Transcript Characterization of Pore Structure: Foundation

Characterization of Pore
Structure: Foundation
Dr. Akshaya Jena
Director of Research
Porous Materials, Inc., USA
Topics
 Pore structure
 Characteristics of pore structure
 Characterization techniques
 Extrusion Flow Porometry
 Liquid Extrusion Porosimetry
 Mercury Intrusion Porosimetry
Topics
 Nonmercury Intrusion Porosimetry
 Vapor Adsorption
 Vapor Condensation
 Conclusions
Pore Structure
Typical Pore Structure
Pore Structure
Three Different Kinds of Pores
Characteristics of Pore Structure
Characteristics
Characteristics of Pore Structure
Characteristics of Inhomogeneous Structure
Each Layer
Each
constituent
(Hydrophobic /
Hydrophilic)
Gradation of
Structure
Each
orientation
Characteristics of Pore Structure
Effects of application environment on pore
structure characteristics
Characterization Techniques
Technique
Liquid Extrusion Liquid Intrusion
1. Extrusion Flow 1. Mercury
Porometry
Intrusion
Porosimetry
2. Extrusion
2. Non-Mercury
Porosimetry
Intrusion
Porosimetry
Gas Adsorption
1. Vapor
Adsorption
2. Vapor
Condensation
Extrusion Flow Porometry
(Capillary Flow Porometry)
Principle
Displacement of a wetting liquid from a
pore
 Wetting liquid:
 Flows spontaneously
into pores
Extrusion Flow Porometry
(Capillary Flow Porometry)
Principle
Displacement of a wetting liquid from a
pore
 For displacement of wetting (gs/l<gs/g)
liquid from a pore by a gas
 Work done by gas
= Increase in interfacial
free energy
Extrusion Flow Porometry
(Capillary Flow Porometry)
 For all small displacement of liquid
Extrusion Flow Porometry
(Capillary Flow Porometry)
p d V = gs/g dSs/g+ gs/l dSs/l + gl/g dSl/g
p = differential pressure
dV = infinitesimal increase in volume of the gas
in the pore
dSs/g = infinitesimal increase in interfacial area
 For a wetting liquid:
p = gl/g cos q (dSs/g/dV)
(dSs/g/dV) = measure of pore size
Extrusion Flow Porometry
(Capillary Flow Porometry)
 For most pores size not defined
Types of pore cross-section
Extrusion Flow Porometry
(Capillary Flow Porometry)
Definition of pore diameter, D
[dS/dV](pore)
= [dS/dV](cylindrical opening of
diameter, D)
= 4/D
D = [4gl/g cos q]/p
Extrusion Flow Porometry
(Capillary Flow Porometry)
Test Method
Dry Curve
 Flow rate, F versus p for a dry sample
Extrusion Flow Porometry
(Capillary Flow Porometry)
Test Method
 For viscous flow
F = [/(256m l ps)]iNiDi4][pi + po]p
 = a constant
m = viscosity of gas
l = thickness
ps = standard pressure
Ni = number of pores of diameter Di
p = differential pressure, inlet pressure, pi minus
outlet pressure, po
Extrusion Flow Porometry
(Capillary Flow Porometry)
 Dry curve normally concave upward
12
25
Wet curve
Dry curve
1/2 Dry curve
Wet curve
Dry curve
1/2 Dry curve
10
Flowrate (L/min)
Flowrate (L/min)
20
15
10
5
8
6
4
2
0
0.5
1
0
1.5
0
Pressure (psi)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
2
4
6
Pressure (psi)
8
10
Wet curve
Dry curve
1/2 Dry curve
Flowrate (L/Min)
0
0
50
100
150
Pressure (psi)
200
250
Membranes showing three different ways in which flow
rate may vary with differential pressure
12
Extrusion Flow Porometry
(Capillary Flow Porometry)
Others possible shape of dry curve
because of:
 High pressure
 Nonviscous flow
 Tortuous paths for flow
 High flow rate
 Pore diameter
 Interaction of sample with liquid
Extrusion Flow Porometry
(Capillary Flow Porometry)
25
Wet curve
Dry curve
1/2 Dry curve
20
Flowrate (L/min)
Wet Curve
 F versus p for a wet sample
 Initially there is no gas flow
 The largest pore is emptied first
and gas flow begins
 With increase in differential
pressure smaller pores are
emptied and gas flow increases
 When all pores are empty wet
curve converges with the dry
curve with the dry curve
15
10
5
0
0
0.5
1
Pressure (psi)
1.5
Extrusion Flow Porometry
(Capillary Flow Porometry)
 Equipment
The PMI Capillary Flow Porometer
Extrusion Flow Porometry
(Capillary Flow Porometry)
Measurable Characteristics
Through pore Throat Diameter
 The technique measured only the
throat diameter
Variation of pore size along pore path and
the measured pore diameter
Extrusion Flow Porometry
(Capillary Flow Porometry)
 The largest pore diameter (Bubble
Point Pore Diameter)
 Bubble point pressure in F vs p plot.
