Characterization of Pore Structure: Foundation

Characterization of Pore Structure: Foundation

Characterization of Pore Structure: Foundation

Dr. Akshaya Jena

Director of Research

Porous Materials, Inc., USA

TopicsTopics

Characteristics of pore structureCharacterization techniques

Extrusion Flow Porometry Liquid Extrusion Porosimetry Mercury Intrusion Porosimetry

Pore structure

TopicsTopics

Vapor Adsorption Vapor Condensation

Conclusions

Nonmercury Intrusion Porosimetry

Pore StructurePore Structure

Typical Pore Structure

Pore StructurePore Structure

Three Different Kinds of Pores

Characteristics of Pore StructureCharacteristics of Pore Structure

Characteristics

Characteristics of Pore StructureCharacteristics of Pore StructureCharacteristics of Inhomogeneous Structure

Each Layer Eachconstituent

(Hydrophobic /Hydrophilic)

Gradation ofStructure

Eachorientation

Characteristics of Pore StructureCharacteristics of Pore Structure

Effects of application environment on pore structure characteristics

Characterization TechniquesCharacterization Techniques

Technique

Liquid Extrusion Liquid Intrusion Gas Adsorption1. Extrusion Flow

Porometry1. Mercury

IntrusionPorosimetry

1. VaporAdsorption

2. ExtrusionPorosimetry

2. Non-MercuryIntrusionPorosimetry

2. VaporCondensation

Extrusion Flow Porometry (Capillary Flow Porometry)Extrusion Flow Porometry (Capillary Flow Porometry)

Flows spontaneously into pores

Principle

Displacement of a wetting liquid from a poreWetting liquid:


For displacement of wetting (s/l<s/g) liquid from a pore by a gas

Principle

Displacement of a wetting liquid from a pore

Work done by gas = Increase in interfacial free energy


For all small displacement of liquid


For a wetting liquid:

p = l/g cos (dSs/g/dV)

(dSs/g/dV) = measure of pore size

p d V = s/g dSs/g+ s/l dSs/l + l/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 most pores size not defined

Types of pore cross-section


= [dS/dV](cylindrical opening of diameter, D)

= 4/D

D = [4l/g cos ]/p

Definition of pore diameter, D [dS/dV](pore)


Test Method

Dry CurveFlow rate, F versus p for a dry sample


Test MethodFor viscous flow

F = [/(256l ps)]iNiDi4][pi + po]p

= a constant

= 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


Dry curve normally concave upward

Membranes showing three different ways in which flow rate may vary with differential pressure

0

5

10

15

20

25

0 0.5 1 1.5Pressure (psi)

Flo

wra

te (

L/m

in)

Wet curve

Dry curve

1/2 Dry curve

0

5

10

15

20

25


Flo

wra

te (

L/m

in)

Wet curve

Dry curve

1/2 Dry curve

0

2

4

6

8

10

12

0 2 4 6 8 10 12Pressure (psi)

Flo

wra

te (

L/m

in)

Wet curve

Dry curve

1/2 Dry curve

0

2

4

6

8

10

12

0 2 4 6 8 10 12Pressure (psi)

Flo

wra

te (

L/m

in)

Wet curve

Dry curve

1/2 Dry curve

00.10.20.30.40.50.60.70.80.9

1

0 50 100 150 200 250Pressure (psi)

Flow

rate

(L/M

in)

Wet curve

Dry curve

1/2 Dry curve

00.10.20.30.40.50.60.70.80.9

1

0 50 100 150 200 250Pressure (psi)

Flow

rate

(L/M

in)

Wet curve

Dry curve

1/2 Dry curve


Nonviscous flowTortuous paths for flowHigh flow ratePore diameter Interaction of sample with liquid

Others possible shape of dry curve because of:High pressure


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

Initially there is no gas flow

0

5

10

15

20

25


Flo

wra

te (

L/m

in)

Wet curve

Dry curve

1/2 Dry curve

0

5

10

15

20

25


Flo

wra

te (

L/m

in)

Wet curve

Dry curve

1/2 Dry curve

Wet Curve F versus p for a wet sample


Equipment

The PMI Capillary Flow Porometer


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


Bubble point pressure in F vs p plot.

