Page 1
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Characterization of Powders and Porous Materialswith
Pharmaceutical Excipinent Case Studies
Jeffrey Kenvin, PhD
Micromeritics Instrument Corporation
July 2008
[email protected] Surface area and porosity
Page 2
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Outline
1 Theory of Adsorption
2 Surface area and porositySurface AreaThicknessPorosityMacro-porosity
3 Micro-Porosity
[email protected] Surface area and porosity
Page 3
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Adsorption
Definitions
Adsorption → Enrichment in an interfacial layerAdsorbate → Substance in the adsorbed stateAdsorptive → Adsorbable substance in the fluid phaseAdsorbent → Solid material on which adsorption occurs
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Page 4
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Definitions cont’d
Preparation
Clean the surface
Remove volatiles1 Water2 CO2
3 Solvents
Controlled environment1 Inert purge or vacuum2 Temperature control
Avoid Phase Changes
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Page 5
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Definitions cont’d
Physical Adsorption
Physisorption → Adsorption without chemical bondingpsat or Psat → Saturation pressure (of the cryogen)p◦ or P◦ → Saturation pressure of the adsorptive
Chemical Adsorption
Chemisorption → Adsorption involving chemical bonding
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Page 6
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Adsorption
Physical Adsorption
General phenomenon with a relatively low degree of specificity.
Retains identity; desorbs to fluid phase in its original form.
Exothermic adsorption similar to the energy of condensation.
Rapid equilibration; transport limited.
Chemical Adsorption
Dependent on reactivity of adsorbent and adsorptive.
Chemisorbed molecule may react or dissociate.
Energy is similar to energy change for chemical reaction.
Activated process at elevated temperature.
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Page 7
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Adsorption
Physical Adsorption
Molecules from the gas phase strike the surface.
At equilibrium the molecule adsorbs, lose the heat ofadsorption (q), and subsequently desorb from surface.
At equilibrium the rate of condensation = the rate ofdesorption
Constant surface coverage at equilibrium.
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Page 8
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Adsorption
Physical Adsorption
Surface features change the adsorption potential.
Surface area models neglect the effects of localizedphenomenon.
Curve surfaces or roughness provide enhanced adsorptionpotential.
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Page 9
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Multi-Layer Physical Adsorption
As the system pressure isincreased (gas concentrationalso increases) multiple layerssorb to the surface.
The monolayer coverage, adensely packed single adsorbedlayer is used for determiningsurface area.
As pressure is further increasedand adsorption proceeds gascondenses in the pores and thisvolume of condensed adsorptiveis used for characterizingporosity.
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Page 10
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Adsorption
Surface area is easily estimated if the number of N2 molecules thatform monolayer is known.
Calculating Surface Area
Surface Area = nm ×Na
w× σA =
Vm
Vg× Na
w× σA
where:
nm = Monolayer quantity, molVm = Monolayer volume, cm3
Vg = Molar volume of gas at STP, 22414 cm3/molNa = Avogadro’s number, 6.023×1023 molecules/molw = sample mass, gσA = Cross-sectional area of the adsorbate, m2
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Page 11
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Physisorption - Hardware
Key Features
Stainless steel manifold
1000, 10, 1 torrtransducers
Dedicated vacuum system
Cryogen level control/longdewar life
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Page 12
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Physisorption - Special Considerations
Saturation pressure and temperature for N2 or Ar
“Measured” value of p◦
Calculate bath temperature from measured p◦
Saturation pressure and temperature for Kr
“Measured” value of psat of N2
Calculate bath temperature from psatN2
Calculate p◦ from calculated temperature
Saturation pressure and temperature for CO2
“Entered” value of bath temperature
Calculate p◦ from entered temperature
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Page 13
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Adsorptive Properties
Gas specific
Non-ideality
Excess N2 at 77 KAll gas accounting calculations
Density conversion factor
Convert from measured volume to a liquid volumet-plot, BJH, pore volume calculations
Cross-sectional area
Size of a nitrogen moleculeBET, Langmuir, BJH, HK
Hard sphere diameter
pressure correction for micro pore analyses
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Page 14
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Non-ideality
Accurately account for the Real gas behavior
z(p◦,T p◦
)=
V measured
V ideal=
6.1103
6.3842= 0.957
The ideal gas law only accounts for 95.7% of the nitrogen; there isa 4.3% excess
α =1z − 1
p◦=
10.957 − 1
755.09= 0.0000594 mmHg−1
The non-ideality factor gives us the excess nitrogen per unit ofpressure
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Page 15
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Density conversion factor
Convert quantity adsorbed to a pore volume
φ =ρgas
ρliquid=
Vliquid
22.414l/mol=
0.0347
22414= 0.00155
http://webbook.nist.gov/chemistry/fluid/
[email protected] Surface area and porosity
Page 16
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Adsorption
Isotherms
Quantity adsorbed vs. pressure.
Pressure is usually varied from vacuum to near atmospheric.
Constant temperature.
Quantity adsorbed is normalized for adsorbent mass.