Extrusion Flow Porometry
(Capillary Flow Porometry)
Calculation of bubble point pore diameter
Bubble point pressure (From Figure 15) = 0.299 psi
= 0.29968,947.6
dynes/cm2
= 16 dynes/cm
Surface tension of wetting liquid, gl/g
Contact angle q of low surface tension  0, (cos q = 1)
liquid
Using Equation 8:
D = [4(16 dynes/cm)1] / [0.299 psi][68,947.6 (dynes/cm2 ) / (psi)]
= 3110-4 cm
= 31 mm
Extrusion Flow Porometry
(Capillary Flow Porometry)
 Mean flow pore diameter
Dry, wet and half-dry curves for a filter and the
mean flow pressure
Extrusion Flow Porometry
(Capillary Flow Porometry)
 Pore diameter range
Largest - Bubble point pressure
Lowest - pressure at which wet and
dry curves meet
25
Wet curve
Dry curve
1/2 Dry curve
Flowrate (L/min)
20
15
10
5
0
0
0.5
1
Pressure (psi)
1.5
Extrusion Flow Porometry
(Capillary Flow Porometry)
Distribution:
 F = [/ (256m l ps)] [iNiDi4][pi+po]p
 (F w,j / Fd,j) = [g(D,N, …)]w,j/[g(D,N,…)]d,j
 Cumulative filter flow
 [(F w,j / Fd,j)x100]
Extrusion Flow Porometry
(Capillary Flow Porometry)
120
cum FF (%)
100
80
60
40
A
20
0
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28
diameter (microns)
Cumulative filter flow
Extrusion Flow Porometry
(Capillary Flow Porometry)
Flow distribution over pore diameter
 fF = - d[Fw/Fd)x100]/dD
Flow distribution over
pore diameter
Pore size distribution
60
50
40
30
20
Area=A
10
0
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28
diameter (microns)
 [(Fw/Fd)x100] = D1D2[-fFdD]
 Area in a pore size range = % flow in
that size range
Extrusion Flow Porometry
(Capillary Flow Porometry)
Fractional pore number distribution
 Fractional pore number = Ni/iNi
0.3
Ni / Sum(Ni)
0.25
0.2
0.15
0.1
0.05
0
0
0.2
0.4
0.6
0.8
Diameter, microns
1
1.2
Fractional pore number distribution
Extrusion Flow Porometry
(Capillary Flow Porometry)
Change of flow rate of water
through paper as a function
of differential pressure
Flow rate (cc/sec)
Liquid permeability
 Computed from flow rate at average
pressure using Darcy’s law
 F = k (A/ml)(pi-po)
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
4
Differential Pressure (psi)
5
6
Extrusion Flow Porometry
(Capillary Flow Porometry)
Gas permeability
 Computed from flow rate at STP
 F = k (A/2mlps)(pi+po)[pi-po]
 Can be expressed in any unit:
Darcy
Gurley
Frazier
Rayls
Flow rate (cc/sec)
1200
1000
800
600
400
200
0
0
1
2
3
4
Differential Pressure (psi)
Flow of air through a filter
5
Extrusion Flow Porometry
(Capillary Flow Porometry)
Envelope Surface Area
 Based on Kozeny-Carman relation
 [F l/p A] = {P3/[K(1-P)2S2m]}
+ [ZP2]/[(1-P) S (2pr)1/2
F = gas flow rate in volume at average pressure,
p per unit time
p = average pressure, [(pi+po)/2], where pi is the
inlet pressure and po is the outlet pressure
Extrusion Flow Porometry
(Capillary Flow Porometry)
Envelope Surface Area
F = gas flow rate in volume at average pressure,
p per unit time
p = average pressure, [(pi+po)/2], where pi is the
inlet pressure and po is the outlet pressure
l = thickness of sample
p = pressure drop, (pi - po)
A = cross-sectional area of sample
P = porosity (pore volume / total volume)
= [1-(rb/ra)]
Extrusion Flow Porometry
(Capillary Flow Porometry)
Envelope Surface Area
rb = bulk density of sample
ra = true density of sample
S = through pore surface area per unit volume
of solid in the sample
m = viscosity of gas
r = density of the gas at the average pressure, p
K = a constant dependent on the geometry of
the pores in the porous media. It has a value
close to 5 for random pored media
Z = a constant. It is shown to be (48/13).
