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Characterization of Powders, Porous Solids and Suspensions Lecture 8
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Characterization of Powders, Porous Solids and Suspensions

Lecture 8

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Main Characteristics of Powders and Porous Solids

Particle size Surface area Porosity

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Why We Care About Particle Size and Surface Area These characteristics control many properties of

materials: Flowability; “Filter-ability” Viscosity-Reology; Agglomeration; Dusting tendency; Settling rate; Activity/Reactivity rate (e.g. of catalyst); Dissolution rate (of pharmaceutical); Gas absorption; Hydration rate (of cement); Moisture absorption; Entry into lungs (shape dependency too); Combustion rate (of fuel) Etc…

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What is Particle Size?

SEM of real ibuprofen particles

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A Concept of Equivalent Sphere Due to symmetry, size of sphere is

completely determined by only one parameter – it’s diameter (radius)

Other properties of sphere are easily computed from its size:

Sphere is just a convenient model! This is why it is found throughout the particle size analysis

3

6

1dV 2dS 3

6dm

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Different Equivalent Spheres

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Particle Size Measurement Techniques

Direct observation (image analysis) Sieving; Sedimentation – settling rate; Coulter counter – electrozone sensing; Gas adsorption – BET (SSA back extrapolation

to size); Permeability (gas or liquid) e.g. Blaine, FSSS Light scattering – laser diffraction and Photon

Correlation Spectroscopy / Dynamic Light Scattering

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And What Do They Measure Direct observation (image analysis) – usually

some 2-D representation of a particle. Which dimension is viable?;

Sieving – combination of particle size and shape;

Sedimentation – settling rate. Stokes Law (spheres, straight line settling);

Coulter counter – electrozone sensing; Gas absorption / Permeability – surface area.

Extrapolate to average particle size only. – BET (SSA back extrapolation to size);

Light scattering – equivalent scatterers;

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Particle Size by Direct Observation

Google for ImageJ

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Dynamic Light Scattering (DLS) DLS measures Brownian motion and relates this to the size of the

particles.

The larger the particle the slower the Brownian motion will be. Smaller particles are “kicked” further by the solvent molecules and move more rapidly.

The velocity of Brownian motion is defined by a property known as the translational diffusion coefficient (D).

The size of a particle is calculated from the translational diffusion coefficient by using the Stokes-Einstein equation:

d(H) – hydrodynamic diameter, D – translational diffusion coefficient, k – Boltzmann’s constant, T – temperature, η - viscosity

D

kTHd

3)(

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What We Measure in DLS? The diameter that is measured in

DLS is a value that refers to how a particle diffuses within a fluid so it is referred to as a hydrodynamic diameter

The diameter that is obtained by this technique is the diameter of a sphere that has the same translational diffusion coefficient as the particle

The translational diffusion coefficient will depend not only on the size of the particle “core”, but also on any surface structure, as well as the concentration and type of ions in the medium

Particle core

Shell formed by solvent particles, ions etc. Low conductivity medium will produce an extended double layer of ions around the particle, reducing the diffusion speed and

resulting in a larger, apparenthydrodynamic diameter.

Thus, the measurements are usually done in 10mM

NaCl (ISO13321 Part 8 1996)

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How DLS Works

The dark spaces in the speckle pattern produced by light scattering are where the phase additions of the scattered light are mutually destructive. The bright spots of light in the speckle pattern are where the light scattered from the particles arrives with the same phase and interfere constructively.

The observed signal depends on the phase addition of the scattered light falling on the detector. In example A, two beams interfere and “cancel each other out” resulting in a decreased intensity detected. In example B, two beams interfere and “enhance each other” resulting in an increased intensity detected.

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How DLS Works

For a system of particles undergoing Brownian motion, a speckle pattern is observed where the position of each speckle is seen to be in constant motion. This is because the phase addition from the moving particles is constantly evolving and forming new patterns.

The rate at which these intensity fluctuations occur will depend on the size of the particles. Figure above schematically illustrates typical intensity fluctuations arising from a dispersion of large particles and a dispersion of small particles.