Six isotherm classifications
� Types I, II, and IV - most materials� Type III - uncommon� Type V - rare� Type IV - highly uniform surface
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Page 17
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Isotherm classifications
I
n ads
II
IV
III
V
P
VI
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Page 18
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Isotherm classifications - rearrangement
I
n ads
II
P
IV
III
V VI
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Page 19
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Isotherm classifications - similarity
I
n ads
II
P
IV
III
VVI
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Page 20
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I - Isotherm
Langmuir Isotherm
Mono-layer adsorption
Micropore filling
Finely divided surface
Limiting amount adsorbedas p/p◦ approaches 1
n ads
P
I
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Page 21
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - Y & X Zeolite
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
Faujasite
Y ZeoliteX Zeolite
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Page 22
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - Y & X Zeolite
0
50
100
150
200
250
1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
Faujasite
Y ZeoliteX Zeolite
[email protected] Surface area and porosity
Page 23
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - Fluid Cracking Catalyst
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
AdsorptionDesorption
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Page 24
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - Fluid Cracking Catalyst
0
10
20
30
40
50
60
70
80
90
100
1e-07 1e-06 1e-05 1e-04 0.001 0.01 0.1 1
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
Fluid Cracking Catalyst, 0.8nm pores
AdsorptionDesorption
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Page 25
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - Y Zeolite & FCC
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
0.8nm pores
Y ZeoliteFCC
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Page 26
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - Y Zeolite & FCC
0
50
100
150
200
250
1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
0.8nm pores
Y ZeoliteFCC
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Page 27
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - ZSM-5
0
20
40
60
80
100
120
140
160
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
ZSM-5, 0.5-0.6nm pores
Adsorption
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Page 28
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - ZSM-5
0
20
40
60
80
100
120
140
160
1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
ZSM-5, 0.5-0.6nm pores
Adsorption
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Page 29
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - TS-1
0
20
40
60
80
100
120
140
160
180
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
Titano-silicate, 0.5nm pores
Adsorption
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Page 30
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - TS-1
0
20
40
60
80
100
120
140
160
180
1e-07 1e-06 1e-05 1e-04 0.001 0.01 0.1 1
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
Titano-silicate, 0.5nm pores
Adsorption
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Page 31
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - TS-1 & ZSM-5
0
20
40
60
80
100
120
140
160
180
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
0.5nm pores
TS-1ZSM-5
[email protected] Surface area and porosity
Page 32
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - TS-1 & ZSM-5
0
20
40
60
80
100
120
140
160
180
1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
0.5nm pores
TS-1ZSM-5
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Page 33
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - Single Wall Carbon Nanotubes
0
50
100
150
200
250
300
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
Carbon Nanotubes
Adsorption
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Page 34
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type I Isotherms - Single Wall Carbon Nanotubes
0
50
100
150
200
250
300
1e-08 1e-07 1e-06 1e-05 1e-04 0.001 0.01 0.1 1
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
Carbon Nanotubes
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Page 35
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Langmuir
Langmuir Model of Type I Isotherm
dNa
dt= ap(1− θ)− βθ exp
(−E
RT
)= 0, equilibrium
ap(1− θ) = βθ exp
(−E
RT
)b = K exp(E/RT )
where: θ ≡ fraction of surface occupieda ≡ adsorption coefficientβ ≡ desorption coefficientp ≡ equilibrium pressureK ≡ a / β
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Page 36
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Langmuir
Langmuir Model
θ
1− θ= bp
θ → 0, Langmuir model → Henry’s law
limθ→0
(θ
1− θ
)= θ
θ = bp
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Page 37
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Langmuir
Langmuir Model of Type I Isotherm
n
nm= θ
rearrange the Langmuir model to a more convenient form . . .
n
nm=
bp
1 + bp
where: n ≡ quantity adsorbednm ≡ monolayer capacity
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Page 38
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
N2 Adsorption on 13x Zeolite
Type I
Crystalline
10 (8) A, pore
Silica-alumina
Ca+ exchangedzeolite
0
20
40
60
80
100
120
140
0 0.2 0.4 0.6 0.8 1
Qua
ntity
Ads
orbe
d, c
m3 /g
STP
Pressure, mmHg
Nitrogen Adsorption, 13x Zeolite
Adsorption
[email protected] Surface area and porosity
Page 39
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
N2 Adsorption on 13x Zeolite
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
Linearized Langmuir Model → 620m2/g , b = 563.5/mmHg
p
n=
1
bnm+
p
nm
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Page 40
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
N2 Adsorption on 13x Zeolite
0
20
40
60
80
100
120
140
0 0.2 0.4 0.6 0.8 1
Qua
ntity
Ads
orbe
d, c
m3 /g
STP
Pressure, mmHg
13x Zeolite
13XLangmuir model
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Page 41
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type II - Isotherm
BET Isotherm
Non-porous surface
Uniform surface
Multilayer adsorption
Infinite adsorption asp/p◦ approaches 1
n ads
P
II
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Page 42
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type II Isotherms - Silica 1000A
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
AdsorptionDesorption
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Page 43
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type II Isotherms - Silica 1000A
0
5
10
15
20
25
30
35
40
1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
Silica, 100nm pores
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Page 44
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type II Isotherms - SRB D5 Carbon Black
0
10
20
30
40
50
60
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
SRB D5 Carbon Black
Adsorption
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Page 45
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type II Isotherms - SRB D5 Carbon Black
0
10
20
30
40
50
60
1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
SRB D5 Carbon Black
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Page 46
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Brunauer, Emmett, and Teller
Surface Area
Stephen Brunauer
Paul Emmett
Edward Teller
N2 adsorption
Fixed Nitrogen Laboratory,1938
Second most cited reference over a 50 year period
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Page 47
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BET Assumptions
Surface Area
Multi-layer adsorption
Non-porous, Uniform surface
Heat of adsorption for the first layer is higher than successivelayers.
Heat of adsorption for second and successive layers equals theheat of liquefaction
Lateral interactions of adsorbed molecules are ignored
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Page 48
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BET Model
First Layer
a1pθ0 = b1θ1 exp
(−E1
RT
)where: a1pθ0 ≡ rate of condensation
b1θ1 exp(−E1RT
)≡ rate of evaporation
θ0 ≡ fraction of bare surfaceθ1 ≡ fraction of covered surface
Rate of condensation = rate of desorption
pθ0 =b1
a1θ1 exp
(−E1
RT
)[email protected] Surface area and porosity
Page 49
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BET Model
All Layers
pθ0 =b1
a1θ1 exp
(−E1
RT
)
pθ1 =b2
a2θ2 exp
(−E2
RT
)pθ2 =
b3
a3θ3 exp
(−E3
RT
)...
pθi−1 =bi
aiθi exp
(−Ei
RT
)
Ei>1 = El
pθ0 =b1
a1θ1 exp
(−E1
RT
)
pθ1 =b2
a2θ2 exp
(−El
RT
)pθ2 =
b3
a3θ3 exp
(−El
RT
)...
pθi−1 =bi
aiθi exp
(−El
RT
)
bi/ai = g
pθ0 =b1
a1θ1 exp
(−E1
RT
)
pθ1 = gθ2 exp
(−El
RT
)pθ2 = gθ3 exp
(−El
RT
)...