Extrusion Flow Porometry
(Capillary Flow Porometry)
Summary
 Flow Porometry measures a large
variety of important pore structure
characteristics.
 Results particularly relevant for
filtration media
 Toxic materials, high pressures &
subzero temperatures not used
 A highly versatile technique
Extrusion Porosimetry
Principle
Prevention of gas from flowing out after
displacing wetting liquid in pore
 Place membrane under the sample
 Largest pore of membrane <Smallest
pore of interest in sample
p(to empty sample pores)<p(to empty
membrane pores)
 D = [4 gl/g cos q]/p
Extrusion Porosimetry
Principle of extrusion porosimetry
 Displaced liquid flows through
membrane & measured
Extrusion Porosimetry
Principle of extrusion porosimetry
 Gas that displaces liquid in sample pores
does not pass through membrane
Extrusion Porosimetry
Test method
 Differential pressure yields pore
diameter
 Extruded liquid (weight or volume)
gives pore volume
Extrusion Porosimetry
Equipment
PMI Liquid Extrusion Porosimeter
Extrusion Porosimetry
Measurable Characteristics
Through pore volume
Pore volume plotted against differential pressure
Extrusion Porosimetry
Through pore diameter
Measured pore volume plotted against pore diameter
Extrusion Porosimetry
Through pore volume distribution
 Distribution function
 fv = -(dV/d logD)
Pore Volume distribution function
 Area in any pore size range
= volume of pores in that range
Extrusion Porosimetry
Through pore surface area
 Integration of Equation:
p = gl/g cos q (dSs/g/dV)
S = p dV/(gl/g cos q)
 Not very accurate
 Sensitive to pore configuration
 Over estimates volume of pore throat
Extrusion Porosimetry
Liquid permeability
 From liquid flow rate
Liquid flow rate as a function of differential pressure
Extrusion Porosimetry
Summary
 Only technique that permits
measurement of through pore volume
 Does not use toxic materials, high
pressures and subzero temperatures.
Mercury Intrusion Porosimetry
Principle
Intrusion of a non-wetting liquid in to pore
 Non-wetting liquid cannot enter pores
spontaneously
 gs/l >gs/g
Mercury Intrusion Porosimetry
 Pressurized liquid can enter pores
 Work done by the liquid = Increase in
interfacial free energy
 (p-pg) dV = (gs/l -gs/g) ds

P = (-gl/g cos q) (dS/dV)
Mercury Intrusion Porosimetry
 From definition of pore diameter
(dS/dV) pore = (dS/dV) circular
opening of diameter, D
= 4/D
p = -4gl/g cos q/D
Mercury Intrusion Porosimetry
Test Method
 Measured intrusion pressure yields
pore diameter
 Measured intrusion volume of
mercury yields pore volume
Mercury Intrusion Porosimetry
 Equipment
The PMI Mercury Intrusion Porosimeter
Mercury Intrusion Porosimeter
Measurable Characteristics
Through and blind pore volume
Intrusion volume with pressure
Mercury Intrusion Porosimetry
Through and blind pore diameter
Measurable pore diameters
Mercury Intrusion Porosimetry
Through and blind pore diameter
0.045
Cumulative pore Volume (cc/g)
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0.001
0.01
0.1
1
10
100
1000
Pore Size (microns)
Cumulative pore volume with pore diameter
Mercury Intrusion Porosimetry
Through and blind pore diameter
Examples of pore configurations in which some of
the diameters are not measurable
Mercury Intrusion Porosimetry
 Pore Volume distribution
 fv = -(dV/d log D)
2
1.8
Pore size
distribution
dV/ (d log p)
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1
10
100
1000
pore diameter (microns)
 Area in a size range = Pore volume in
that range
Mercury Intrusion Porosimetry
Through and blind pore surface are
 S = [1/(-gl/g cos q)] p dV
Cumulative surface area
Mercury Intrusion Porosimetry
Surface area not very accurate
 Wide parts of ink-bottle pores
measured as pores with neck
diameter
Inkbottle pore
Mercury Intrusion Porosimetry
Surface area not very accurate
 For very small pores, large pressure
increases cause small increases in
volume. The integral is less accurate.