The largest pore diameter (Bubble Point Pore Diameter)


Calculation of bubble point pore diameterBubble point pressure (From Figure 15) = 0.299 psi

= 0.29968,947.6dynes/cm2

Surface tension of wetting liquid, l/g = 16 dynes/cmContact angle of low surface tensionliquid

0 , (cos = 1)

Using Equation 8:

D = [4(16 dynes/cm)1] / [0.299 psi][68,947.6 (dynes/cm2 ) / (psi)]= 3110-4 cm= 31 m


Mean flow pore diameter

Dry, wet and half-dry curves for a filter and the mean flow pressure


Pore diameter range

Largest - Bubble point pressure

Lowest - pressure at which wet and dry curves meet

0

5

10

15

20

25


Flo

wra

te (

L/m

in)

Wet curve

Dry curve

1/2 Dry curve

0

5

10

15

20

25


Flo

wra

te (

L/m

in)

Wet curve

Dry curve

1/2 Dry curve


(F w,j / Fd,j) = [g(D,N, …)]w,j/[g(D,N,…)]d,j

Cumulative filter flow

[(F w,j / Fd,j)x100]

Distribution:

F = [/ (256 l ps)] [iNiDi4][pi+po]p


Cumulative filter flow

[(Fw/Fd)x100] = D1D2[-fFdD]


fF = - d[Fw/Fd)x100]/dD

Flow distribution over pore diameter

Flow distribution over pore diameter

Area in a pore size range = % flow in that size range


Fractional pore number = Ni/iNi

Fractional pore number distribution

Fractional pore number distribution

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.2 0.4 0.6 0.8 1 1.2

Diameter, microns

Ni / S

um

(Ni)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.2 0.4 0.6 0.8 1 1.2

Diameter, microns

Ni / S

um

(Ni)


F = k (A/l)(pi-po)

Liquid permeabilityComputed from flow rate at average

pressure using Darcy’s law

Change of flow rate of water through paper as a function of

differential pressure

00.050.1

0.150.2

0.250.3

0.350.4

0.450.5

0 1 2 3 4 5 6

Differential Pressure (psi)

Flow

rat

e (c

c/se

c)

00.050.1

0.150.2

0.250.3

0.350.4

0.450.5

0 1 2 3 4 5 6


Flow

rat

e (c

c/se

c)


F = k (A/2lps)(pi+po)[pi-po]

Can be expressed in any unit:DarcyGurleyFrazierRayls

Gas permeabilityComputed from flow rate at STP

Flow of air through a filter

0

200

400

600

800

1000

1200

0 1 2 3 4 5


Flow

rat

e (c

c/se

c)

0

200

400

600

800

1000

1200

0 1 2 3 4 5


Flow

rat

e (c

c/se

c)


p = average pressure, [(pi+po)/2], where pi is the inlet pressure and po is the outlet pressure

Envelope Surface AreaBased on Kozeny-Carman relation [F l/p A] = {P3/[K(1-P)2S2]}

+ [ZP2]/[(1-P) S (2p)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

l = thickness of sample

p = pressure drop, (pi - po)

A = cross-sectional area of sample

P = porosity (pore volume / total volume)

= [1-(b/a)]

Envelope Surface Area

F = gas flow rate in volume at average pressure, p per unit time


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).

Envelope Surface Areab = bulk density of sample

a = true density of sample


Results particularly relevant for filtration media

Toxic materials, high pressures & subzero temperatures not used

A highly versatile technique

SummaryFlow Porometry measures a large

variety of important pore structure characteristics.

Extrusion PorosimetryExtrusion Porosimetry

Largest pore of membrane <Smallest pore of interest in sample p(to empty sample pores)<p(to empty membrane pores)

D = [4 l/g cos ]/p

Principle

Prevention of gas from flowing out after displacing wetting liquid in pore

Place membrane under the sample


Displaced liquid flows through membrane & measured

Principle of extrusion porosimetry


Gas that displaces liquid in sample pores does not pass through membrane

Principle of extrusion porosimetry


Extruded liquid (weight or volume) gives pore volume

Test methodDifferential pressure yields pore

diameter


Equipment

PMI Liquid Extrusion Porosimeter



Through pore volume

Pore volume plotted against differential pressure


Through pore diameter

Measured pore volume plotted against pore diameter

Extrusion PorosimetryExtrusion PorosimetryThrough pore volume distributionDistribution function

Area in any pore size range = volume of pores in that range

Pore Volume distribution function

fv = -(dV/d logD)


S = p dV/(l/g cos )Not very accurateSensitive to pore configurationOver estimates volume of pore throat

Through pore surface area Integration of Equation:

p = l/g cos (dSs/g/dV)


Liquid permeabilityFrom liquid flow rate

Liquid flow rate as a function of differential pressure


Does not use toxic materials, high pressures and subzero temperatures.