The small particles cause the intensity to fluctuate more rapidly than the large ones.

It is possible to directly measure the spectrum of frequencies contained in the intensity fluctuations arising from the Brownian motion of particles, but it is inefficient to do so. The best way is to use a device called a digital auto correlator.

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How an Auto Correlator Works

If the intensity of a signal is compared with itself at a particular point in time and a time much later, then for a randomly fluctuating signal it is obvious that the intensities are not going to be related in any way, i.e. there will be no correlation between the two signals.

However, if the intensity of signal at time t is compared to the intensity a very small time later (t+δt), there will be a strong relationship or correlation between the intensities of two signals.

Perfect correlation is indicated by unity (1.00) and no correlation is indicated by zero (0.00).

If the signals at t+2δt, t+3δt, t+4δt etc. are compared with the signal at t, the correlation of a signal arriving from a random source will decrease with time until at some time, effectively t = ∞, there will be no correlation.

If the particles are large the signal will be changing slowly and the correlation will persist for a long time. If the particles are small and moving rapidly then correlation will reduce more quickly.

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Different Forms of Particle Size Distribution

Consider 2 populations of spherical particles of diameter 5nm and 50nm present in equal numbers.

If a number distribution of these 2 particle populations is plotted, a plot consisting of 2 peaks (positioned at 5 and 50nm) of a 1 to 1 ratio would be obtained.

If this number distribution was converted into volume, then the 2 peaks would change to a 1:1000 ratio (because the volume of a sphere is proportional to d3).

If this was further converted into an intensity distribution, a 1:1000000 ratio between the 2 peaks would be obtained (because the intensity of scattering is proportional to d6 from Rayleigh’s approximation).

In DLS, the distribution obtained from a measurement is based on intensity.

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Schematics of Zetasizer Nano

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Measurement of Porosity and Specific Surface Area by

Gas Adsorption

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F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 1-25, 1999

What are Porous Materials?

Non-porous solid Low specific surface area Low specific pore volume

Porous solid High specific surface area High specific pore volume

Porous materials have highly developed internal surface area that can be used to perform specific function.Almost all solids are porous except for ceramics fired at extremely high temperatures

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Measure of Porosity

Pore size and its distribution

Specific Surface Area, m2/g =

Porosity

There are three parameters used as a measure of porosity; specific surface area, specific pore volume or porosity, and pore size and its distribution.

Mass of the solid, g

Total surface area, m2

Specific Pore volume, cm3/g

Mass of the solid, g

Total pore volume, cm3

=

Porosity, % =

Volume of solid (including pores)

Volume of poresX 100

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Concept of Porosity: Open vs. Closed Pores

Dead end (open)

ClosedInter-connected (open)

Passing (open)

F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 1-25, 1999

Open pores are accessible whereas closed pores are inaccessible pores. Open pores can be inter-connected, passing or dead end.

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Size of Pores (IUPAC Standard)

2 nm 50 nm

Micropores Mesopores Macropores

Zeolite,Activated carbon,Metal organicframework

Mesoporous silica, Activated carbon

Sintered metals and ceramics

Porous material are classified according to the size of pores: material with pores less than 2 nm are called micropores, materials with pores between 2 and 50 nm are called mesopores, and material with pores greater than 50 nm are macrospores

Sing, K. S. W. et al. Reporting Physisorption Data for Gas/Solid Systems. Pure & Appl. Chem. 57, 603-619 (1985).

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Shapes of Pores

Conical

Interstices

SlitsCylindrical

Spherical orInk Bottle

Pore Shapes

F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 1-25, 1999

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Experimental Techniques

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Techniques for Porosity Analysis

Mercuryporosimetry

TEM

SEM

Small angleX-ray

scattering

SmallAngle

Neutron scattering

Gas adsorption

Techniques

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Mercuryporosimetry

TEM

SEM

Small angleX-ray

scattering

SmallAngle

Neutron scattering

Gas adsorption

Techniques

Can measure only open pores Pore size : 0.4 nm – 50 nm Easy Established technique