 At high pressures, correction terms in
the small volume of small pores is
appreciable
Mercury Intrusion Porosiemtry
Extrusion volume and hysteresis
0.045
Pore Volume (cc/g)
0.04
0.035
0.03
0.025
0.02
0.015
0.01
Intrusion
Extrusion
0.005
0
1
10
100
1000
10000
100000
Pressure (psi)
Hysteresis in the intrusion-extrusion cycle
Mercury Intrusion Porosimetry
Inkbottle pore
Mercury Intrusion Porosimetry
Summary
 Almost any material can be tested mercury in non-wetting to most
materials
 No flow characteristics are
measurable
 Uses toxic materials and high
pressures
Non-Mercury Intrusion Porosimetry
Principle
 Exactly same as mercury intrusion
porosimetry
 Non-wetting intrusion liquid is
NOT MERCURY
Water
Oil
Application liquid
Non-Mercury Intrusion Porosimetry
Measurable Characteristics
 All characteristics measurable by
mercury intrusion porosimetry measurable
Non-Mercury Intrusion Porosimetry
Measurable Characteristics
 Advantages over Mercury Intrusion
Porosimetry
 No toxic material used
 An order of magnitude low pressures
used
 Smaller pores measurable
 Can measure one kind of pores in a
mixture like the mixture of
hydrophobic and hydrophilic pores
Non-Mercury Intrusion Porosimetry
Summary
 Can measure all characteristics
measurable by Mercury Intrusion
without using any toxic material or
high pressures
 Can detect one kind of pore in a
mixture
Vapor Adsorption
Principle
 Physical Adsorption
 Weak van der Waal’s type interaction
with surface
 Multi-layer adsorption
Adsorbed layers of molecules on a surface
Vapor Adsorption
 BET theory of physical adsorption
[p/(po-p)W] = [1/(WmC)] + [(c-1)/WmC](p/po)
 W = amount of adsorbed gas
 Wm = amount of gas that can form a
monomolecular layer
 C = a dimensionless constant
 = (A1v2/A2v1) exp [(E-L)/RT]
Vapor Adsorption
 [p/po-p)W]versus(p/po)-linear
Wm = 1/[(intercept)+(slope)]
 Surface area:
S = WmNoa
No = Avogadro’s number
a = cross-sectional area of the
adsorbed gas molecule
Vapor Adsorption
Chemisorption
 Chemical interaction between the gas
and the surface
 Only one layer of molecules gets
bonded to the material
Vapor Adsorption
 Model for chemisorption (Langmuir)
 p/W = [1(KWm)]+p[1/Wm]
 p = pressure of gas
 W = amount of adsorbed gas
 K = Ko exp(E/RT)
 Wm = amount of adsorbed gas for a
completed monomolecular layer
Vapor Adsorption
Test Method
 Sample maintained at constant
temperature
 Volumetric method:
 A known amount of gas is introduced
in to the sample chamber of known
volume
 Amount of gas left in the sample
chamber is computed from change in
gas pressure
Vapor Adsorption
Test Method
 Gravimetric method
 Weight gain of sample in the sample
chamber is measured
Vapor Adsorption
 Equipment
The PMI Sorptometer
Vapor Adsorption
Measurable Characteristics
Through and blind pore surface area
 Multipoint surface area
 [p/(po-p)W]versus(p/po)linear in the
range 0.05< (p/po)<0.35
 Plot of [p/(po-p)W]versus (p/po)
Vapor Adsorption
Plot of [p/(po-p)W]versus (p/po)
Vapor Adsorption
Single point surface area
 Assuming large C, Wm, is computed
from a single measurement
 Good approximation for large C
Vapor Adsorption
Chemisorption
 Chemisorption of many chemicals
measurable
 Water
 Carbon monoxide
 Carbon dioxide
 Poisonous chemicals
 Many others
 Over a wide range of temperature and
pressure
/
Vapor Adsorption
Chemisorption of ammonia at 25C plotted after
p/W = [1/KWm)]+p[1/Wm]
Vapor Adsorption
Summary
 Technique determines surface area
accurately
 Both through pore and blind pore
surface areas are measured.
