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### Characterization of Pore Structure: Foundation

Dr. Akshaya Jena

Director of Research

Porous Materials, Inc., USA

Topics

- Characteristics of pore structure
- Characterization techniques
- Extrusion Flow Porometry
- Liquid Extrusion Porosimetry
- Mercury Intrusion Porosimetry

- Pore structure

Extrusion Flow Porometry (Capillary Flow Porometry)

- Flows spontaneously into pores

Principle

Displacement of a wetting liquid from a pore

- Wetting liquid:

Extrusion Flow Porometry (Capillary Flow Porometry)

- For displacement of wetting (gs/l<gs/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

Extrusion Flow Porometry (Capillary Flow Porometry)

- For all small displacement of liquid

Extrusion Flow Porometry (Capillary Flow Porometry)

- For a wetting liquid:

p = gl/g cos q (dSs/g/dV)

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

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

Extrusion Flow Porometry (Capillary Flow Porometry)

- For most pores size not defined

Extrusion Flow Porometry (Capillary Flow Porometry)

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

= 4/D

D = [4gl/g cos q]/p

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

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

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

Extrusion Flow Porometry (Capillary Flow Porometry)- Dry curve normally concave upward

Extrusion Flow Porometry (Capillary Flow Porometry)

- Nonviscous flow
- Tortuous paths for flow
- High flow rate
- Pore diameter
- Interaction of sample with liquid

Others possible shape of dry curve because of:

- High pressure

Extrusion Flow Porometry (Capillary Flow Porometry)

Wet Curve

- F versus p for a wet sample

- 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

Variation of pore size along pore path and the measured pore diameter

Extrusion Flow Porometry (Capillary Flow Porometry)Measurable Characteristics

Through pore Throat Diameter

- The technique measured only the throat diameter

Extrusion Flow Porometry (Capillary Flow Porometry)

- Bubble point pressure in F vs p plot.

- The largest pore diameter (Bubble Point Pore Diameter)

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

Extrusion Flow Porometry (Capillary Flow Porometry)- Mean flow pore diameter

Extrusion Flow Porometry (Capillary Flow Porometry)

- Pore diameter range

Largest - Bubble point pressure

Lowest - pressure at which wet and dry curves meet

Extrusion Flow Porometry (Capillary Flow Porometry)

- (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

Flow distribution over pore diameter

Extrusion Flow Porometry (Capillary Flow Porometry)- fF = - d[Fw/Fd)x100]/dD

Flow distribution over pore diameter

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

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

Fractional pore number distribution

Extrusion Flow Porometry (Capillary Flow Porometry)- Fractional pore number = Ni/iNi

Fractional pore number distribution

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

Extrusion Flow Porometry (Capillary Flow Porometry)- F = k (A/ml)(pi-po)

Liquid permeability

- Computed from flow rate at average pressure using Darcy’s law

Extrusion Flow Porometry (Capillary Flow Porometry)

- F = k (A/2mlps)(pi+po)[pi-po]
- Can be expressed in any unit: Darcy Gurley Frazier Rayls

Gas permeability

- Computed from flow rate at STP

Extrusion Flow Porometry (Capillary Flow Porometry)

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

Envelope Surface Area

- Based on Kozeny-Carman relation

- [F l/p A] = {P3/[K(1-P)2S2m]} + [ZP2p]/[(1-P) S (2ppr)1/2

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

Extrusion Flow Porometry (Capillary Flow Porometry)

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)]

Envelope Surface Area

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

Extrusion Flow Porometry (Capillary Flow Porometry)

Envelope Surface Area

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 (48/13p).

rb = bulk density of sample

ra = true density of sample

Extrusion Flow Porometry (Capillary Flow Porometry)

- Results particularly relevant for filtration media
- Toxic materials, high pressures & subzero temperatures not used
- A highly versatile technique

Summary

- Flow Porometry measures a large variety of important pore structure characteristics.

Extrusion Porosimetry

- 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

Principle

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

- Place membrane under the sample

Principle of extrusion porosimetry

Extrusion Porosimetry- Displaced liquid flows through membrane & measured

Principle of extrusion porosimetry

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

Extrusion Porosimetry

- Extruded liquid (weight or volume) gives pore volume

Test method

- Differential pressure yields pore diameter

Pore volume plotted against differential pressure

Extrusion PorosimetryMeasurable Characteristics

Through pore volume

Pore Volume distribution function

Extrusion PorosimetryThrough pore volume distribution

- Distribution function

- fv = -(dV/d logD)

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

Extrusion Porosimetry

S = p dV/(gl/g cos q)

- Not very accurate
- Sensitive to pore configuration
- Over estimates volume of pore throat

Through pore surface area

- Integration of Equation:p = gl/g cos q (dSs/g/dV)