pθi−1 = gθi exp
(−El
RT
)[email protected] Surface area and porosity
Page 50
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BET Model
Sum of Surface Fractions
θ0 + θ1 + θ2 + θ3 + . . .+ θi + · · · = 1
Total Quantity Adsorbed
n = nm (1θ1 + 2θ2 + 3θ3 + . . .+ iθi + · · · )
Multilayer has Infinite Thickness
p
p◦= 1, i → inf
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Page 51
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Brunauer, Emmett, and Teller
Type II Isotherm
n
nm=
Cx
(1− x)(1− x + Cx)
where: n ≡ quantity adsorbednm ≡ monolayer capacity
C ≡ adsorption coefficient, ≈ exp E1−ElRT
x ≡ relative pressure at equilibrium, p/p◦
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Page 52
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Brunauer, Emmett, and Teller
Linearized BET
p
n(p◦ − p)=
1
nmC+
C − 1
nmC× p
p◦
1 Plot pn(p◦−p) vs. p
p◦ , 0.05 ≤ pp◦ ≤ 0.30
2 nm = 1slope+intercept
3 C = 1 + slopeintercept
4 C > 0
[email protected] Surface area and porosity
Page 53
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
N2 Adsorption on Macro-Porous Silica
Type II
Amorphous
1000A, pore
Desorption
Lack ofHysteresis
0
5
10
15
20
25
30
35
40
0 0.2 0.4 0.6 0.8 1
Qua
ntity
Ads
orbe
d, c
m3 /g
STP
Relative Pressure, p/po
Nitrogen Isotherm, Lichrosphere 1000
AdsorptionDesorption
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Page 54
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
N2 - BET Transformation - 25.7 m2/g
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
[email protected] Surface area and porosity
Page 55
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
N2 Adsorption on Carbon Black
Type II
Amorphous
Nano-particle
0
10
20
30
40
50
60
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
SRB D5 Carbon Black
Adsorption
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Page 56
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
SRB D5 Carbon Black - 21.2 m2/g
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 0.05 0.1 0.15 0.2 0.25 0.3
1/(q
ads(
po /p -
1))
p/po
SRB D5
[email protected] Surface area and porosity
Page 57
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Special considerations
Low Surface Area Materials
Krypton - p◦ is 1/300 of N2 p◦
Eliminate “void space errors”
Approximately same quantity adsorbed for Kr or N2
Same error for “void space”
Error is proportional to peVfs
Typical N2 experiment 35 - 220 mmHg
Typical Kr experiment 0.01 - 0.5 mmHg
Additonal Hardware
Turbo-pump
10 torr transducer
[email protected] Surface area and porosity
Page 58
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Alternate approach to Kr
Balanced Tube Design
Balance tubeeliminates “voidspace” errors
Rapid analysis
[email protected] Surface area and porosity
Page 59
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Special Case - Single Point Surface Area
Linearized BET Transformation
p
n(p◦ − p)=
1
nmC+
C − 1
nmC× p
p◦
Assume C →∞ (C > 100)
limC→∞
(1
nmC
)= 0
limC→∞
(C − 1
nmC
)=
1
nm
Single point estimate of nm
nm = n
(1− p
p◦
)[email protected] Surface area and porosity
Page 60
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Physisorption - Dynamic Adsorption Hardware
Key Features
Rapid Analysis
Wide range of materials
High-sensitivity
Low cost
[email protected] Surface area and porosity
Page 61
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Physisorption - Dynamic Adsorption
Analysis Tips
1 Desorption peak isused for Vm
2 Simple calibration
N2 injections
3 Not limited to N2
adsorption
Kr ,Ar ,CO2, . . .
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8 9
TC
D S
igna
l, V
time, minutes
Dynamic N2 Adsorption/Desorption, SiO2-Al2O3
N2 Adsorption
N2 Desorption
[email protected] Surface area and porosity
Page 62
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Physisorption - Special Case - Magnesium Stearate
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
Qua
ntity
Ads
orbe
d, c
m3 /g
Relative Pressure, p/po
Static N2 Adsorption, Magnesium Stearate
[email protected] Surface area and porosity
Page 63
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Physisorption - BET Surface Area Magnesium Stearate
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0 0.05 0.1 0.15 0.2 0.25 0.3
p/(Q
*(po -p
))
Relative Pressure, p/po
Static N2 Adsorption, Magnesium Stearate
7.14 m2/g
9.3 m2/g
[email protected] Surface area and porosity
Page 64
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Excipients
Pharmaceutical excipients
Substances other than the pharmacologically active drug orprodrug which are included in the manufacturing process or arecontained in a finished pharmaceutical product dosage form.
Commonly used excipients
Calcium stearate
Gelatin
Lactose
Magnesium stearate
Microcrystalline cellulose
Silicon dioxide
Sodium stearate
Stearic acid
Sucrose
Talc
Titanium dioxide
[email protected] Surface area and porosity
Page 65
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Investigate the impact of preparation temperature
Both excipients and APIs may be sensitive to temperature.
The preparation (removal of moisture, solvents, and ambientgases) is often performed at or near room temperature.
1 Purge with inert gas (nitrogen) or evacuate2 Control temperature at 40◦C3 Duration 4 - 24 hours
[email protected] Surface area and porosity
Page 66
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Oxides
Commonly used oxides
1 Aluminum oxideAlumina - Al2O3
2 Silicon dioxideSilica - SiO2
3 Titanium dioxideTitania - TiO2
Not chemically active
Stable
Do not dissolve
Range of particle sizes
Range of surface area andporosity
[email protected] Surface area and porosity
Page 67
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of preparation temperature on the SSA of Al2O3
0.3
0.32
0.34
0.36
0.38
0.4
0.42
0.44
20 40 60 80 100 120
Sur
face
Are
a, m
2 /g
Preparation Temperature, °C
α-alumina
Surface area increases 33% as preparation temperature is increasedfrom 40 to 100◦C as CO2 is removed.
[email protected] Surface area and porosity
Page 68
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of preparation temperature on the SSA of SiO2
367
368
369
370
371
372
373
374
375
376
20 40 60 80 100 120
Sur
face
Are
a, m
2 /g
Preparation Temperature, °C
Silicon Dioxide
Surface area increases 3% as preparation temperature is increasedfrom 40 to 60◦C as H2O is removed.
[email protected] Surface area and porosity
Page 69
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of preparation temperature on the SSA of TiO2
8.95
9
9.05
9.1
9.15
9.2
9.25
9.3
50 100 150 200 250 300
Sur
face
Are
a, m
2 /g
Preparation Temperature, °C
Titanium Dioxide
A slight increase in SSA is observed for the titania.