SummaryOnly technique that permits

measurement of through pore volume

Mercury Intrusion PorosimetryMercury Intrusion Porosimetry

Principle

Intrusion of a non-wetting liquid in to poreNon-wetting liquid cannot enter pores

spontaneously

s/l >s/g


Work done by the liquid = Increase in interfacial free energy

(p-pg) dV = (gs/l -gs/g) ds

P = (-l/g cos ) (dS/dV)

Pressurized liquid can enter pores


From definition of pore diameter(dS/dV) pore = (dS/dV) circular opening of diameter, D = 4/Dp = -4l/g cos /D

Test MethodMeasured intrusion pressure yields

pore diameter


Measured intrusion volume of mercury yields pore volume


Equipment

The PMI Mercury Intrusion Porosimeter

Mercury Intrusion PorosimeterMercury Intrusion Porosimeter


Through and blind pore volume

Intrusion volume with pressure


Through and blind pore diameter

Measurable pore diameters



Cumulative pore volume with pore diameter

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.001 0.01 0.1 1 10 100 1000

Pore Size (microns)

Cu

mu

lati

ve p

ore

Vo

lum

e (

cc/g

)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.001 0.01 0.1 1 10 100 1000

Pore Size (microns)

Cu

mu

lati

ve p

ore

Vo

lum

e (

cc/g

)



Examples of pore configurations in which some of the diameters are not measurable


Pore Volume distribution fv = -(dV/d log D)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 10 100 1000

pore diameter (microns)

dV

/ (d

lo

g p

)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 10 100 1000

pore diameter (microns)

dV

/ (d

lo

g p

)

Pore size distribution

Area in a size range = Pore volume in that range


Through and blind pore surface are

Cumulative surface area

S = [1/(-l/g cos )] p dV


Surface area not very accurateWide parts of ink-bottle pores

measured as pores with neck diameter

Inkbottle pore


At high pressures, correction terms in the small volume of small pores is appreciable

For very small pores, large pressure increases cause small increases in volume. The integral is less accurate.

Surface area not very accurate

Mercury Intrusion PorosiemtryMercury Intrusion Porosiemtry

Extrusion volume and hysteresis

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

1 10 100 1000 10000 100000

Pressure (psi)

Po

re V

olu

me

(cc/

g)

Intrusion

Extrusion

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

1 10 100 1000 10000 100000

Pressure (psi)

Po

re V

olu

me

(cc/

g)

Intrusion

Extrusion

Hysteresis in the intrusion-extrusion cycle

Mercury Intrusion Porosimetry Mercury Intrusion Porosimetry

Inkbottle pore


No flow characteristics are measurable

Uses toxic materials and high pressures

SummaryAlmost any material can be tested -

mercury in non-wetting to most materials

Non-Mercury Intrusion PorosimetryNon-Mercury Intrusion Porosimetry

Non-wetting intrusion liquid is NOT MERCURY

Water

Oil

Application liquid

Principle Exactly same as mercury intrusion

porosimetry


Measurable CharacteristicsAll characteristics measurable by

mercury intrusion porosimetry - measurable


Smaller pores measurableCan measure one kind of pores in a

mixture like the mixture of hydrophobic and hydrophilic pores


An order of magnitude low pressures used

Advantages over Mercury Intrusion Porosimetry

No toxic material used


Can detect one kind of pore in a mixture

SummaryCan measure all characteristics

measurable by Mercury Intrusion without using any toxic material or high pressures

Vapor AdsorptionVapor Adsorption

Weak van der Waal’s type interaction with surface

Multi-layer adsorption

PrinciplePhysical Adsorption

Adsorbed layers of molecules on a surface


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]

BET theory of physical adsorption

[p/(po-p)W] = [1/(WmC)] + [(c-1)/WmC](p/po)


Wm = 1/[(intercept)+(slope)]

Surface area:

S = WmNo

No = Avogadro’s number

= cross-sectional area of the adsorbed gas molecule

[p/po-p)W]versus(p/po)-linear


Only one layer of molecules gets bonded to the material

ChemisorptionChemical interaction between the gas

and the surface


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

Model for chemisorption (Langmuir)


Volumetric method:A known amount of gas is introduced in to

the sample chamber of known volumeAmount of gas left in the sample chamber

is computed from change in gas pressure

Test MethodSample maintained at constant

temperature


Weight gain of sample in the sample chamber is measured

Test MethodGravimetric method


Equipment

The PMI Sorptometer


[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)


Through and blind pore surface areaMultipoint surface area


Plot of [p/(po-p)W]versus (p/po)


Single point surface areaAssuming large C, Wm, is computed

from a single measurement

Good approximation for large C


Water Carbon monoxide Carbon dioxide Poisonous chemicals Many others

Over a wide range of temperature and pressure

ChemisorptionChemisorption of many chemicals

measurable


Chemisorption of ammonia at 25C plotted after p/W = [1/KWm)]+p[1/Wm]

/


Both through pore and blind pore surface areas are measured.