Techniques for Porosity Analysis

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Mercuryporosimetry

TEM

SEM

Small angleX-ray

scattering

SmallAngle

Neutron scattering

Gas adsorption

Techniques

Similar to gas adsorption

Can measure only open pores

Pore size >1.5 nm Easy Established technique

Techniques for Porosity Analysis

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Mercuryporosimetry

TEM

SEM

Small angleX-ray

scattering

SmallAngle

Neutron scattering

Gas adsorption

Techniques

Provide information regarding pore connectivity

Pore size can be measured if the materials contains ordered pores

Rarely used for pore analysis

Techniques for Porosity Analysis

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Mercuryporosimetry

TEM

SEM

Small angleX-ray

scattering

SmallAngle

Neutron scattering

Gas adsorption

Techniques

Pore size > 5nm Rarely used for pore

analysis

Techniques for Porosity Analysis

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Mercuryporosimetry

TEM

SEM

Small angleX-ray

scattering

SmallAngle

Neutron scattering

Gas adsorption

Techniques

Any pore size Open + Close

porosity

Techniques for Porosity Analysis

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Mercuryporosimetry

TEM

SEM

Small angleX-ray

scattering

SmallAngle

Neutron scattering

Gas adsorption

Techniques

Any pore size Open & Close

porosity Costly

Techniques for Porosity Analysis

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Theory of Adsorption

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Adsorption Process

Adsorption is brought by the forces acting between the solid and the molecules of the gas. These forces are of two kinds: physical (physiosorption) and chemical (chemisorption)

Adsorbent - the solid where adsorption takes place

Adsorbate - the gas adsorbed on the surface of solids

Adsorptive - adsorbate before being adsorbed on the surface

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PHYSISORPTION CHEMISORPTIONWEAK, LONG RANGE BONDING

Van der Waals interactions

STRONG, SHORT RANGE BONDING

Chemical bonding involved.

NOT SURFACE SPECIFIC

Physisorption takes place between all molecules on any surface providing the

temperature is low enough.

SURFACE SPECIFIC

E.g. Chemisorption of hydrogen takes place on transition metals but not on gold or mercury.

ΔHads = 5 ….. 50 kJ mol-1 ΔHads = 50 ….. 500 kJ mol-1

Non activated with equilibrium achieved relatively quickly. Increasing temperature

always reduces surface coverage.

Can be activated, in which case equilibrium can be slow and increasing temperature can favour

adsorption.

No surface reactions. Surface reactions may take place:- Dissociation, reconstruction, catalysis.

MULTILAYER ADSORPTION

BET Isotherm used to model adsorption equilibrium.

MONOLAYER ADSORPTION

Langmuir Isotherm is used to model adsorption equilibrium.

Physisorption vs Chemisorption

http://www.soton.ac.uk

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Adsorption Process

1. Diffusion to adsorbent surface2. Migration into pores of adsorbent3. Monolayer builds up of adsorbate

1 2 3

Gas molecules admitted under increasing pressure to a clean, cold surface.

Data treatment techniques find the quantity of gas that forms the first layer. 1 2 3

S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991

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Adsorption Process

Adsorbent

Adsorbate

adsorptive of pressure saturated

adsorbate of pressure

where

:as written becan equation

above theconstant, made are I and T, W,If

adsorbent. and adsorbatebetween n interactio

re; temperatu

adsorbate; theof pressure

adsorbent; of weight

adsorbed; gas of volume

where

),,,(

p

p

p

pf

I

T

P

W

PITWf

o

oV

V

V

a

a

a

Equation of adsorption isotherm

S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991

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Gas Sorption: Isotherm

Adsorption isotherm Isotherm is a measure of the volume of gas adsorbed at a constant temperature as a function of gas pressure.Isotherms can be grouped into six classes.

adsorptive of pressure saturated

adsorbate of pressure

where

p

p

p

pf

o

oV a

V a

Desorption isotherm

ppo

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Gas Sorption: IsothermV a

1P/Po

Type Ior

Langmuir

S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991

Concave to the P/Po axisExhibited by microporous solids ( < 2nm )

