BET Notes

Surface Area and

Porosity

Outline• Background

✦ Techniques

• Surface area

✦ Total - physical adsorption

✦ External

✦ Porosity

✦ meso

✦ micro

1

2Tuesday, December 4, 12

Length1 mm1 µm1 nm1 Å

macromeso

micrometal

crystallite

10-3m10-4m10-5m10-6m10-7m10-8m10-9m10-10m

humanhair

red bloodcell

red ant

C-Cbond

Carbonnanotube

Transistorgate

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

• DifferentiateGas Adsorption

• Quantity adsorbed on a surface as a function of pressure, volume, and temperature

• Modeled properties

• Surface area

• Pore structure

• Non-destructuve

5


Static Adsorption

XX

PV G

X

AdsorptionQuantity adsorbed - always normalized for mass - cm3/g or moles/gRelative pressure - equilibrium pressure divided by saturation pressure - p/po

• Equilibrium pressure - vapor pressure above the sample - corrected for temperature (thermal transpiration)

• Saturation pressure - vapor pressure above a liquidSurface energy - solid/fluid interaction, strength, and heterogeneity

7


Sample PreparationClean the surface Remove volatiles

• Water

• CO2

• SolventsControlled environment!

• Inert purge or vacuum

• Temperature controlAvoid Phase Changes

Physical AdsorptionMolecules 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.

9


!100

!80

!60

!40

!20

0

20

40

60

0 1 2 3 4 5 6 7

Pot

entia

l Ene

rgy,

kJ/

mol

Distance from Surface, Å

Physical AdsorptionNot 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

Pot

entia

l Ene

rgy,

kJ/

mol

Distance from Surface, Å

Chemical AdsorptionMay be activated

Covalent, metallic, ionic

Strong (> 35 kJ/mol)

May be dissociative

Often irreversible

Specific - surface symmetry

Limited to a monolayer

Wide temperature range

11


Isotherm TypesI

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.

qa

ds

p/po

IV

A

A

13


Adsorbed Layer Density

• The first layer begins to form below 1x10-4 p/po

• The density continues to increase with pressure/adsorption

• The monolayer is completed below 0.1 p/po

qa

ds

p/po

IV

AB


As the system pressure is increased (gas concentration also increases) multiple layers sorb to the surface. A

B

15



• The monolayer is completed below 0.1 p/po

• The second layer continues to form as pressure is increased

• The third layer appears at < 0.5 p/po

qa

ds

p/po

IV

AB

C

Classical View of AdsorptionAs pressure is further increased we may observe capillary condensation in mesopores.

AB-C

17



• Layer formation continues as p/po increases

• As p/po approaches 1, the density becomes constant or nearly liquid-like

qa

ds

p/po

IV

AB

C

D


As pressure approaches the saturation pressure, the pores are filled and we may estimate total pore volume. A

B-CD

19


Adsorptives

Nitrogen

Argon

Krypton

NitrogenBroad 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 < 1m2/g (10µmol/g monolayer)

21


0

50

100

150

200

250

1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1

Va

ds,

cm

3/g

p/po

ZSM-5Faujasite

Confinement

ArgonPore size distributions

• H-K calculations

• NLDFT - excess density

Benefits

• Reduced interaction compared to N2

• Molecular size < N2

and faster diffusion due to size and T (87K)

Limitations

• Ar molecular area not a generally accepted value

• Statistical t-curves based upon N2

• Not used for BJH - bulk fluid methods

23


0

50

100

150

200

250

1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1

Vads,

cm

3/g

p/po

Faujasite (H+)

NitrogenArgon

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

Va

ds,

cm

3/g

p/po

ZSM-5 (LN2)

NitrogenArgon

ZSM-5, Ar Adsorption

25


0

20

40

60

80

100

120

140

1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1

Vads,

cm

3/g

p/po

AdsorptionDesorption

ZSM-5 Low P Desorption

KryptonSurface area estimates - BET

• Low specific surface area (< 1m2/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/po)

• General agreement with N2

• Cost

• Limited to surface area applications

27


Error analysisGas Law calculations

Error

Typical values

Relative error

Error Reduction

Probe Temperature, K Reference P ratioRelative Error

Ar 77 N2 200/760 0.26

Kr 77 N2 2.4/760 0.003

Kr 87 Ar 50/760 0.07

29


Surface Area

Surface Area• Area from adsorption

• nm - monolayer

• NA - 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

31


nads

P

I

Type I Isotherm - Langmuir Isotherm

Mono-layer adsorption

• Chemical Adsorption

Micropore filling

Finely divided surface

Limiting amount adsorbed as p/po 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

33


Nitrogen adsorption on Graphitized Carbon

CarboPack F

• 6 m2/gSterling FT

• 10 m2/gHenry’s law constant

• 19 (mmols/m2) / atm

0.0001

0.001

0.01

0.1

1

1e-05 0.0001 0.001 0.01 0.1 1

nads,

(m

mo

les/

m2)/

g

P

Henry’s LawAdsorptionDesorption

1e-05

0.0001

0.001

0.01

0.1

1e-06 1e-05 0.0001 0.001 0.01

na

ds,

(m

mole

s/m

2)/

g

P

Henry’s Law - Sterling FTCarbopack F - MICCarbopack F - Kruk

Sterling FT - MIC

Langmuir Estimate of nm

13X

620 m2/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

Qua

ntity

Ads

orbe

d, c

m3 /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

, mm

Hg/

(cm

3 /g S

TP)

Pressure, mmHg

Langmuir Transformation, 13x Zeolite

13X

35


Type II Isotherm

Non-porous

• Macro-porous

• Flat Surfaces

Uniform surface energy

Multilayer adsorption

Infinite adsorption as pressure approaches saturation

nads

P

II

BET Surface AreaEstimate monolayer capacityMulti-layer adsorptionNon-porous, Uniform surfaceHeat of adsorption for the first layer is higher than successive layers.Heat of adsorption for second and successive layers equals the heat of liquefactionLateral interactions of adsorbed molecules are ignored

37


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/po there are only 3 layers

0 1 2 3 4 5 6 7 8

!