SummaryTechnique determines surface area

accurately

Vapor CondensationVapor Condensation

PrincipleCondensation of vapor in pore

Condensation in pore


dV = volume of condensed liquid V = molar volume of liquid dS = solid/liquid interfacial area

G[v(p)l (pore)]

dV({G[v(p)l(bulk)]}/V)+dSGs[s/vs/l] = 0


dV({G[v(p)l(bulk) = G[v(p)v(po)]

= RT ln (po/p)

Gs[s/vs/l] = (s/l - s/v)

ln(p/po) = -[4Vl/v cos /RT]/D


Definition of pore diameter (dS/dV) Pore

= (dS/dV)Cyliderical opening of diameter, D

= 4/D

ln(p/po) = -[4Vl/v cos /RT]/D


Measures amount of condensed vapor At a given pressure

Test methodMeasures relative vapor pressure

(p/po)


Equipment

The PMI Sorptometer



Through and blind pore volumeCondensation occurs in through &

blind pores

Variation of cumulative pore volume with relative pressure


Prior to condensation, pores contain adsorbed films True pore radius, rp

rp = (D/2)+t

t = thickness of adsorbed layer

Through and blind diameterDiameter of pore from condensation

ln(p/po) = -[4V l/v cos /RT]D


Variation of cumulative pore volume with pore diameter


Pore Volume DistributionDistribution function fv:

fv = -(dV/dD)

Area in any pore diameter range = volume of pores in that range

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 100 200 300 400

Pore Diameter (Angstorms)

dV

p/d

Dp

(cc/g

/A)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 100 200 300 400

Pore Diameter (Angstorms)

dV

p/d

Dp

(cc/g

/A)

Pore size distribution by gas adsorption


Macropores: >0.05m Mesopores: 0.002-0.05m Micropores: <0.002m

Pore structure of materials containing very small pores

Type of pores


Validity of relations: 0.0015mFor micropores data need to be

analyzed using other models

Capability Technique: 0.2-0.00035m

Pore structure of materials containing very small pores


Adsorption and desorption isotherms and hystersis

Adsorption and desorption isotherms

0

200

400

600

800

1000

1200

0 0.2 0.4 0.6 0.8 1P/Po

V@

ST

P (

cc/g

)

Adsorption

Desorption

0

200

400

600

800

1000

1200

0 0.2 0.4 0.6 0.8 1P/Po

V@

ST

P (

cc/g

)

Adsorption

Desorption


Adsorption/desorption isotherms for chemisorption of ammonia at 25C


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

Shape of adsorption curve many factors


Examples of a few different type of adsorption curves


No other technique can measure such characteristics

SummaryMeasure volume and diameter of very

small through and blind pores

ConclusionsConclusions

Extrusion TechniquesTwo recent techniques

Extrusion Flow Porometry & Liquid Extrusion Porosimetry have been

discussed in detail

ConclusionsConclusions

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

ConclusionConclusion

The techniques do not use toxic materials, high pressures or subzero temperatures

All characteristics particularly relevant for filtration are measurable


This technique can measure pore volume and pore diameters of through and blind pores in almost any material

Mercury Intrusion TechniquesThe widely used mercury intrusion

porosimetry has been briefly discussed


Uses very high pressures and mercury, which is toxic

Fluid flow characteristics cannot be measured


This technique can measure pore volume and diameter of through and blind pores like mercury intrusion porosimetry

Non- Mercury Intrusion TechniquesThe novel technique non-mercury

intrusion porosimetry has been discussed


No toxic material is used and pressure required is almost an order of magnitude less.


These techniques can measure surface area, pore diameter and pore volume of through and blind pores

Characteristics of very small pores are measurable

Gas adsorption & condensation techniquesThe widely used gas adsorption and condensation

techniques were discussed briefly


Flow properties are not measurableMany require subzero temperatures

Thank YouThank You

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Characterization of Pore Structure: Foundation