Surface Area and Porosity

(1)

Surface Area

and

Porosity

Outline

• Background

✦

Techniques

• Surface area

✦

Total - physical adsorption

✦

External

✦

Porosity

✦

meso

✦

micro

(2)

Length

1 mm

1 µm

1 nm

1 Å

macro

meso

micro

metal

crystallite

10 -3

_m

10 -4

_m

10 -5

_m

10 -6

_m

10 -7

_m

10 -8

_m

10 -9

_m

10 -10

_m

human

hair

red blood

cell

red

ant

C-C

bond

Carbon

nanotube

Transistor

gate

cell

membrane

10

100

10

100

Techniques

Mercury intrusion

• Adsorption

Physical

Chemical

Temperature Programmed Methods

(3)

Physical Adsorption

Characterization via

Adsorption

Material Characterization

• Physical properties

• Differentiate

Gas Adsorption

• Quantity adsorbed on a surface as a function of pressure,

volume, and temperature

• Modeled properties

• Surface area

• Pore structure

• Non-destructuve

(4)

Static Adsorption

X

P

V

G

X

Adsorption

Quantity adsorbed - always normalized for mass -

cm

3 _{/g or moles/g}

Relative pressure - equilibrium pressure divided by

saturation pressure - p/p

o

• Equilibrium pressure - vapor pressure above the

sample - corrected for temperature (thermal

transpiration)

• Saturation pressure - vapor pressure above a liquid

Surface energy - solid/fluid interaction, strength, and

heterogeneity

(5)

Sample Preparation

Clean the surface

Remove volatiles

• Water

• CO

2

• Solvents

Controlled environment!

• Inert purge or vacuum

• Temperature control

Avoid Phase Changes

Physical Adsorption

Molecules from the gas phase strike the surface.

At equilibrium the molecule adsorbs, lose the heat

of adsorption, and subsequently desorb from

surface.

At equilibrium the rate of condensation = the rate of

desorption

Constant surface coverage at equilibrium.

Surface features change the adsorption potential.

Surface area models neglect the effects of localized

phenomenon.

Curve surfaces or roughness provide enhanced

adsorption potential.

(6)

−100

−80

−60

−40

−20

0

20

40

60

0

1

2

3

4

5

6

7 Potential Energy, kJ/mol

Distance from Surface, Å

Physical Adsorption

Not activated (no barrier)

Rapid

Weak (< 38 kJ/mol)

Atomic/Molecular

Reversible

Non-specific

May form multilayers

van der Waals/dipole interactions

Often measured near the

condensation temperature

−100

−80

−60

−40

−20

0

20

40

60

0

1

2

3

4

5

6

7 Potential Energy, kJ/mol

Distance from Surface, Å

Chemical Adsorption

May be activated

Covalent, metallic, ionic

Strong (> 35 kJ/mol)

May be dissociative

Often irreversible

Specific - surface symmetry

Limited to a monolayer

Wide temperature range

(7)

Isotherm Types

I

n

ads

II

P

IV

III

V

VI

• Constant temperature

• Quantity adsorbed as a

function of pressure

• Vacuum to atmospheric

• Six classifications

• Quantity is normalized for

sample mass

Classical View of

Adsorption

As the system pressure is

increased the formation of a

monolayer may be observed.

q

ads

p/p

o IV A

A

13

(8)

Adsorbed Layer Density

• The first layer begins to form

below 1x10

-4

_p/p

o

• The density continues to increase

with pressure/adsorption

• The monolayer is completed

below 0.1 p/p

o

q

ads

p/p

o IV A B

Classical View of

Adsorption

As the system pressure is increased

(gas concentration also increases)

multiple layers sorb to the surface.

A

B

(9)

Adsorbed Layer Density

• The monolayer is completed below

0.1 p/p

o

• The second layer continues to

form as pressure is increased

• The third layer appears at < 0.5 p/

p

o

q

ads

p/p

o IV A B C

Classical View of

Adsorption

As pressure is further increased

we may observe capillary

condensation in mesopores.

