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Characterization of Powders, Porous Solids and Suspensions
Lecture 8
Main Characteristics of Powders and Porous Solids
Particle size Surface area Porosity
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…
What is Particle Size?
SEM of real ibuprofen particles
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
Different Equivalent Spheres
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
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;
Particle Size by Direct Observation
Google for ImageJ
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)(
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)
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.
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.
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.
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.
Schematics of Zetasizer Nano
Measurement of Porosity and Specific Surface Area by
Gas Adsorption
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
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
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.
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).
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
Experimental Techniques
Techniques for Porosity Analysis
Mercuryporosimetry
TEM
SEM
Small angleX-ray
scattering
SmallAngle
Neutron scattering
Gas adsorption
Techniques
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
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
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
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
Mercuryporosimetry
TEM
SEM
Small angleX-ray
scattering
SmallAngle
Neutron scattering
Gas adsorption
Techniques
Any pore size Open + Close
porosity
Techniques for Porosity Analysis
Mercuryporosimetry
TEM
SEM
Small angleX-ray
scattering
SmallAngle
Neutron scattering
Gas adsorption
Techniques
Any pore size Open & Close
porosity Costly
Techniques for Porosity Analysis
Theory of Adsorption
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
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
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
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
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
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
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
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
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
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
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
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
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
Porosity Analyzer
Outgassing station
Analysis station
Liquid nitrogen bath
Steps for Measurement
3. Interpretation
2. Adsorption Analysis
1. Sample Preparation
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
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
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
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
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
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.
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.
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
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
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
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