1P/Po

Type II

Exhibited by nonporous or macroporous solids ( > 50nm )Unrestricted monolayer-multilayer adsorptionPoint B indicates the relative pressure at which monolayer coverage is complete

B

V a

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Gas Sorption: IsothermV a

1P/Po

Type III Convex to the P/Po axisExhibited by nonporous solids

V a

1P/Po

Type IVExhibited by mesoporous solidsInitial part of the type IV follows the same path as the type II

S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991

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Gas Sorption: IsothermV a

1P/Po

Type V

1P/Po

Type VI

Highly uncommonExhibited by mesoporous solids

Exhibited by nonporous solids with an almost completely uniform surface

S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991

V a

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Gas Sorption: Hysteresis

Hysteresis indicates the presence of mesopores.

Hysteresis gives information regarding pore shapes .

Types I, II and III isotherms are generally reversible but type I can have a hysteresis. Types IV and V exhibit hysteresis.

1P/Po

HysteresisV a

S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991

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Gas Sorption: HysteresisV a

1P/Po

Type A

Cylindrical Slits

Type B

1P/Po 1P/Po

Type C Type D

1P/Po

Type E

1P/Po

Conical Bottle neck

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Adsorption Theories: Langmuir

Adsorbate

Adsorbent

Assumptions:

homogeneous surface (all adsorption sites energetically identical)

monolayer adsorption (no multilayer adsorption)

no interaction between adsorbed molecules

adsorbate. of pressure

and constant; empirical

monolayer; form torequired gas of volume

; pressureat adsorbed gas of volume

where

1

P

b

V

PV

V

P

bVV

P

m

a

mma

I. Langmuir The Constitution and Fundamental Properties of Solids and Liquids. Part I. Solids. J. Am. Chem. Soc., 1916, 38 (11), 2221-2295

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Adsorption Theories: BET

adsorbate. of pressure relative

and layer);1st of adsorption ofenergy to(relatedconstant BET C

monolayer; form torequired gas of volume

; pressureat adsorbed gas of volume

where

)1(1

)(

o

m

a

omm

oa

P

P

V

PV

P

P

CV

C

CVPPV

P

Modification of Langmuir isotherm

Both monolayer and multilayer adsorption

Assumptions:

(a) gas molecules physically adsorb on a solid in layers infinitely;

(b) there is no interaction between each adsorption layer;

(c) the Langmuir theory can be applied to each layer.

Adsorbate

Adsorbent

S.Brunauer, P.Emmett, E.Teller Adsorption of Gases in Multimolecular Layers, J. Am. Chem. Soc., 1938, 60 (2), pp 309–319

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Specific Surface Area Calculation

CVP

P

CV

C

PPV

P

mo

mo

a

1)1(

)(

imXY

imVm

1

P/Po

1

V[(Po/P)-1]

0-1 0-2 0-3

At least three data points in the relative pressure range 0.05 to 0.30

adsorbate ofWeight area surface Total csavm ANV

sample ofWeight

area surface Totalarea) surface (SpecificSSA

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Porosity Analyzer

Outgassing station

Analysis station

Liquid nitrogen bath

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Steps for Measurement

3. Interpretation

2. Adsorption Analysis

1. Sample Preparation

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Sample Preparation (Outgassing) Surface contamination is

removed by application of: Temperature Flowing gas (helium or

nitrogen) or vacuum

Backfill can be done using helium or adsorbate gas.

According to IUPAC standards, materials should be outgassed for at least 16 hours.

Adsorbate

Helium

Vacuum

Po

Outgassing station

Analysis station

Sample Cell

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Adsorption Analysis

Adsorbate (nitrogen, argon, carbon dioxide, krypton)

Analysis temperature (liquid nitrogen, liquid argon, 0 oC)

Quantity of sample (1 mg sample is sufficient)

Number of points (single point, five points, seven points, eleven points, full analysis)

Adsorbate

Helium

Vacuum

Po

Outgassing station

Analysis station

Sample Cell

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Interpretation

Points P/Po Volume adsorbed

1

2

3

Weight of sample

OUTPUT

OUTPUT

Pore shape

Specific surface area

Pore volume

Pore size&

distribution

Results

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Common Adsorbates

Gas Temperature Cross sectional area (nm2)

N2 -195.8 oC (liquid nitrogen) -183 oC (liquid argon).

