Characterization of Powders and Porous Materials …...Outline Theory of Adsorption Surface area and...

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

jeff.kenvin@micromeritics.com Surface area and porosity

Outline

1 Theory of Adsorption

2 Surface area and porositySurface AreaThicknessPorosityMacro-porosity

3 Micro-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

Definitions cont’d

Preparation

Clean the surface

Remove volatiles1 Water2 CO2

3 Solvents

Controlled environment1 Inert purge or vacuum2 Temperature control

Avoid Phase Changes

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

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.

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.

Adsorption

Physical Adsorption

Surface features change the adsorption potential.

Surface area models neglect the effects of localizedphenomenon.

Curve surfaces or roughness provide enhanced adsorptionpotential.

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.

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 =

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

Physisorption - Hardware

Key Features

Stainless steel manifold

1000, 10, 1 torrtransducers

Dedicated vacuum system

Cryogen level control/longdewar life

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

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

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

10.957 − 1

755.09= 0.0000594 mmHg−1

The non-ideality factor gives us the excess nitrogen per unit ofpressure

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/

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

Isotherm classifications

Isotherm classifications - rearrangement

Isotherm classifications - similarity

Surface AreaThicknessPorosityMacro-porosity

Type I - Isotherm

Langmuir Isotherm

Mono-layer adsorption

Micropore filling

Finely divided surface

Limiting amount adsorbedas p/p◦ approaches 1

Type I Isotherms - Y & X Zeolite

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Faujasite

Y ZeoliteX Zeolite

Type I Isotherms - Y & X Zeolite

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

Faujasite

Y ZeoliteX Zeolite

Type I Isotherms - Fluid Cracking Catalyst

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fluid Cracking Catalyst, 0.8nm pores

AdsorptionDesorption

Type I Isotherms - Fluid Cracking Catalyst

1e-07 1e-06 1e-05 1e-04 0.001 0.01 0.1 1

Fluid Cracking Catalyst, 0.8nm pores

Type I Isotherms - Y Zeolite & FCC

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.8nm pores

Y ZeoliteFCC

Type I Isotherms - Y Zeolite & FCC

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

0.8nm pores

Y ZeoliteFCC

Type I Isotherms - ZSM-5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

ZSM-5, 0.5-0.6nm pores

Adsorption

Type I Isotherms - ZSM-5

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

ZSM-5, 0.5-0.6nm pores

Adsorption

Type I Isotherms - TS-1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Titano-silicate, 0.5nm pores

Adsorption

Type I Isotherms - TS-1

1e-07 1e-06 1e-05 1e-04 0.001 0.01 0.1 1

Titano-silicate, 0.5nm pores

Adsorption

Type I Isotherms - TS-1 & ZSM-5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.5nm pores

TS-1ZSM-5

Type I Isotherms - TS-1 & ZSM-5

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

0.5nm pores

TS-1ZSM-5

Type I Isotherms - Single Wall Carbon Nanotubes

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Carbon Nanotubes

Adsorption

Type I Isotherms - Single Wall Carbon Nanotubes

1e-08 1e-07 1e-06 1e-05 1e-04 0.001 0.01 0.1 1

Carbon Nanotubes

Langmuir

Langmuir Model of Type I Isotherm

dt= ap(1− θ)− βθ exp

)= 0, equilibrium

ap(1− θ) = βθ exp

)b = K exp(E/RT )

where: θ ≡ fraction of surface occupieda ≡ adsorption coefficientβ ≡ desorption coefficientp ≡ equilibrium pressureK ≡ a / β

Langmuir

Langmuir Model

1− θ= bp

θ → 0, Langmuir model → Henry’s law

limθ→0

1− θ

θ = bp

Langmuir

Langmuir Model of Type I Isotherm

nm= θ

rearrange the Langmuir model to a more convenient form . . .