"

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 EquationSimilar 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

39


BET Equation

• Linear form of BET

BET surface area

41


BET estimate of nm

100 nm SiO2

25.7 m2/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

Qua

ntity

Ads

orbe

d, c

m3 /g

p/po

Silica, 100nm pores


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

(po /p

-1)

Relative Pressure, p/po

Linear BET, Lichrosphere 1000

Lic 1000

Type IV Isotherm

Meso-porous

Multilayer adsorption

Capillary condensation

na

ds

P

IV

43


Amorphous Silica-Alumina

11 nm pores

215.5 m2/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

Qua

ntity

ads

orbe

d, c

m3 /g

p/po

Amorphous Silica Alumina, 11nm pores


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(

po /p -

1))

p/po

BET Surface Area = 215.5 m2/g

MCM-41

4 nm pores

926.8 m2/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

Qua

ntity

ads

orbe

d, c

m3 /g

p/po

Silica, 4 nm pores


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(

po /p -

1))

p/po

BET Surface Area = 926.8

45


100 nm pores

25.7 m2/g

4 nm pores

926.8 m2/g

11 nm pores

215.5 m2/g

MCM-41SiO2-Al2O3SiO2

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

Qua

ntity

Ads

orbe

d, c

m3 /g

p/po

Silica, 100nm pores


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

Qua

ntity

ads

orbe

d, c

m3 /g

p/po



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

Qua

ntity

ads

orbe

d, c

m3 /g

p/po

Silica, 4 nm pores


FCC catalyst

Y & binder

173.5 m2/g

BET range reduced to 0.16 p/po 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

Qua

ntity

Ads

orbe

d, c

m3 /g

p/po

Fluid Cracking Catalyst, 0.8nm pores


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(

po /p -

1))

p/po

BET Surface Area = 173.5 m2/g

47


FCC

FCC - Rouquerol

49


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

51


t-PlotStandard 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

qa

ds

p/po

IV

AB

C


Slope of a linear region corresponds to areaIntercept from a linear region is a pore volumeBased on BET surface area

n ads

thickness, Å thickness, Å

53


n ads

thickness, Å

Flat Surface

External Area

µ Pore Vol

thickness, Å


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


Low ”t” slope is areaIntercept is meso pore volumeHigh ”t” slope is external area

55


0

5

10

15

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Th

ickn

ess,

ang

stro

ms

p/po

HalseyHarkins and Jura

Jaroniec et. al.Broekhoff de Boer

Statistical t-curves

Halsey

• BJHHarkins-Jura

• t-plot

Jaroniec et. al.

• Silica

Broehkhoff de Boer

• difficult to use near saturation

t-Plot

57


Surface Modifications

The reference surface may be modified to be similar to the porous materialHydrophilic 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

Qua

ntity

Ads

orbe

d, c

m3 /g

p/po

Silica, 100nm pores


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

Thic

knes

s, a

ngst

rom

s

p/po

DFTODMS

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

Qua

ntity

Ads

orbe

d, c

m3 /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

Qua

ntity

Ads

orbe

d, c

m3 /g

Thickness, angstroms

Micropore filling

External area

59


Amorphous Silica-Alumina

Negligible micro-pore volumeCapillary condensation at large “t” values

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

Qua

ntity

ads

orbe

d, c

m3 /g

p/po



0

50

100

150

200

250

300

350

400

0 2 4 6 8 10 12 14

Qua

ntity

Ads

orbe

d, c

m3 /g


MCM-41

Ideal t-plot sampleArea, 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

Qua

ntity

ads

orbe

d, c

m3 /g

p/po

Silica, 4 nm pores


0

100

200

300

400

500

600

700

0 2 4 6 8 10 12 14

Qua

ntity

Ads

orbe

d, c

m3 /g


Pore area

61


t-Plot summaryArea

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-porosityCapillary condensationFluid has bulk behaviorBJH or DH models

• Adsorbed layer

• Liquid core

63


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

65


Amorphous Silica-aluminaBJHFirst ∆V is assumed to be from pore emptyingSubsequent ∆V are a combination of pore emptying and thinning of the adsorbed layer

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

Qua

ntity

ads

orbe

d, c

m3 /g

p/po



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

vol

ume,

cm

3 /g

dV/d

(log(

D)),

(cm

3 /g)/Å

width, Å

Amorphous Silica-alumina

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

Qua

ntity

ads

orbe

d, c

m3 /g

p/po



0

50

100

150

200

250

300

10 100 1000

Cum

ulat

ive

Pore

Are

a, m

2 /g

dSA/

dD

D, angstroms

BJHFrom ∆pore volume and calculated diameter, we can estimate surface area for a cylinderCommon to observe the BJH estimate of area is greater than the BET estimate

67


Amorphous Silica-alumina

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

Qua

ntity

ads

orbe

d, c

m3 /g

p/po



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

vol

ume,

cm

3 /g

dV/d

(log(

D)),

(cm

3 /g)/Å

width, Å

BJHDesorption data has been used - historicallyBest to use both Adsorption and Desorption - they should share common features

BJH - PVD Pt/Al2O3

69


Pore Area vs BET AreaHg Pore Area

Based upon a work function

Gas Adsorption Pore Area

Geometric area of a cylinder

BET Area

Based upon the area occupied by adsorbed nitrogen (krypton)

Thank-you

71


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