Liquid flow rate as a function of differential pressure

Extrusion PorosimetryLiquid permeability

- From liquid flow rate

Extrusion Porosimetry

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

Summary

- Only technique that permits measurement of through pore volume

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

- Work done by the liquid = Increase in interfacial free energy
- (p-pg) dV = (gs/l -gs/g) dsP = (-gl/g cos q) (dS/dV)

- Pressurized liquid can enter pores

Mercury Intrusion Porosimetry

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

Mercury Intrusion Porosimetry

Test Method

- Measured intrusion pressure yields pore diameter

- Measured intrusion volume of mercury yields pore volume

Intrusion volume with pressure

Mercury Intrusion PorosimeterMeasurable Characteristics

Through and blind pore volume

Cumulative pore volume with pore diameter

Mercury Intrusion PorosimetryThrough and blind pore diameter

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

Mercury Intrusion PorosimetryThrough and blind pore diameter

Mercury Intrusion Porosimetry

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

- Area in a size range = Pore volume in that range

Mercury Intrusion Porosimetry

Surface area not very accurate

- Wide parts of ink-bottle pores measured as pores with neck diameter

Mercury Intrusion Porosimetry

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

Surface area not very accurate

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

Hysteresis in the intrusion-extrusion cycle

Mercury Intrusion PorosiemtryExtrusion volume and hysteresis

Mercury Intrusion Porosimetry

- No flow characteristics are measurable
- Uses toxic materials and high pressures

Summary

- Almost any material can be tested - mercury in non-wetting to most materials

Non-Mercury Intrusion Porosimetry

- Non-wetting intrusion liquid is NOT MERCURY

Water

Oil

Application liquid

Principle

- Exactly same as mercury intrusion porosimetry

Non-Mercury Intrusion Porosimetry

Measurable Characteristics

- All characteristics measurable by mercury intrusion porosimetry - measurable

Non-Mercury Intrusion Porosimetry

Measurable Characteristics

- Smaller pores measurable
- Can measure one kind of pores in a mixture like the mixture of hydrophobic and hydrophilic pores

- Advantages over Mercury Intrusion Porosimetry
- No toxic material used

- An order of magnitude low pressures used

Non-Mercury Intrusion Porosimetry

- Can detect one kind of pore in a mixture

Summary

- Can measure all characteristics measurable by Mercury Intrusion without using any toxic material or high pressures

Adsorbed layers of molecules on a surface

Vapor Adsorption- Weak van der Waal’s type interaction with surface
- Multi-layer adsorption

Principle

- Physical Adsorption

Vapor Adsorption

- 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)

Vapor Adsorption

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

- Surface area:

S = WmNoa

No = Avogadro’s number

a = cross-sectional area of the adsorbed gas molecule

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

Vapor Adsorption

- Only one layer of molecules gets bonded to the material

Chemisorption

- Chemical interaction between the gas and the surface

Vapor Adsorption

- 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)

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

- Weight gain of sample in the sample chamber is measured

Test Method

- Gravimetric method

Vapor Adsorption

- [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)

Measurable Characteristics

Through and blind pore surface area

- Multipoint surface area

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

- Both through pore and blind pore surface areas are measured.

Summary

- Technique determines surface area accurately

Vapor Condensation

- 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

Vapor Condensation

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

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

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

= RT ln (po/p)

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

- Measures amount of condensed vapor At a given pressure

Test method

- Measures relative vapor pressure (p/po)

Variation of cumulative pore volume with relative pressure

Vapor CondensationMeasurable Characteristics

Through and blind pore volume

- Condensation occurs in through & blind pores

Vapor Condensation

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

rp = (D/2)+t

t = thickness of adsorbed layer

Through and blind diameter

- Diameter of pore from condensation

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

Pore size distribution by gas adsorption

Vapor CondensationPore Volume Distribution

- Distribution function fv:fv = -(dV/dD)

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

Vapor Condensation

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

Pore structure of materials containing very small pores

- Type of pores

Vapor Condensation

- Validity of relations: 0.0015mm
- For micropores data need to be analyzed using other models

Pore structure of materials containing very small pores

- Capability
- Technique: 0.2-0.00035mm

Adsorption and desorption isotherms

Vapor CondensationAdsorption and desorption isotherms and hystersis

Vapor Condensation

- 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

Vapor Condensation

- No other technique can measure such characteristics

Summary

- Measure volume and diameter of very small through and blind pores

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

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

- All characteristics particularly relevant for filtration are measurable

Conclusion

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

Mercury Intrusion Techniques

- The widely used mercury intrusion porosimetry has been briefly discussed

Conclusion

- Uses very high pressures and mercury, which is toxic

- Fluid flow characteristics cannot be measured

Conclusion

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

Non- Mercury Intrusion Techniques

- The novel technique non-mercury intrusion porosimetry has been discussed

Conclusion

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

Conclusion

- 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 techniques

- The widely used gas adsorption and condensation techniques were discussed briefly

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