1 + bp

where: n ≡ quantity adsorbednm ≡ monolayer capacity

N2 Adsorption on 13x Zeolite

Type I

Crystalline

10 (8) A, pore

Silica-alumina

Ca+ exchangedzeolite

0 0.2 0.4 0.6 0.8 1

Pressure, mmHg

Nitrogen Adsorption, 13x Zeolite

Adsorption

0 0.2 0.4 0.6 0.8 1

3 /g S

Pressure, mmHg

Langmuir Transformation, 13x Zeolite

Linearized Langmuir Model → 620m2/g , b = 563.5/mmHg

0 0.2 0.4 0.6 0.8 1

Pressure, mmHg

13x Zeolite

13XLangmuir model

Type II - Isotherm

BET Isotherm

Non-porous surface

Uniform surface

Multilayer adsorption

Infinite adsorption asp/p◦ approaches 1

Type II Isotherms - Silica 1000A

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Silica, 100nm pores

Type II Isotherms - Silica 1000A

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

Silica, 100nm pores

Type II Isotherms - SRB D5 Carbon Black

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

SRB D5 Carbon Black

Adsorption

Type II Isotherms - SRB D5 Carbon Black

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

SRB D5 Carbon Black

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

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

BET Model

First Layer

a1pθ0 = b1θ1 exp

(−E1

)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

)jeff.kenvin@micromeritics.com Surface area and porosity

BET Model

All Layers

pθ0 =b1

a1θ1 exp

(−E1

pθ1 =b2

a2θ2 exp

(−E2

)pθ2 =

a3θ3 exp

(−E3

pθi−1 =bi

aiθi exp

(−Ei

Ei>1 = El

pθ0 =b1

a1θ1 exp

(−E1

pθ1 =b2

a2θ2 exp

(−El

)pθ2 =

a3θ3 exp

(−El

pθi−1 =bi

aiθi exp

(−El

bi/ai = g

pθ0 =b1

a1θ1 exp

(−E1

pθ1 = gθ2 exp

(−El

)pθ2 = gθ3 exp

(−El

pθi−1 = gθi exp

(−El

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◦= 1, i → inf

Type II Isotherm

(1− x)(1− x + Cx)

where: n ≡ quantity adsorbednm ≡ monolayer capacity

C ≡ adsorption coefficient, ≈ exp E1−ElRT

x ≡ relative pressure at equilibrium, p/p◦

Linearized BET

n(p◦ − p)=

C − 1

nmC× 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

N2 Adsorption on Macro-Porous Silica

Type II

Amorphous

1000A, pore

Desorption

Lack ofHysteresis

0 0.2 0.4 0.6 0.8 1

Relative Pressure, p/po

Nitrogen Isotherm, Lichrosphere 1000

N2 - BET Transformation - 25.7 m2/g

0 0.05 0.1 0.15 0.2 0.25 0.3

(po /p

Linear BET, Lichrosphere 1000

Lic 1000

N2 Adsorption on Carbon Black

Type II

Amorphous

Nano-particle

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

SRB D5 Carbon Black

Adsorption

SRB D5 Carbon Black - 21.2 m2/g

0 0.05 0.1 0.15 0.2 0.25 0.3

po /p -

SRB D5

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

Alternate approach to Kr

Balanced Tube Design

Balance tubeeliminates “voidspace” errors

Rapid analysis

Special Case - Single Point Surface Area

Linearized BET Transformation

n(p◦ − p)=

C − 1

nmC× p

Assume C →∞ (C > 100)

limC→∞

(C − 1

Single point estimate of nm

nm = n

(1− p

Physisorption - Dynamic Adsorption Hardware

Key Features

Rapid Analysis

Wide range of materials

High-sensitivity

Low cost

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, . . .

0 1 2 3 4 5 6 7 8 9

time, minutes

Dynamic N2 Adsorption/Desorption, SiO2-Al2O3

N2 Adsorption

N2 Desorption

Physisorption - Special Case - Magnesium Stearate

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Static N2 Adsorption, Magnesium Stearate

Physisorption - BET Surface Area Magnesium Stearate

0 0.05 0.1 0.15 0.2 0.25 0.3

*(po -p

Static N2 Adsorption, Magnesium Stearate

7.14 m2/g

9.3 m2/g

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

Titanium dioxide

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

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

Effect of preparation temperature on the SSA of Al2O3

20 40 60 80 100 120

Preparation Temperature, °C

α-alumina

Surface area increases 33% as preparation temperature is increasedfrom 40 to 100◦C as CO2 is removed.

Effect of preparation temperature on the SSA of SiO2

20 40 60 80 100 120

Silicon Dioxide

Surface area increases 3% as preparation temperature is increasedfrom 40 to 60◦C as H2O is removed.

Effect of preparation temperature on the SSA of TiO2

50 100 150 200 250 300

Titanium Dioxide

A slight increase in SSA is observed for the titania.

Glidants and Lubricants

for making tablets

1 Stearic Acid

2 Calcium Stearate

3 Magnesium Stearate

4 Sodium Stearate

5 Talc

Effect of temperature on the SSA of Stearic Acid

20 40 60 80 100 120

Stearic Acid

The loss is surface area indicates the melting of the stearic acidsmall particles → large particles.

