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and application in

Surface Area and Porosity Analysis

References1. Robert J. Silbey, Robert A. Alberty and Mougi G. Bawendi. 2005. Physical Chemistry,

4th ed., John Wiley & Sons.2. Atkins, P. W. and J. Paula, 2002. Physical Chemistry. 7th ed. London: Oxford

University Press3. Laidler, K. J. and Meiser, J. H. 1999. Physical Chemsitry. 3rd ed. Boston: Houghton

Mifflin Co.4. Levine, I. N., 2003, Physical Chemistry. 5th ed. Boston: McGraw Hill5. James E. House, 2007, Principles of Chemical Kinetics, 2nd ed. Amsterdam: Elsevier

6. Paul A. Webb and Clyde Orr, Analytical Methods in Fine Particle Technology,

Micromeritics, Norcross USA (1997)

7. Terence Allen, Particle Size Measurement, 4th ed., Chapman and Hall, London (1990)

Adsorption

Introduction

• Base on gas adsorption – N2, Ar, Kr, CO2

• Application

– Catalysts, activated carbons, carbons, pharmaceuticals, building materials, silicas and aluminas, metal powders, oxides and salts, adsorbents, ceramics, zeolites, pigments, glass, clay, LDH, nanocomposites etc

• Information

– Surface area, type of pore (non, micro, meso), pore size, pore volume, pore distribution,

• Principles

– Amount gas adsorbed depends on nature of the solids (adsorbent) and the pressure during adsorption. The amount adsorbed calculated by gravimetric or volumetric method.

– Isotherm - graph of amount adsorbed (V) vs P or P/Po (Po – saturated pressure) – the amount for complete monolayer coverage is determined, Vm

–

/g)(m substance ofweight

molecule of area sectional cross molecule ofnumber area surface 2∑

×=

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Surface area of regular shape objects can be easily determined from their

dimensions. However materials occur in nature are irregular in shape, complex

and often contain pores and channels.

If the internal structures of these materials are accessible by certain gas

molecule it is possible to determine their total surface area by adsorption

process.

Quantitative analysis of adsorption process

The extent of surface coverage is normally expressed as the fractional coverage,

θ where:

mV

V==

available sites adsorption ofnumber

occupied sites adsorption ofnumber θ

Often expressed in terms of the volume of adsorbate adsorbed V, where Vm is the

volume of adsorbate corresponding to complete monolayer coverage.

The rate of adsorption, dθ/dt, is the rate of change of surface coverage, and can be

determined by observing the change of fractional coverage with time.

Adsorption

STPat cmin where354

Nfor

4

4

3

2

2

2

mm

molar

Am

molar

Am

Vm

V.s

m

As

V

NVdnA

V

NVn

d

=

=

==

=

=

πσ

πσ

adsorbent

adsorbate

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What is θ θ θ θ ????

Schematic representation of

absorption process of N2(g)

on an adsorbent,

eg. aerogel

θ = 1

θ = 2

θ > 2

θ < 1

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Thermodynamic

N2(g) ⇌ N2(g) (adsorbed) ∆S = -ve

∆H = ∆G + T∆S = -ve (exothermic)

Factors affecting adsorption

Chemical and physical properties of gas

Chemical and physical properties of solid

Temperature

Pressure

Spontaneous process ∆G = -ve

Lenard-Jones potential

r

ε(r)

Molecule in contact with the surface for a

certain time before desorbed into gaseous

phase

There are two principal modes of adsorption of molecules on surfaces:

Physisorption: the only bonding is by weak Van der Waals - type forces.

There is no significant redistribution of electron density in either the

molecule or at the substrate surface.

Chemisorption: a chemical bond, involving substantial rearrangement of

electron density, is formed between the adsorbate and substrate. The

nature of this bond may lie anywhere between the extremes of virtually

complete ionic or complete covalent character.

Types of adsorption

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Physisorption Chemisorption

1. Caused by Van der Waals forces. No

electron transfer. Molecules adsorbed intact

Electron tranfer/sharing occurs.