0.162

Ar -183 oC (liquid argon). -195.8 oC (liquid nitrogen)

0.142

CO2 -78 oC, -25 oC, 0 oC 0.195

CO -183 oC (liquid argon) 0.163

Kr -195.8 oC (liquid nitrogen) 0.205

O2 -183 oC (liquid argon) 0.141

C4H10 0 oC, 25 oC 0.469

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Choice of Adsorptive

N2(g) in N2(l) is the most commonly used adsorbate.

Not completely inert. Dipole movement and

thus can have localized adsorption.

Cross-sectional area of 0.162 nm2 is questionable.

S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991Quantachrome Autosorb-I Operational Manual

Oxy

gen

Arg

on

Nitr

ogen

Car

bon

mon

ooxi

deC

arbo

n di

oxid

e

Kry

pton

n-bu

tane

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Cro

ss-s

ecti

on

al a

rea,

nm

2

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Oxy

gen

Arg

on

Nitr

ogen

Car

bon

mon

ooxi

deC

arbo

n di

oxid

e

Kry

pton

n-bu

tane

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Cro

ss-s

ecti

on

al a

rea,

nm

2

Choice of Adsorptive

S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991Quantachrome Autosorb-I Operational Manual

Ar(g) in Ar(l) is preferable but because of unavailability of Ar(l) (87K), N2(l) (77 K) is used.

Ar can reach to somewhat smaller pores than N2.

Accurate measurement of micropores is possible using Ar.

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Oxy

gen

Arg

on

Nitr

ogen

Car

bon

mon

ooxi

deC

arbo

n di

oxid

e

Kry

pton

n-bu

tane

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Cro

ss-s

ecti

on

al a

rea,

nm

2

Choice of Adsorptive

S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991Quantachrome Autosorb-I Operational Manual

In case of activated carbon, CO2 is often the most preferred adsorbate.

Adsorption analysis of CO2 takes less time.

Limited to micropore analysis.

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Shape of Microporous Materials

Va

1P/Po

Type Ior

Langmuir

Type I isotherms don’t have hysteresis.

Pore shape cannot be determined by isotherm.

As various methods for pore size calculation are based on shape of pores, reliability of pore size calculation is questionable.

F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 439-446, 1999

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2 nm 50 nm

Micropores Mesopores Macropores

Methods Assumption

Pore Shape Based on ..

Brunauer MP method Cylindrical or Slit shaped de Boer’s t-method

Dubinin-Astakhov method - Polanyi potential theory

Independent of Kelvin equation

HK (Horvath-Kawazoe) method Slit Everett and Powl method

Independent of Kelvin equation

Saito-Foley method Cylindrical HK method

Choice of Method

P. A. Webb, C. Orr, Analytical Methods in Fine Particle Technology, Micromeritics, 53 – 152, 1997Quantachrome Autosorb-I Operational Manual

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2 nm 50 nm

Micropores Mesopores Macropores

Methods Assumption

Pore Shape Based on ..

BJH (Barrett, Joyner and Halenda) method

Cylindrical, Slit-shaped Kelvin equation

DH (Dollimore Heal) methodCylindrical t-method

Choice of Method

P. A. Webb, C. Orr, Analytical Methods in Fine Particle Technology, Micromeritics, 53 – 152, 1997Quantachrome Autosorb-I Operational Manual

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2 nm 50 nm

Micropores Mesopores Macropores

Methods Assumption

Pore Shape Based on ..

NLDFT (Non Local Density Functional Theory) and Monte Carlo simulation method

Cylindrical and slit Statistical thermodynamics

Choice of Method

P. A. Webb, C. Orr, Analytical Methods in Fine Particle Technology, Micromeritics, 53 – 152, 1997Quantachrome Autosorb-I Operational Manual