[email protected] Surface area and porosity
Page 70
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Glidants and Lubricants
for making tablets
1 Stearic Acid
2 Calcium Stearate
3 Magnesium Stearate
4 Sodium Stearate
5 Talc
[email protected] Surface area and porosity
Page 71
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of temperature on the SSA of Stearic Acid
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
20 40 60 80 100 120
Sur
face
Are
a, m
2 /g
Preparation Temperature, °C
Stearic Acid
The loss is surface area indicates the melting of the stearic acidsmall particles → large particles.
[email protected] Surface area and porosity
Page 72
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of temperature on the SSA of Ca2+ Stearate
5.6
5.8
6
6.2
6.4
6.6
6.8
7
20 40 60 80 100 120
Sur
face
Are
a, m
2 /g
Preparation Temperature, °C
Calcium Stearate
SSA drops as temperature increases.
[email protected] Surface area and porosity
Page 73
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of temperature on the SSA of Mg2+ Stearate
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
20 40 60 80 100 120
Sur
face
Are
a, m
2 /g
Preparation Temperature, °C
Magnesium Stearate
SSA decreases 20% as temperature increases.
[email protected] Surface area and porosity
Page 74
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of temperature on the SSA of Na+ Stearate
7.35
7.4
7.45
7.5
7.55
7.6
7.65
7.7
20 40 60 80 100 120
Sur
face
Are
a, m
2 /g
Preparation Temperature, °C
Sodium Stearate
SSA reaches at optimum at 60◦C and then decreases withincreasing temperature.
[email protected] Surface area and porosity
Page 75
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of temperature on the SSA of Stearates
0
1
2
3
4
5
6
7
8
20 40 60 80 100 120
Sur
face
Are
a, m
2 /g
Preparation Temperature, °C
Na+, Ca2+, Mg2+ Stearate, and Stearic Acid
Na+ StearateCa2+ StearateMg2+ StearateStearic Acid
[email protected] Surface area and porosity
Page 76
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of temperature on the SSA of Talc
7.35
7.4
7.45
7.5
7.55
7.6
7.65
7.7
20 40 60 80 100 120
Sur
face
Are
a, m
2 /g
Preparation Temperature, °C
Talc
[email protected] Surface area and porosity
Page 77
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Other Excipients
Binders and fillers
1 Gelatin - solution binder
2 Lactose - binder
3 Microcrystalline Cellulose - binder
4 Sucrose - filler
[email protected] Surface area and porosity
Page 78
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of temperature on the SSA of Gelatin
0.205
0.21
0.215
0.22
0.225
0.23
0.235
0.24
0.245
0.25
20 40 60 80 100 120
Sur
face
Are
a, m
2 /g
Preparation Temperature, °C
Gelatin
[email protected] Surface area and porosity
Page 79
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of temperature on the SSA of Lactose
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
20 40 60 80 100 120
Sur
face
Are
a, m
2 /g
Preparation Temperature, °C
Lactose Monohydrate
Significant increase in SSA as preparation temperature is increased.
[email protected] Surface area and porosity
Page 80
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of temperature on the SSA of MicrocrystallineCellulose
1.48
1.5
1.52
1.54
1.56
1.58
1.6
1.62
20 40 60 80 100 120
Sur
face
Are
a, m
2 /g
Preparation Temperature, °C
Microcrystalline Cellulose
[email protected] Surface area and porosity
Page 81
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of temperature on the SSA of Sucrose
0.16
0.17
0.18
0.19
0.2
0.21
0.22
0.23
20 40 60 80 100 120
Sur
face
Are
a, m
2 /g
Preparation Temperature, °C
Sucrose
[email protected] Surface area and porosity
Page 82
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Type IV - Isotherm
Mesoporous Materials
Multi-layer adsorption
Reduced saturationpressure in pores
Hysteresis
� Shape� Tortuosity
n ads
P
IV
[email protected] Surface area and porosity
Page 83
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
N2 Adsorption on Amorphous Silica-Alumina
Type IV
Amorphous
100A, pore
Desorption
Hysteresis
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
AdsorptionDesorption
[email protected] Surface area and porosity
Page 84
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
N2 - BET Transformation - 215.5 m2/g
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
[email protected] Surface area and porosity
Page 85
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
N2 Adsorption on MCM-41
Type IV
MesoporousSilica
40A,cylindricalpore
Desorption
Lack ofHysteresis 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
AdsorptionDesorption
[email protected] Surface area and porosity
Page 86
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
N2 - BET Transformation - 926.8 m2/g
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
[email protected] Surface area and porosity
Page 87
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Standard Isotherms
Thickness
Monolayer region is sensitive to isotherm shape
Multilayer region is not sensitive to isotherm shape
Multilayer region is less dependent on the adsorbent structure
Multilayer Thickness
t = d ′n
nm
where: d ′ ≡ thickness of the monolayer, d ′ = 3.54A for N2
[email protected] Surface area and porosity
Page 88
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
t-Plot → “Rules of Thumb”
Plot Va vs. t
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 thickness, Å
[email protected] Surface area and porosity
Page 89
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
t-Plot → “Micro Porous Sample”
Plot Va vs. t
Slope corresponds to external (matrix) area
Intercept is the micro pore volume
t-curve is critical
n ads
thickness, Å
Flat Surface
External Area
µ Pore Vol
thickness, Å
[email protected] Surface area and porosity
Page 90
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
t-Plot → “Meso Porous Sample”
Plot Va vs. t
Low ”t” slope is pore area
Intercept is meso pore volume
High ”t” slope is external area
n ads
thickness, Å
Flat Surface
External Area
µ Pore Vol
thickness, Å
Flat Surface
External Area
Pore Area
Meso Pore Vol
[email protected] Surface area and porosity
Page 91
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Statistical t-Curve
Halsey
t = 3.54×
(−5
ln pp◦
) 13
Harkins and Jura
t =
(13.99
0.034− log10pp◦
) 12
[email protected] Surface area and porosity
Page 92
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Statistical t-Curve
Jaroniec et. al.
t =
(60.65
0.03071− log10pp◦
)0.3968
Broekhoff de Boer
F (te) = 2.303R
(−16.11
t2e
+ 0.1682e−0.1137te
), F (t) = R ln
(p
p◦
)
[email protected] Surface area and porosity
Page 93
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Statistical t-Curve
Exteranl Surface Area of Carbon Black
Special application of t-plot to determine the external area ofcarbon.