Vapor Condensation
Principle
 Condensation of vapor in pore
Condensation in pore
Vapor Condensation
 G[v(p)l (pore)]
dV({G[v(p)l(bulk)]}/V)
+dSGs[s/vs/l] = 0
 dV = volume of condensed liquid
 V = molar volume of liquid
 dS = solid/liquid interfacial area
Vapor Condensation
dV({G[v(p)l(bulk) = G[v(p)v(po)]
= RT ln (po/p)
Gs[s/vs/l] = (gs/l - gs/v)
ln(p/po) = -[4Vgl/v cos q/RT]/D
Vapor Condensation
 Definition of pore diameter (dS/dV)
Pore
= (dS/dV)Cyliderical opening of
diameter, D
= 4/D
ln(p/po) = -[4Vgl/v cos q/RT]/D
Vapor Condensation
Test method
 Measures relative vapor pressure
(p/po)
 Measures amount of condensed
vapor At a given pressure
Vapor Condensation
 Equipment
The PMI Sorptometer
Vapor Condensation
Measurable Characteristics
Through and blind pore volume
 Condensation occurs in through &
blind pores
Variation of cumulative pore volume with
relative pressure
Vapor Condensation
Through and blind diameter
 Diameter of pore from condensation
ln(p/po) = -[4V gl/v cos q/RT]D
 Prior to condensation, pores contain
adsorbed films
 True pore radius, rp
rp = (D/2)+t
t = thickness of adsorbed layer
Vapor Condensation
Variation of cumulative pore volume with
pore diameter
Vapor Condensation
Pore Volume Distribution
 Distribution function fv:
fv = -(dV/dD)
0.035
0.03
Pore size distribution
by gas adsorption
dVp/dDp (cc/g/A)
0.025
0.02
0.015
0.01
0.005
0
0
100
200
300
Pore Diameter (Angstorms)
 Area in any pore diameter range =
volume of pores in that range
400
Vapor Condensation
Pore structure of materials containing
very small pores
 Type of pores
 Macropores: >0.05mm
 Mesopores: 0.002-0.05mm
 Micropores: <0.002mm
Vapor Condensation
Pore structure of materials containing
very small pores
 Capability
 Technique: 0.2-0.00035mm
 Validity of relations:  0.0015mm
 For micropores data need to be
analyzed using other models
Vapor Condensation
Adsorption and desorption isotherms
and hystersis
1200
Adsorption
1000
V@STP (cc/g)
Desorption
800
600
400
200
0
0
0.2
0.4
0.6
0.8
1
P/Po
Adsorption and desorption isotherms
Vapor Condensation
Adsorption/desorption isotherms for
chemisorption of ammonia at 25C
Vapor Condensation
 Shape of adsorption curve  many
factors
 Large number of larger pores  High
adsorption at high pressure
 Large number of small pores 
saturation
 Strong interaction of adsorbate with
the adsorbed  increasing
adsorption
Vapor Condensation
Examples of a few different type of adsorption curves
Vapor Condensation
Summary
 Measure volume and diameter of very
small through and blind pores
 No other technique can measure such
characteristics
Conclusions
Extrusion Techniques
 Two recent techniques
Extrusion Flow Porometry & Liquid
Extrusion Porosimetry have been
discussed in detail
Conclusions
 The techniques are capable of
measuring a wide variety of pore
structure characteristics of through
pores including fluid flow
characteristics, which other
techniques cannot measure
Conclusion
 All characteristics particularly
relevant for filtration are measurable
 The techniques do not use toxic
materials, high pressures or subzero
temperatures
Conclusion
Mercury Intrusion Techniques
 The widely used mercury intrusion
porosimetry has been briefly
discussed
 This technique can measure pore
volume and pore diameters of
through and blind pores in almost
any material
Conclusion
 Fluid flow characteristics cannot be
measured
 Uses very high pressures and
mercury, which is toxic
Conclusion
Non- Mercury Intrusion Techniques
 The novel technique non-mercury
intrusion porosimetry has been
discussed
 This technique can measure pore
volume and diameter of through and
blind pores like mercury intrusion
porosimetry
Conclusion
 No toxic material is used and
pressure required is almost an order
of magnitude less.
Conclusion
Gas adsorption & condensation techniques
 The widely used gas adsorption and
condensation techniques were
discussed briefly
 These techniques can measure
surface area, pore diameter and pore
volume of through and blind pores
 Characteristics of very small pores
are measurable
Conclusion
 Flow properties are not measurable
 Many require subzero temperatures
Thank You