Caused by covalent/electrostatic forces.

Dissociates into atoms, ions, or radicals

2. Heat of adsorption ≈2-6 kcal/mol. Heat of adsorption ≈10-200 kcal/mol.

3. A general phenomenon. i.e. condensation

of a gas.

Specific and selective

4. Physisorbed layer can be removed by

evacuation at the temperature of adsorption.

Removed only by evacuation and heating

above adsorption temperature.

5. Multi-layer adsorption below the critical

temperature of the gas

Never exceeds a mono-layer.

6. Appreciable only below the critical

temperature.

Appreciable at high temperatures also

7. Rate: May be fast or slow Rate: Instantaneous, A spontaneous process

requires ∆G<0 i.e ∆G = ∆H - T∆S <0.

8. Adsorption not strongly affected. Highly affected. Surface compounds

formation because of true chemical

reaction.

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Langmuir Theory• The first adsorption theory proposed by Langmuir (J. Am. Chem. Soc. 40,

1361 (1918)).

• Adsorption limited to monolayer. Limited applicability to physical adsorption, more suitable for adsorption in solution such dye, ion exchange, etc

• Surface force is short range thus only molecules striking bare surface is adsorbed while other molecules reflected back into gas phase.

• Localised adsorption and enthalpy of adsorption is independent of the covered area. Uniform surface. Adsorbed molecule do not interact.

• At equilibrium the number of molecule evaporating is equal to the number condensing.

−∝

mV

Vrate 1

mV

Vrate ∝

−∝

RT

Eadsexpfactor Arrhenius

Rate of collision gas -surface

proportional to P

Proportional to adsorbed surface

Rate of adsorption = Rate of desorption

−∝RT

Edesexpfactor Arrhenius

Thus at equilibrium it can be written

−

=

−

−

RT

E

V

Vk

RT

E

V

VP des

m

ads

m

expexp1

Where k is constant and since desadsads EEH −=∆

)/1(

/exp

m

mads

VV

VV

RT

HkP

−

∆=

the eq is becomes

Since enthalpy of adsorption is independent of covered surface, thus

bRT

Hk ads 1exp =

∆a constant

)/1(

/

m

m

VV

VVbP

−=thus or

bP

bPVV m

+=1

At low pressure bP<<1 thus V =VmbP

At high pressure bP>>1 thus V=Vm

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The above equation can be written as

mm V

P

bVV

P+=

1

isotherm

Vm

Vadsorbed

P/Po

(Relative pressure)

Po = saturated vapour pressure

V

P

P

mV

1slope =

mbV

1intercept =

Most of the Langmuir assumption are false. Surface of solids not uniform thus

desorption depends on the location of adsorption. Interaction force between

molecules is substantial. Adsorbed molecule can move from one site to

another.

Type 1 isotherm

DIY

Isotherm plot of CO (molecular radius 57 pm) on 0.1 g activated carbon at STP

is as follows

)/( 3cmtorrV

P

9

10

11

12

100 200 300 400

P (torr)

y = 0.0082 x + 7.783

R2 = 0.998

Calculate the specific surface area for the activated carbon.

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Following are data for the adsorption of H2 on Cu at 25 oC. Confirm that they

fit Langmuir at low coverage. Find the value of equilibrium rate constant and

the adsorption volume at complete coverage

P (Pa) 25 129 253 540 1000 1593

V (cm3) 0.042 0.163 0.221 0.321 0.411 0.471

DIY

Below are data for the adsorption of CO on charcoal at 273 K. Confirm that

they fit Langmuir. Find the value of equilibrium rate constant and the

adsorption volume at complete coverage

P (kPa) 13.3 26.7 40.0 53.3 80.0 93.3

V (cm3) 10.3 19.3 27.3 34.1 45.5 48.0

DIY

BET Theory

• Important step forward in adsorption theory Brunauer, Emment, Teller (J.

Am. Chem. Soc., 60, 309 (1938))

• Multilayer adsorption

• Assumption:

– Forces that produce condensation responsible for multimolecular

adsorption.