Replaces the traditional CTAB
cetyltrimethyl ammonium bromide
Carbon STSA
t = 0.88
(p
p◦
)2
+ 6.45
(p
p◦
)+ 2.98
[email protected] Surface area and porosity
Page 94
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method
t-Plot
Statistical curves
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
Thi
ckne
ss, a
ngst
rom
s
p/po
HalseyHarkins and Jura
Jaroniec et. al.Broekhoff de Boer
[email protected] Surface area and porosity
Page 95
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method
t-Plot
Silica surface with 1000 A pores
DFT used to determine monolayer capacity
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
Thi
ckne
ss, a
ngst
rom
s
p/po
[email protected] Surface area and porosity
Page 96
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method
t-Plot
Silica surface with 1000 A pores
BET used to determine monolayer capacity
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
Thi
ckne
ss, a
ngst
rom
s
p/po
DFTBET
[email protected] Surface area and porosity
Page 97
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method
t-Plot
Silica surface with 1000 A pores
Silane treatment to remove OH−1
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
Thi
ckne
ss, a
ngst
rom
s
p/po
DFTODMS
[email protected] Surface area and porosity
Page 98
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method → Microporous sample - 13X
t-Plot → external area = 201.3 m2/g
Faujasite - 13X
Silica surface with 1000 A pores - DFT used for Vm
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
[email protected] Surface area and porosity
Page 99
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method → Microporous sample - Y Zeolite
t-Plot → external area = 21.3 m2/g
Faujasite - Y Zeolite
Silica reference curve
0
50
100
150
200
250
0 2 4 6 8 10 12 14 16
q ads
, cm
3 /g
thickness, Å
[email protected] Surface area and porosity
Page 100
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method → Microporous sample - FCC
t-Plot → external area = 28.5 m2/g
FCC - Y Zeolite & binder
Silica reference curve
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12 14 16
q ads
, cm
3 /g
thickness, Å
[email protected] Surface area and porosity
Page 101
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method → Microporous sample - ZSM-5
t-Plot → external area = 116.7 m2/g
ZSM-5
Silica reference curve
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
q ads
, cm
3 /g
thickness, Å
[email protected] Surface area and porosity
Page 102
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method → Microporous sample - TS-1
t-Plot → external area = 119.9 m2/g
Titano-silicate
Silica reference curve
0
20
40
60
80
100
120
140
160
180
200
0 2 4 6 8 10 12 14 16
q ads
, cm
3 /g
thickness, Å
[email protected] Surface area and porosity
Page 103
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method → Mesoporous sample - MCM 41
t-Plot → pore area = 699.4 m2/g
40 A mesoporous silica, cylindrical pores
Silica surface with 1000 A pores - DFT used for Vm
0
100
200
300
400
500
600
700
0 2 4 6 8 10 12 14
Qua
ntity
Ads
orbe
d, c
m3 /g
Thickness, angstroms
Pore area
[email protected] Surface area and porosity
Page 104
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method → Mesoporous sample - MCM 41
t-Plot → external area = 140.7 m2/g
40 A mesoporous silica, cylindrical pores
Silica surface with 1000 A pores - DFT used for Vm
0
100
200
300
400
500
600
0 2 4 6 8 10 12 14
Qua
ntity
Ads
orbe
d, c
m3 /g
Thickness, angstroms
External area
[email protected] Surface area and porosity
Page 105
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method → Mesoporous sample - Silicaalumina
t-Plot → external area = 143 m2/g
110 A mesoporous silica
Silica surface with 1000 A pores - DFT used for Vm
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
Thickness, angstroms
[email protected] Surface area and porosity
Page 106
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method
0
100
200
300
400
500
600
0 2 4 6 8 10 12 14
Qua
ntity
Ads
orbe
d, c
m3 /g
Thickness, angstroms
40 angstrom30 angstrom
110 angstrom8 angstrom
[email protected] Surface area and porosity
Page 107
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
The t-Method → SRB D5 - Carbon Black
t-Plot → external area = 18.3 m2/g
D5
STSA for Carbon Black
0
2
4
6
8
10
12
0 1 2 3 4 5 6 7 8 9
q ads
, cm
3 /g
thickness, Å
SRB D5
[email protected] Surface area and porosity
Page 108
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Excipients - t-plot
Pharmaceutical excipients
Use the t-plot method to determine if select excipients exhibitmicro porosity or meso porosity
Commonly used excipients
Calcium stearate
Gelatin
Lactose
Magnesium stearate
Microcrystalline cellulose
Silicon dioxide
Sodium stearate
Stearic acid
Sucrose
Talc
Titanium dioxide
[email protected] Surface area and porosity
Page 109
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of preparation temperature on the porosity ofCalcium Stearate
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 2 4 6 8 10
Qua
ntity
, cm
3 /g
thickness, Å
Calcium Stearate
[email protected] Surface area and porosity
Page 110
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of preparation temperature on the porosity ofMagnesium Stearate
0
0.5
1
1.5
2
2.5
0 2 4 6 8 10
Qua
ntity
, cm
3 /g
thickness, Å
Magnesium Stearate
[email protected] Surface area and porosity
Page 111
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of preparation temperature on the porosity ofMicrocrystalline cellulose
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10
Qua
ntity
, cm
3 /g
thickness, Å
Microcrystalline Cellulose
[email protected] Surface area and porosity
Page 112
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of preparation temperature on the porosity of SiO2
0
50
100
150
200
250
0 2 4 6 8 10
Qua
ntity
, cm
3 /g
thickness, Å
Silicon Dioxide
[email protected] Surface area and porosity
Page 113
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of preparation temperature on the porosity of Talc
0
1
2
3
4
5
6
0 2 4 6 8 10
Qua
ntity
, cm
3 /g
thickness, Å
Talc
[email protected] Surface area and porosity
Page 114
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of preparation temperature on the porosity of TiO2
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 2 4 6 8 10
Qua
ntity
, cm
3 /g
thickness, Å
Titanium Dioxide
[email protected] Surface area and porosity
Page 115
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Capillary Condensation
Mesoporous
Adsorbed layer
Condensed phase
Liquid Nitrogen
t t
r r
[email protected] Surface area and porosity
Page 116
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Calculations
tt
rr
Pore Width
Hydraulic radius
Kelvin equation
Adsorbed Layer
Thickness equation or curve
[email protected] Surface area and porosity
Page 117
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Calculations
Combine Kelvin Equation with the Thickness of the Adsorbed Layer
rp = rk + t
wp = 2× (rk + t)
where: wp ≡ pore width (diameter)rp ≡ pore radiusrk ≡ hydraulic radiust ≡ thickness of the adsorbed layer
[email protected] Surface area and porosity
Page 118
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Calculations
Kelvin Equation for Cylindrical Pores
Calculate the hydraulic radius for capillary condensation inMeso-pores.