Effect of temperature on the SSA of Ca2+ Stearate

20 40 60 80 100 120

Calcium Stearate

SSA drops as temperature increases.

Effect of temperature on the SSA of Mg2+ Stearate

20 40 60 80 100 120

Magnesium Stearate

SSA decreases 20% as temperature increases.

Effect of temperature on the SSA of Na+ Stearate

20 40 60 80 100 120

Sodium Stearate

SSA reaches at optimum at 60◦C and then decreases withincreasing temperature.

Effect of temperature on the SSA of Stearates

20 40 60 80 100 120

Na+, Ca2+, Mg2+ Stearate, and Stearic Acid

Na+ StearateCa2+ StearateMg2+ StearateStearic Acid

Effect of temperature on the SSA of Talc

20 40 60 80 100 120

Other Excipients

Binders and fillers

1 Gelatin - solution binder

2 Lactose - binder

3 Microcrystalline Cellulose - binder

4 Sucrose - filler

Effect of temperature on the SSA of Gelatin

20 40 60 80 100 120

Gelatin

Effect of temperature on the SSA of Lactose

20 40 60 80 100 120

Lactose Monohydrate

Significant increase in SSA as preparation temperature is increased.

Effect of temperature on the SSA of MicrocrystallineCellulose

20 40 60 80 100 120

Microcrystalline Cellulose

Effect of temperature on the SSA of Sucrose

20 40 60 80 100 120

Sucrose

Type IV - Isotherm

Mesoporous Materials

Multi-layer adsorption

Reduced saturationpressure in pores

Hysteresis

� Shape� Tortuosity

N2 Adsorption on Amorphous Silica-Alumina

Type IV

Amorphous

100A, pore

Desorption

Hysteresis

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Amorphous Silica Alumina, 11nm pores

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

po /p -

BET Surface Area = 215.5 m2/g

N2 Adsorption on MCM-41

Type IV

MesoporousSilica

40A,cylindricalpore

Desorption

Lack ofHysteresis 0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Silica, 4 nm pores

0.0002

0.0004

0.0006

0.0008

0.0012

0.0014

0.0016

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

po /p -

BET Surface Area = 926.8

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

where: d ′ ≡ thickness of the monolayer, d ′ = 3.54A for N2

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

thickness, Å thickness, Å

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

thickness, Å

Flat Surface

External Area

µ Pore Vol

thickness, Å

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

thickness, Å

Flat Surface

External Area

µ Pore Vol

thickness, Å

Flat Surface

External Area

Pore Area

Meso Pore Vol

Statistical t-Curve

Halsey

t = 3.54×

ln pp◦

Harkins and Jura

(13.99

0.034− log10pp◦

Statistical t-Curve

Jaroniec et. al.

(60.65

0.03071− log10pp◦

)0.3968

Broekhoff de Boer

F (te) = 2.303R

(−16.11

+ 0.1682e−0.1137te

), F (t) = R ln

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

+ 6.45

)+ 2.98

The t-Method

t-Plot

Statistical curves

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

HalseyHarkins and Jura

Jaroniec et. al.Broekhoff de Boer

The t-Method

t-Plot

Silica surface with 1000 A pores

DFT used to determine monolayer capacity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

The t-Method

t-Plot

BET used to determine monolayer capacity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

DFTBET

The t-Method

t-Plot

Silane treatment to remove OH−1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