– They proceeded further from Langmuir theory, where the formation of

first monolayer serves a site for the second layer and so on.

– Thus the concept of localization prevails and mutual interaction

neglected.

The equation

−+=

− ommo P

P

CV

C

CVPPV

P 11

)(

RT

qEC L−

≈= 1expconstant and

Where E1 = heat of adsorption of the first layer

qL = latent heat of condensation of the adsorbate

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isotherm

Vm

Vadsorbed

P/Po

)( PPV

P

o −

P/Po

CV

C

m

1slope

−=

CVm

1intercept =

m

mmm

V

VCVCV

C

=+

=+−

=+

interceptslope

1

111interceptslope

Value of P/Po for BET plot are taken between 0.05 to 0.3. The upper limit can

be lower. The value of C frequently between 50 and 100 for N2.

What about C value?

)( PPV

P

o −

P/Po

410100slope −×=

4105.1intercept −×=

DIY

The following result was obtained for N2 adsorption on 0.85 g of titania

at STP

(cm-3)

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Single Point BET

−+=

− ommo P

P

CV

C

CVPPV

P 11

)(

10

mV C≈

Usually the intercept is small compared to the slope and may be

considered insignificant. Thus the line may be forced to pass through

origin. This equivalent by assuming C is large, C>>1, thus

1

( )o m o

P P

V P P V P

=

−

and C-1 ≈ C

Usually done for P/Po around 0.3 and C > 100. If C < 80 large error.

DIY

The following is the adsorption data of N2 adsorption on 1 g of TiO2(rutile) at 75

K.

P(torr) 1.20 14.0 45.8 87.5 127.7

V (mm3) 601 720 822 935 1046

Po=570 torr and the volumes have been corrected to STP.

a. Show that the data agree with BET

b. Determine the BET surface area.

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Adsorption desorption isotherms

Nonporous Porous

Interaction with

most energetic

region of the

solid

Completion of first layer

and beginning of

additional layers

Adsorbing beginning

bulk condesation

into liquid

Same but rise more rapid at

intermediate and hysteresis loop occur

on desorption. Typical meso (> 2 nm)

and macroporous (50 nm). Adsorbate

molecules within the pores experience

enhanced attraction thus lead to early

condensation.

Desorption branch,

behaves, according to

Kelvin equation

Micropores: dpore< 2 nm (N2 diameter around 0.35 nm)

Mesopores: 2 nm < dpore< 50 nm

Macropores: dpore> 50 nm

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Type of adsorption isotherm (IUPAC)

Characteristic of

microporous and the

amount adsorbed is

micropore volume

Nonporous or

large pores

C>2

Low affinity

adsorption.

Valueless in surface

and pore analysis

C<2

Type 2 with

hysteresis due to

capillary

condensation

Type 3 with hysteresis Multisteps

adsorption for noble

gas. Rare

Aaron Nackos, Adsorption, surface area and porosity - web

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de Boer’s hysteresis Loops

Catalysis Rate

bP

bPk

V

VkkRate

m +===1

θ

Reaction catalysed by solid surface. The rate is determined by the amount

of gas adsorbed or fraction of active site covered.

Rate = kθ

If reactant gas strongly adsorbed or high pressure, bP>>1

kRate = Zero order reaction

If reactant gas weakly adsorbed or low pressure, bP<<1

Rate = kbP First order reaction

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Reaction can be followed by the change of pressure of reacting gas.

For first order

AA Pk

dt

dPrate '=−=

Where k’=kb. Integration gives

tkP

P

A

A 'ln 0. =

Found to be correct model for many reactions on solid surface.

For cases of strongly adsorbed, zero order

kdt

dPrate A =−=

Integrated form

ktPP AA =−0,

There are also intermediate cases

bP

bPk

dt

dPA

+=−1

In can be shown to the integrated form is (DIY)

ktPPP

P

bAA

A

A =−+ )(ln1

0,

0,

1st order

Zero order

intermediate

θ

P