Cylindrical geometry is the standard for BJH calculations.
Pore size > 20 A, (reduced precision below 75 A)
RT lnp
p◦= −2γv l
rk
where: γ ≡ surface tensionv l ≡ liquid molar volumerk ≡ hydraulic radius
[email protected] Surface area and porosity
Page 119
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Calculations
Kelvin Equation for Slit-shaped Pores
Calculate the hydraulic radius for capillary condensation inMeso-pores.
Hydraulic radius is 2D, width of an infinite slit.
RT lnp
p◦= −γv
l
rk
where: γ ≡ surface tensionv l ≡ liquid molar volumerk ≡ hydraulic radius
[email protected] Surface area and porosity
Page 120
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Example Data
AmorphousSilicaAlumina
Surface area -214 m2/g
0
50
100
150
200
250
300
350
400
0 0.2 0.4 0.6 0.8 1
Qua
ntity
Ads
orbe
d, c
m3 /g
ST
P
Relative Pressure, p/po
Nitrogen Isotherm, Amorphous Silica-Alumina
AdsorptionDesorption
[email protected] Surface area and porosity
Page 121
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Example Data
AmorphousSilicaAlumina
BET Surfacearea - 214m2/g
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
10 100 1000
Cum
ulat
ive
Por
e V
olum
e, c
m3 /g
D, angstroms
[email protected] Surface area and porosity
Page 122
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Example Data
AmorphousSilicaAlumina
BET Surfacearea - 214m2/g
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
10 100 1000
Cum
ulat
ive
Por
e V
olum
e, c
m3 /g
dV/d
D
D, angstroms
[email protected] Surface area and porosity
Page 123
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Example Data
AmorphousSilicaAlumina
BET Surfacearea - 214m2/g
0
50
100
150
200
250
300
10 100 1000
Cum
ulat
ive
Por
e A
rea,
m2 /g
D, angstroms
[email protected] Surface area and porosity
Page 124
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Example Data
AmorphousSilicaAlumina
BET Surfacearea - 214m2/g
0
50
100
150
200
250
300
10 100 1000
Cum
ulat
ive
Por
e A
rea,
m2 /g
dSA
/dD
D, angstroms
[email protected] Surface area and porosity
Page 125
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Pore Calculations Adsorption Data
AmorphousSilicaAlumina
BET Surfacearea - 214m2/g
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
[email protected] Surface area and porosity
Page 126
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Pore Calculations Desorption Data
AmorphousSilicaAlumina
BET Surfacearea - 214m2/g
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
[email protected] Surface area and porosity
Page 127
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Example Data
MesoporousSilica
Surface area -926.8 m2/g
0
100
200
300
400
500
600
0 0.2 0.4 0.6 0.8 1
Qua
ntity
Ads
orbe
d, c
m3 /g
ST
P
Relative Pressure, p/po
Nitrogen Adsorption, MCM-41
Adsorption
[email protected] Surface area and porosity
Page 128
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Example Data
AmorphousSilicaAlumina
BET Surfacearea - 926.8m2/g
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
10 100 1000
Cum
ulat
ive
Por
e V
olum
e, c
m3 /g
D, angstroms
[email protected] Surface area and porosity
Page 129
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Example Data
AmorphousSilicaAlumina
BET Surfacearea - 926.8m2/g
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
10 100 1000
Cum
ulat
ive
Por
e V
olum
e, c
m3 /g
dV/d
D
D, angstroms
[email protected] Surface area and porosity
Page 130
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Example Data
AmorphousSilicaAlumina
BET Surfacearea - 926.8m2/g
0
100
200
300
400
500
600
700
800
900
1000
10 100 1000
Cum
ulat
ive
Por
e A
rea,
m2 /g
D, angstroms
[email protected] Surface area and porosity
Page 131
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
BJH Example Data
AmorphousSilicaAlumina
BET Surfacearea - 926.8m2/g
0
100
200
300
400
500
600
700
800
900
1000
10 100 1000
Cum
ulat
ive
Por
e A
rea,
m2 /g
dSA
/dD
D, angstroms
[email protected] Surface area and porosity
Page 132
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Mercury Intrusion Porosimetry
[email protected] Surface area and porosity
Page 133
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Sample cell - Penetrometer
[email protected] Surface area and porosity
Page 134
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Low Pressure Analysis
[email protected] Surface area and porosity
Page 135
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
High Pressure Analysis
[email protected] Surface area and porosity
Page 136
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Sample cell - Penetrometer
[email protected] Surface area and porosity
Page 137
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Washburn equation
Intrusion Force
P · A = P · πd2
4
Resistance Forcefriction = πdγ cos(θ)
Force Balance
P · πd2
4= πdγ cos(θ)
Washburn Equation
d =4γ cos(θ)
P
[email protected] Surface area and porosity
Page 138
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
“Ink-bottle” Pores
Trap Hg in the sample - extrusion rarely follows intrusion
[email protected] Surface area and porosity
Page 139
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
“Ink-bottle” Pores
[email protected] Surface area and porosity
Page 140
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of equillibrium time
[email protected] Surface area and porosity
Page 141
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Pore size distributions
[email protected] Surface area and porosity
Page 142
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Alumina
Total Intrusion Volume 1.2166 mL/gTotal Pore Area 305.880 m2/gMedian Pore Diameter (Volume) 0.0171 µmMedian Pore Diameter (Area) 0.0084 µmAverage Pore Diameter (4V/A) 0.0159 µmBulk Density at 0.56 psia 0.6636 g/mLApparent (skeletal) Density 3.4454 g/mLPorosity 80.7390 %Stem Volume Used 60 %
[email protected] Surface area and porosity
Page 143
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Summary Data
Total Intrusion Volume - capacitance to volume measurement
Total Pore Area - we have used the Washburn equation tocalculate a size for each pressure. This diameter is then usedwith the incremental volume to determine the area of acylinder.