A

B-C

(10)

Adsorbed Layer Density

• Layer formation continues

as p/p

o

_increases

• As p/p

o

_{approaches 1, the}

density becomes constant

or nearly liquid-like

q

ads

p/p

o IV A B C D

Classical View of

Adsorption

As pressure approaches the saturation

pressure, the pores are filled and we

may estimate total pore volume.

A

B-C

D

(11)

Adsorptives

Nitrogen

Argon

Krypton

Nitrogen

Broad usage

• Surface area

• t-plot

• Pore size

distributions

• BJH - bulk fluid

properties

• NLDFT - excess

density

Limitations

• Strong interactions

• Slow diffusion < 0.5

nm pores

• Reduced precision

for materials with <

1m

2 _{/g (10µmol/g}

monolayer)

(12)

0

50

100

150

200

250 1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

1 V

ads

, cm

3 /g

p/p

o

ZSM-5

Faujasite

Confinement

Argon

Pore size distributions

• H-K calculations

• NLDFT - excess

density

Benefits

• Reduced interaction

compared to N

2

• Molecular size < N

2 and faster diffusion due

to size and T (87K)

Limitations

• Ar molecular area not

a generally accepted

value

• Statistical t-curves

based upon N

2

• Not used for BJH -

bulk fluid methods

(13)

0

50

100

150

200

250 1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

1 V

ads

, cm

3 /g

p/p

o

Faujasite (H

+

)

Nitrogen

Argon

Y zeolite, Ar Adsorption

0

20

40

60

80

100

120

140

160

180

200 1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

1 V

ads

, cm

3 /g

p/p

o

ZSM-5 (LN

₂

)

Nitrogen

Argon

ZSM-5, Ar Adsorption

25

(14)

0

20

40

60

80

100

120

140 1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

1 V

ads

, cm

3 /g

p/p

o

Adsorption

Desorption

ZSM-5 Low P Desorption

Krypton

Surface area estimates -

BET

• Low specific surface

area (< 1m

2 _/g)

• Low absolute area -

limited sample

quantity

Benefits

• High precision, low

pressure analysis

Limitations

• Pressure range

limited to < 1 torr at

77 K (<0.3 p/p

o

₎

• General agreement

with N

2

• Cost

• Limited to surface

area applications

27

(15)

Error analysis

Gas Law calculations

Error

Typical values

Relative error

Error Reduction

Probe

Temperature, K Reference

P ratio

Relative

_Error

Ar

77 N

2 200/760

0.26 Kr

77 N

2 2.4/760

0.003 Kr

87 Ar

50/760

0.07

(16)

Surface Area

• Area from adsorption

• n

m

- monolayer

• N

A

- Avogadro’s number

• Total area - physical adsorption

• area of adsorbed molecule - nitrogen or

krypton

• Active area - chemical adsorption

• area of a surface site - metal atom

• Stoichiometry

(17)

n

ads

P

I

Type I Isotherm -

Langmuir Isotherm

Mono-layer adsorption

• Chemical Adsorption

Micropore filling

Finely divided surface

Limiting amount

adsorbed as p/p

o

approaches 1

Langmuir

Reduces to the familiar form of the

Langmuir equation for associative

adsorption

At low coverage, the Langmuir equation

converges with Henry’s Law

(18)

Nitrogen adsorption on

Graphitized Carbon

CarboPack F

• 6 m

2 _/g

Sterling FT

• 10 m

2 _/g

Henry’s law constant

• 19 (mmols/m

2 _{) / atm}

0.0001 0.001 0.01 0.1 1 1e-05 0.0001 0.001 0.01 0.1 1 nads , (mmoles/m 2)/g P Henry’s Law Adsorption Desorption 1e-05 0.0001 0.001 0.01 0.1 1e-06 1e-05 0.0001 0.001 0.01 nads , (mmoles/m 2)/g P Henry’s Law - Sterling FT

Carbopack F - MIC Carbopack F - Kruk Sterling FT - MIC

Langmuir

Estimate of n

m

13X

620 m

2 _/g

0 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Quantity Adsorbed, cm 3/g p/po X Zeolite, 0.8nm pores Adsorption 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0 0.2 0.4 0.6 0.8 1 p/Q, mmHg/(cm 3/g STP) Pressure, mmHg Langmuir Transformation, 13x Zeolite 13X

(19)

Type II Isotherm

Non-porous

• Macro-porous

• Flat Surfaces

Uniform surface energy

Multilayer adsorption

Infinite adsorption as

pressure approaches

saturation

n

ads

P

II

BET Surface Area

Estimate monolayer capacity

Multi-layer adsorption

Non-porous, Uniform surface

Heat of adsorption for the first layer is higher than

successive layers.