DFTODMS

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 0.5 1 1.5 2 2.5

Thickness, angstroms

Micropore filling

External area

The t-Method → Microporous sample - Y Zeolite

Faujasite - Y Zeolite

Silica reference curve

0 2 4 6 8 10 12 14 16

thickness, Å

The t-Method → Microporous sample - FCC

FCC - Y Zeolite & binder

0 2 4 6 8 10 12 14 16

thickness, Å

The t-Method → Microporous sample - ZSM-5

0 2 4 6 8 10 12

thickness, Å

The t-Method → Microporous sample - TS-1

Titano-silicate

0 2 4 6 8 10 12 14 16

thickness, Å

The t-Method → Mesoporous sample - MCM 41

t-Plot → pore area = 699.4 m2/g

40 A mesoporous silica, cylindrical pores

0 2 4 6 8 10 12 14

Pore area

The t-Method → Mesoporous sample - MCM 41

40 A mesoporous silica, cylindrical pores

0 2 4 6 8 10 12 14

External area

The t-Method → Mesoporous sample - Silicaalumina

t-Plot → external area = 143 m2/g

110 A mesoporous silica

0 2 4 6 8 10 12 14

The t-Method

0 2 4 6 8 10 12 14

40 angstrom30 angstrom

110 angstrom8 angstrom

The t-Method → SRB D5 - Carbon Black

STSA for Carbon Black

0 1 2 3 4 5 6 7 8 9

thickness, Å

SRB D5

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

Titanium dioxide

Effect of preparation temperature on the porosity ofCalcium Stearate

0 2 4 6 8 10

thickness, Å

Calcium Stearate

Effect of preparation temperature on the porosity ofMagnesium Stearate

0 2 4 6 8 10

thickness, Å

Magnesium Stearate

Effect of preparation temperature on the porosity ofMicrocrystalline cellulose

0 2 4 6 8 10

thickness, Å

Microcrystalline Cellulose

Effect of preparation temperature on the porosity of SiO2

0 2 4 6 8 10

thickness, Å

Silicon Dioxide

Effect of preparation temperature on the porosity of Talc

0 2 4 6 8 10

thickness, Å

Effect of preparation temperature on the porosity of TiO2

0 2 4 6 8 10

thickness, Å

Titanium Dioxide

Capillary Condensation

Mesoporous

Adsorbed layer

Condensed phase

Liquid Nitrogen

BJH Calculations

Pore Width

Hydraulic radius

Kelvin equation

Adsorbed Layer

Thickness equation or curve

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

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

where: γ ≡ surface tensionv l ≡ liquid molar volumerk ≡ hydraulic radius

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

where: γ ≡ surface tensionv l ≡ liquid molar volumerk ≡ hydraulic radius

BJH Example Data

AmorphousSilicaAlumina

Surface area -214 m2/g

0 0.2 0.4 0.6 0.8 1

Nitrogen Isotherm, Amorphous Silica-Alumina

BJH Example Data

BET Surfacearea - 214m2/g

10 100 1000

D, angstroms

BJH Example Data

10 100 1000

D, angstroms

BJH Example Data

10 100 1000

D, angstroms

BJH Example Data

10 100 1000

D, angstroms

BJH Pore Calculations Adsorption Data

10 100 0

3 /g)/

width, Å

BJH Pore Calculations Desorption Data

10 100 0

3 /g)/

width, Å

BJH Example Data

MesoporousSilica

Surface area -926.8 m2/g

0 0.2 0.4 0.6 0.8 1

Nitrogen Adsorption, MCM-41

Adsorption

BJH Example Data

BET Surfacearea - 926.8m2/g

10 100 1000

D, angstroms

BJH Example Data

10 100 1000

D, angstroms

BJH Example Data

10 100 1000

D, angstroms

BJH Example Data

10 100 1000

D, angstroms

Mercury Intrusion Porosimetry

Sample cell - Penetrometer

Low Pressure Analysis

High Pressure Analysis

Sample cell - Penetrometer

Washburn equation

Intrusion Force

P · A = P · πd2

Resistance Forcefriction = πdγ cos(θ)

Force Balance

P · πd2

4= πdγ cos(θ)

Washburn Equation

d =4γ cos(θ)

“Ink-bottle” Pores

Trap Hg in the sample - extrusion rarely follows intrusion

“Ink-bottle” Pores

Effect of equillibrium time

Pore size distributions

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 %

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

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)