Median Pore Diameter1 by Volume - the diameter is calculated at the pressure
corresponding to 50% of the total intrussion volume.2 by Area - the diameter is calculated at the pressure
corresponding to 50% of the total intrussion Area.
Average pore diameter - 4V/A
[email protected] Surface area and porosity
Page 144
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Density and porosity
Bulk density - actually an envelope density determined by thequantity of Hg in the penetrometer empty (calibrated) versusthe quantity at low pressure with the sample.
Apparent density - similar to true density - density of thematerial determined at high pressure and subject tocompressibility effects.
Porosity - using both the bulk and apparent density todetermine percentage of void space = 100*(1 - ρB/ρA)
[email protected] Surface area and porosity
Page 145
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Pore size distributions
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.001 0.01 0.1 1 10 100 1000
Intr
usio
n, m
l/g
Pore width, µm
DV
Volume
[email protected] Surface area and porosity
Page 146
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Pore size distributions
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.001 0.01 0.1 1 10 100 10000.0
50.0
100.0
150.0
200.0
250.0
300.0
350.0In
trus
ion,
ml/g
Por
e ar
ea, m
2 /g
Pore width, µm
DV DA
VolumeArea
[email protected] Surface area and porosity
Page 147
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Pore size distributions
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.001 0.01 0.1 1 10 100 10000.0
50.0
100.0
150.0
200.0
250.0
300.0
350.0In
trus
ion,
ml/g
Por
e ar
ea, m
2 /g
Pore width, µm
DV DA
4V/A
VolumeArea
[email protected] Surface area and porosity
Page 148
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Pore size distributions
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.001 0.01 0.1 1 10 100 10000.0
0.5
1.0
1.5
2.0
2.5In
trus
ion,
ml/g
Log
diffe
rent
ial i
ntru
sion
Pore width, µm
Cumulative IntrusionLog Differential Intrusion
[email protected] Surface area and porosity
Page 149
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Porosity of tablets
Tableting process influences pore size and ultimately dissolution
Use the mercury intrusion to evaluate the porosity of tablets
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
1 10 100 1000 10000 100000
Intr
usio
n V
olum
e, c
m3 /g
Pressure, psia
Excedrin Tablet
IntrusionExtrusion
[email protected] Surface area and porosity
Page 150
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Intrusion volume of Excedrin tablet
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.001 0.01 0.1 1 10 100
Intr
usio
n V
olum
e, c
m3 /g
Pressure, psia
Excedrin Tablet
Intrusion
[email protected] Surface area and porosity
Page 151
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Intrusion and pore size of an Excedrin tablet
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.001 0.01 0.1 1 10 100 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
Intr
usio
n V
olum
e, c
m3 /g
Log
Diff
eren
tial I
ntru
sion
Size, µm
Excedrin Tablet
[email protected] Surface area and porosity
Page 152
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Effect of breaking the Excedrin tablet
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.001 0.01 0.1 1 10 100 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Intr
usio
n V
olum
e, c
m3 /g
Log
Diff
eren
tial I
ntru
sion
Size, µm
Excedrin
TabletBroken
[email protected] Surface area and porosity
Page 153
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Acetaminophen tablet
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.001 0.01 0.1 1 10 100 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Intr
usio
n V
olum
e, c
m3 /g
Log
Diff
eren
tial I
ntru
sion
Size, µm
Acetaminophen Tablet
TabletBroken
[email protected] Surface area and porosity
Page 154
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Acetaminophen caplet
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.001 0.01 0.1 1 10 100 0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Intr
usio
n V
olum
e, c
m3 /g
Log
Diff
eren
tial I
ntru
sion
Size, µm
Acetaminophen Caplet
CapletBroken
[email protected] Surface area and porosity
Page 155
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Tablets and Caplets
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.001 0.01 0.1 1 10 100
Intr
usio
n V
olum
e, c
m3 /g
Size, µm
Excedrin, Acetaminophen Tablets and Caplets
ExcedrinAcetaminophen TabAcetaminophen Cap
[email protected] Surface area and porosity
Page 156
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Surface AreaThicknessPorosityMacro-porosity
Tablets and Caplets
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.001 0.01 0.1 1 10 100
Log
Diff
eren
tial I
ntru
sion
, cm
3 /g
Size, µm
Excedrin, Acetaminophen Tablets and Caplets
ExcedrinAcetaminophen TabAcetaminophen Cap
[email protected] Surface area and porosity
Page 157
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Structures
Common Structures
1 ZSM-5
� Nan[AlnSi96−nO192], n > 27� MFI - Structure Code
2 13x
� (Na2,Ca,Mg)29[Al58Si134O184]� FAU - Structure Code
3 H-Y
� H53.3[Al53.3Si138.7O357.3]� FAU - Structure Code
[email protected] Surface area and porosity
Page 158
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Structures
Common Structures
1 ZSM-5
� Nan[AlnSi96−nO192], n > 27� MFI - Structure Code
2 13x
� (Na2,Ca,Mg)29[Al58Si134O184]� FAU - Structure Code
3 H-Y
� H53.3[Al53.3Si138.7O357.3]� FAU - Structure Code
[email protected] Surface area and porosity
Page 159
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Adsortives
Nitrogen
Argon
[email protected] Surface area and porosity
Page 160
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
N2 Adsorption on Faujasite, 13X
FAU Structures
13x
H-Y
0
20
40
60
80
100
120
140
160
1e-008 1e-007 1e-006 1e-005 0.0001 0.001 0.01
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
CationNa+
[email protected] Surface area and porosity
Page 161
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
N2 Adsorption on Faujasite, H-Y
FAU Structures
13x
H-Y
0
50
100
150
200
250
1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
CationH+
[email protected] Surface area and porosity
Page 162
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
N2 Adsorption on Faujasite
FAU Structures
13x
H-Y
0
50
100
150
200
250
1e-008 1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
CationH+
Na+
[email protected] Surface area and porosity
Page 163
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Ar Adsorption on ZSM-5
0
20
40
60
80
100
120
140
160