Heat of adsorption for second and successive

layers equals the heat of liquefaction

Lateral interactions of adsorbed molecules are

ignored

(20)

NLDFT estimate for the

density of the adsorbed layers

• The density varies with distance from the surface.

• This is contrast to BET assumptions

• However, at 0.5 p/p

o

_{there are only 3 layers}

0

1

2

3

4

5

6

7

8 ρ

σ

p = 0.0001

p = 0.0002

p = 0.0010

p = 0.0100

p = 0.1000

p = 0.2000

p = 0.5000

p = 0.7000

p = 0.9000

p = 0.9900

BET Equation

Similar to Langmuir - a mass

balance for each layer is used

The first layer is unique and

subsequent layers are common

E is the heat of liquefaction

An infinite series is formed

The sum of surface fractions is 1

The total quantity adsorbed is a function

of the monolayer and the surface fractions

The multilayer may approach infinite

thickness as pressure approaches

saturation

(21)

BET Equation

• Linear form of

BET

BET surface area

(22)

BET

estimate of n

m

100 nm SiO

2 25.7 m

2 _/g

0 5 10 15 20 25 30 35 40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Quantity Adsorbed, cm 3/g p/po Silica, 100nm pores Adsorption Desorption 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0 0.05 0.1 0.15 0.2 0.25 0.3 1/Q(p o/p-1) Relative Pressure, p/po

Linear BET, Lichrosphere 1000 Lic 1000

Type IV Isotherm

Meso-porous

Multilayer adsorption

Capillary condensation

n

ads

P

IV

43

(23)

Amorphous

Silica-Alumina

11 nm pores

215.5 m

2 _/g

0 50 100 150 200 250 300 350 400 450 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Quantity adsorbed, cm 3/g p/po

Amorphous Silica Alumina, 11nm pores Adsorption Desorption 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 1/(q ads (p o/p - 1)) p/po

BET Surface Area = 215.5 m2_/g

MCM-41

4 nm pores

926.8 m

2 _/g

0 100 200 300 400 500 600 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Quantity adsorbed, cm 3/g p/po Silica, 4 nm pores Adsorption Desorption 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 1/(q ads (p o/p - 1)) p/po

BET Surface Area = 926.8

(24)

100 nm pores

25.7 m

2 _/g

4 nm pores

926.8 m

2 _/g

11 nm pores

215.5 m

2 _/g

MCM-41

SiO

2 -Al

2 O

3 SiO

2

0 5 10 15 20 25 30 35 40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Quantity Adsorbed, cm 3/g p/po Silica, 100nm pores Adsorption Desorption 0 50 100 150 200 250 300 350 400 450 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Quantity adsorbed, cm 3/g p/po

Amorphous Silica Alumina, 11nm pores Adsorption Desorption 0 100 200 300 400 500 600 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Quantity adsorbed, cm 3/g p/po Silica, 4 nm pores Adsorption Desorption

FCC catalyst

Y & binder

173.5 m

2 _/g

BET range reduced

to 0.16 p/p

o

_maximum

0 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Quantity Adsorbed, cm 3/g p/po

Fluid Cracking Catalyst, 0.8nm pores Adsorption Desorption 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 1/(q ads (p o/p - 1)) p/po

BET Surface Area = 173.5 m2_/g

(25)

FCC

FCC - Rouquerol

(26)

BET surface area summary

Nitrogen or Krypton

Krypton for low surface area or small sample quantity

Isotherm

LP to 0.3 p/p°

Adjust range used to fit BET parameters for µ-porous

materials - Rouquerol transform

“C” must be “+”