0.001 0.01 0.1 1 10 100 1000

Pore width, µm

Volume

0.001 0.01 0.1 1 10 100 10000.0

350.0In

Pore width, µm

VolumeArea

0.001 0.01 0.1 1 10 100 10000.0

350.0In

Pore width, µm

VolumeArea

0.001 0.01 0.1 1 10 100 10000.0

Pore width, µm

Cumulative IntrusionLog Differential Intrusion

Porosity of tablets

Tableting process influences pore size and ultimately dissolution

Use the mercury intrusion to evaluate the porosity of tablets

1 10 100 1000 10000 100000

Pressure, psia

Excedrin Tablet

IntrusionExtrusion

Intrusion volume of Excedrin tablet

0.001 0.01 0.1 1 10 100

Pressure, psia

Excedrin Tablet

Intrusion

Intrusion and pore size of an Excedrin tablet

0.001 0.01 0.1 1 10 100 0

tial I

Size, µm

Excedrin Tablet

Effect of breaking the Excedrin tablet

0.001 0.01 0.1 1 10 100 0

tial I

Size, µm

Excedrin

TabletBroken

Acetaminophen tablet

0.001 0.01 0.1 1 10 100 0

tial I

Size, µm

Acetaminophen Tablet

TabletBroken

Acetaminophen caplet

0.001 0.01 0.1 1 10 100 0

tial I

Size, µm

Acetaminophen Caplet

CapletBroken

Tablets and Caplets

0.001 0.01 0.1 1 10 100

Size, µm

Excedrin, Acetaminophen Tablets and Caplets

ExcedrinAcetaminophen TabAcetaminophen Cap

Tablets and Caplets

0.001 0.01 0.1 1 10 100

tial I

Size, µm

Excedrin, Acetaminophen Tablets and Caplets

ExcedrinAcetaminophen TabAcetaminophen Cap

Structures

Common Structures

1 ZSM-5

� Nan[AlnSi96−nO192], n > 27� MFI - Structure Code

� (Na2,Ca,Mg)29[Al58Si134O184]� FAU - Structure Code

� H53.3[Al53.3Si138.7O357.3]� FAU - Structure Code

Structures

Common Structures

1 ZSM-5

� Nan[AlnSi96−nO192], n > 27� MFI - Structure Code

� (Na2,Ca,Mg)29[Al58Si134O184]� FAU - Structure Code

� H53.3[Al53.3Si138.7O357.3]� FAU - Structure Code

Adsortives

Nitrogen

N2 Adsorption on Faujasite, 13X

FAU Structures

1e-008 1e-007 1e-006 1e-005 0.0001 0.001 0.01

CationNa+

N2 Adsorption on Faujasite, H-Y

FAU Structures

1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1

CationH+

N2 Adsorption on Faujasite

FAU Structures

1e-008 1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1

CationH+

Ar Adsorption on ZSM-5

1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1

SiO2:Al2O330:155:180:1

MFI Structure

SiO2:Al2O3 ratios -30, 55, 80, and 280

Argon isothermscollected at 77 K

Significanttransition

Ar Adsorption on ZSM-5

1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1

SiO2:Al2O330:155:180:1

MFI Structure

SiO2:Al2O3 ratios -30, 55, 80, and 280

Argon isothermscollected at 77 K

Significanttransition

Microporosity - Dubinin

Common Models

Dubinin

Horwath and Kawazoe

Density Functional Theory

Generalized Form

A = RT ln

)W = W0 exp

Microporosity - HK Slit Pores

Common Models

Dubinin

Horwath and Kawazoe

Slit-shape Pore Geometry

[(NaAa + NAAA)

σ4 (l − d)

3 (l − d/2)3− σ10

9 (l − d/2)9− σ4

4 (d/2)4+

9 (d/2)9

Microporosity - HK Cylindrical Pores

Common Models

Dubinin

Horwath and Kawazoe

Cylindrical-shape Pore Geometry

[(NaAa + NAAA)

inf∑k=0

2k + 1

(1− d

− βk

Microporosity - DFT

Common Models

Dubinin

Horwath and Kawazoe

Integral Equation of Adsorption

Q(p) =

∫dH q(p, h) f (H)

ZSM-5 Pore Size Distribution

H-K Model

Saito-Foley Model

Cylindrical PoreGeometry

Nitrogen, 77 K

1e-008 1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1

SiO2:Al2O330:1

H-K Model

Saito-Foley Model

Nitrogen, 77 K

4 5 6 7 8 9 10 11 12 13

SiO2:Al2O330:1

H-K Model

Saito-Foley Model

Nitrogen, 77 K

4 5 6 7 8 9 10 11 12 13

SiO2:Al2O330:155:180:1

H-K Model

Saito-Foley Model

Argon, 87 K

1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1

SiO2:Al2O3280:1

H-K Model

Saito-Foley Model

Argon, 87 K

4 5 6 7 8 9 10 11 12 13 14 15

SiO2:Al2O3280:1

H-K Model

Saito-Foley Model

Argon, 87 K

4 6 8 10 12 14 16

SiO2:Al2O3280:155:180:1

DFT Pore Size Distribution

1 10 100 1000

SiO2:Al2O3ZSM-5 30:1

DFT Model

Tarazona Model

Nitrogen, 77 K

1 10 100 1000

SiO2:Al2O3ZSM-5 30:1

H-Y 5:1

DFT Model

Tarazona Model

Nitrogen, 77 K

10 100 0

3 /g)/

Åwidth, Å

DFT Model

Cylindrical PoresOxide Model

Nitrogen, 77 K

MCM-41

X Zeolite

1 10 100 0

3 /g)/

width, Å

Y Zeolite

1 10 100 0

3 /g)/

width, Å

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

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.

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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