180
200
1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1
SiO2:Al2O330:155:180:1
280:1
MFI Structure
SiO2:Al2O3 ratios -30, 55, 80, and 280
Argon isothermscollected at 77 K
Significanttransition
[email protected] Surface area and porosity
Page 164
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Ar Adsorption on ZSM-5
0
50
100
150
200
250
1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1
SiO2:Al2O330:155:180:1
280:1
MFI Structure
SiO2:Al2O3 ratios -30, 55, 80, and 280
Argon isothermscollected at 77 K
Significanttransition
[email protected] Surface area and porosity
Page 165
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Microporosity - Dubinin
Common Models
Dubinin
Horwath and Kawazoe
Density Functional Theory
Generalized Form
A = RT ln
(po
p
)W = W0 exp
[−(
A
βE0
)n]
[email protected] Surface area and porosity
Page 166
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Microporosity - HK Slit Pores
Common Models
Dubinin
Horwath and Kawazoe
Density Functional Theory
Slit-shape Pore Geometry
RT ln
(p
po
)= K
[(NaAa + NAAA)
σ4 (l − d)
]×[
σ4
3 (l − d/2)3− σ10
9 (l − d/2)9− σ4
4 (d/2)4+
σ10
9 (d/2)9
]
[email protected] Surface area and porosity
Page 167
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Microporosity - HK Cylindrical Pores
Common Models
Dubinin
Horwath and Kawazoe
Density Functional Theory
Cylindrical-shape Pore Geometry
RT ln
(p
po
)=
3
4πK
[(NaAa + NAAA)
d4
]×
inf∑k=0
[1
2k + 1
(1− d
rp
)2k
−
(21
32αk
(d
rp
)10
− βk
(d
rp
)4)]
[email protected] Surface area and porosity
Page 168
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
Microporosity - DFT
Common Models
Dubinin
Horwath and Kawazoe
Density Functional Theory
Integral Equation of Adsorption
Q(p) =
∫dH q(p, h) f (H)
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Surface area and porosityMicro-Porosity
ZSM-5 Pore Size Distribution
H-K Model
Saito-Foley Model
Cylindrical PoreGeometry
Nitrogen, 77 K
0
20
40
60
80
100
120
140
160
180
200
1e-008 1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
SiO2:Al2O330:1
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OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
ZSM-5 Pore Size Distribution
H-K Model
Saito-Foley Model
Cylindrical PoreGeometry
Nitrogen, 77 K
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
4 5 6 7 8 9 10 11 12 13
dV/d
W, c
m3 /g
-A
W, A
SiO2:Al2O330:1
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OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
ZSM-5 Pore Size Distribution
H-K Model
Saito-Foley Model
Cylindrical PoreGeometry
Nitrogen, 77 K
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
4 5 6 7 8 9 10 11 12 13
dV/d
W, c
m3 /g
-A
W, A
SiO2:Al2O330:155:180:1
280:1
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OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
ZSM-5 Pore Size Distribution
H-K Model
Saito-Foley Model
Cylindrical PoreGeometry
Argon, 87 K
0
20
40
60
80
100
120
140
160
1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1
Qua
ntity
Ads
orbe
d, c
m3 /g
p/po
SiO2:Al2O3280:1
[email protected] Surface area and porosity
Page 173
OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
ZSM-5 Pore Size Distribution
H-K Model
Saito-Foley Model
Cylindrical PoreGeometry
Argon, 87 K
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
4 5 6 7 8 9 10 11 12 13 14 15
dV/d
W, c
m3 /g
-A
W, A
SiO2:Al2O3280:1
[email protected] Surface area and porosity
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OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
ZSM-5 Pore Size Distribution
H-K Model
Saito-Foley Model
Cylindrical PoreGeometry
Argon, 87 K
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
4 6 8 10 12 14 16
dV/d
W, c
m3 /g
-A
W, A
SiO2:Al2O3280:155:180:1
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OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
DFT Pore Size Distribution
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
1 10 100 1000
dV/d
W, c
m3 /g
-A
W, A
SiO2:Al2O3ZSM-5 30:1
DFT Model
Tarazona Model
Cylindrical PoreGeometry
Nitrogen, 77 K
ZSM-5
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OutlineTheory of Adsorption
Surface area and porosityMicro-Porosity
DFT Pore Size Distribution
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
1 10 100 1000
dV/d
W, c
m3 /g
-A
W, A
SiO2:Al2O3ZSM-5 30:1
H-Y 5:1
DFT Model
Tarazona Model
Cylindrical PoreGeometry
Nitrogen, 77 K
ZSM-5
H-Y
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Surface area and porosityMicro-Porosity
DFT Pore Size Distribution
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
10 100 0
2
4
6
8
10
12
14
16
18
20
pore
vol
ume,
cm
3 /g
dV/d
(log(
D))
, (cm
3 /g)/
Åwidth, Å
DFT Model
Cylindrical PoresOxide Model
Cylindrical PoreGeometry
Nitrogen, 77 K
MCM-41
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Surface area and porosityMicro-Porosity
X Zeolite
0
0.05
0.1
0.15
0.2
0.25
1 10 100 0
1
2
3
4
5
6
7
pore
vol
ume,
cm
3 /g
dV/d
(log(
D))
, (cm
3 /g)/
Å
width, Å
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Surface area and porosityMicro-Porosity
Y Zeolite
0
0.05
0.1
0.15
0.2
0.25
0.3
1 10 100 0
0.5
1
1.5
2
2.5
pore
vol
ume,
cm
3 /g
dV/d
(log(
D))
, (cm
3 /g)/
Å
width, Å
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Surface area and porosityMicro-Porosity
Summary
Chemistry effects
Composition influnces the adsorption potential - for example thealkaline zeolites adsorbed nitrogen at very low pressure.
Structure
Adsorption potential also follows pore size - for example a 5A poreadsorbs nitrogen at lower pressures than an 8A pore.
Surface Area
Surface area increases as pore size decreases
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Surface area and porosityMicro-Porosity
Summary cont’d
Preparation
The preparation temperature strongly influences surface area. Asprep temperature was increased for oxides the SSA increased; whilethe opposite was observed for stearates - increasing preptemperature reduced the surface area.
Porosity
Mesoporosity is a function of pressure and not as stronglydependent upon chemistry like the micro porous materials.
Porosity of Excipients
Common excipients do not exhibit significant levels of porosity aswe observed with silica.
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Surface area and porosityMicro-Porosity
Summary cont’d
Macro porosity
Mercury porosimetry allows us to understand the larger pores in amaterial
Tablets
The pore size of consumer tablets is very consistent and breaking atablet does not provide additional access to the API. This shouldprovide a consistent release of the API.
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