Physical constraint

Linearity

External Surface Area

(27)

t-Plot

Standard Isotherms

Monolayer region is sensitive to isotherm shape

Multilayer region is not sensitive to isotherm shape

Multilayer region is less dependent on the

adsorbent structure

q

ads

p/p

o IV A B C

t-Plot

Standard Isotherms

Slope of a linear region corresponds to area

Intercept from a linear region is a pore volume

Based on BET surface area

n

ads

thickness, Å

(28)

n

ads

thickness, Å

Flat Surface External Area µ Pore Vol

thickness, Å

t-Plot

Standard Isotherms

Slope corresponds to external (matrix) area

Intercept is the micro pore volume

t-curve is critical

• Statistical curves give comparative results

• Reference curves are preferred

n

ads

thickness, Å

Flat Surface External Area µ Pore Vol

thickness, Å

Flat Surface External Area Pore Area Meso Pore Vol

t-Plot

Standard Isotherms

Low ”t” slope is area

Intercept is meso pore volume

High ”t” slope is external area

(29)

0 5 10 15 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Thickness, angstroms p/po Halsey

Harkins and Jura Jaroniec et. al. Broekhoff de Boer

Statistical

t-curves

Halsey

• BJH

Harkins-Jura

• t-plot

Jaroniec et. al.

• Silica

Broehkhoff de Boer

• difficult to use near saturation

t-Plot

(30)

Surface

Modifications

The reference

surface may be

modified to be similar

to the porous material

Hydrophilic vs.

hydrophobic

0 5 10 15 20 25 30 35 40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Quantity Adsorbed, cm 3/g p/po Silica, 100nm pores Adsorption Desorption 0 5 10 15 20 25 30 35 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Thickness, angstroms p/po DFT ODMS

t-Plot for 13X

Reference curve

“0” intercept

0 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Quantity Adsorbed, cm 3/g p/po X Zeolite, 0.8nm pores Adsorption 0 20 40 60 80 100 120 140 160 0 0.5 1 1.5 2 2.5 Quantity Adsorbed, cm 3/g Thickness, angstroms Micropore filling External area

59

(31)

Amorphous

Silica-Alumina

Negligible

micro-pore volume

Capillary

condensation at

large “t” values

Amorphous Silica Alumina, 11nm pores Adsorption Desorption 0 50 100 150 200 250 300 350 400 0 2 4 6 8 10 12 14 Quantity Adsorbed, cm 3/g Thickness, angstroms

MCM-41

Ideal t-plot sample

Area, pore volume,

and external area

0 100 200 300 400 500 600 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Quantity adsorbed, cm 3/g p/po Silica, 4 nm pores Adsorption Desorption 0 100 200 300 400 500 600 700 0 2 4 6 8 10 12 14 Quantity Adsorbed, cm 3/g Thickness, angstroms Pore area

61

(32)

t-Plot summary

Area

Pore area

External area (matrix)

Pore volume

Isotherm

LP to 0.7 p/p°

Positive or “0” intercept

t-curve

Reference curve is preferred

Statistical curve is convenient

Meso-porosity

Capillary

condensation

Fluid has bulk

behavior

BJH or DH models

• Adsorbed layer

• Liquid core

(33)

Meso-porosity

BJH models

• Thickness curve to

estimate the

adsorbed layer

• Kelvin equation to

estimate the radius

of the liquid core

Model Isotherms -

Kelvin Condensation

V =

Ad

4

(34)

Amorphous

Silica-alumina

BJH

First ∆V is assumed to be

from pore emptying

Subsequent ∆V are a

combination of pore

emptying and thinning of

the adsorbed layer

Amorphous Silica Alumina, 11nm pores Adsorption Desorption 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 10 100 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 pore volume, cm 3/g dV/d(log(D)), (cm 3/g)/Å width, Å

Amorphous

Silica-alumina

Amorphous Silica Alumina, 11nm pores Adsorption Desorption 0 50 100 150 200 250 300 10 100 1000

Cumulative Pore Area, m

2/g

dSA/dD

D, angstroms

BJH

From ∆pore volume and calculated

diameter, we can estimate surface

area for a cylinder

Common to observe the BJH

estimate of area is greater than the

BET estimate

(35)

Amorphous

Silica-alumina

Amorphous Silica Alumina, 11nm pores Adsorption Desorption 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 10 100 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 pore volume, cm 3/g dV/d(log(D)), (cm 3/g)/Å width, Å