

VSTP

pNitrogen

Linear region

Mono Layer ads

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0.00

0.02

0.04

0.06

0.08

0.10

1 10 100 1000dpore (nm)

dV/dd

(ml/g/nm

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Hg Intrusion Curves & PoreVolume Distributions

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Thank You