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**Characterization of Pore Structure: Foundation**

Dr. Akshaya Jena Director of Research Porous Materials, Inc., USA

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**Topics Pore structure Characteristics of pore structure**

Characterization techniques Extrusion Flow Porometry Liquid Extrusion Porosimetry Mercury Intrusion Porosimetry

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**Topics Conclusions Nonmercury Intrusion Porosimetry Vapor Adsorption**

Vapor Condensation Conclusions

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**Typical Pore Structure**

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**Three Different Kinds of Pores**

Pore Structure Three Different Kinds of Pores

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**Characteristics of Pore Structure**

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**Characteristics of Pore Structure**

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**Characteristics of Pore Structure**

Effects of application environment on pore structure characteristics

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**Characterization Techniques**

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

Principle Displacement of a wetting liquid from a pore Wetting liquid: Flows spontaneously into pores

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**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

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

For all small displacement of liquid

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**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

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

For most pores size not defined Types of pore cross-section

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**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

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

Test Method Dry Curve Flow rate, F versus p for a dry sample

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**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

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

Dry curve normally concave upward Membranes showing three different ways in which flow rate may vary with differential pressure

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**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

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

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

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

Equipment The PMI Capillary Flow Porometer

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**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

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

The largest pore diameter (Bubble Point Pore Diameter) Bubble point pressure in F vs p plot.

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

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

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

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

Pore diameter range Largest - Bubble point pressure Lowest - pressure at which wet and dry curves meet

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

Distribution: F = [/ (256 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]

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

Cumulative filter flow

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

Flow distribution over pore diameter 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

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

Fractional pore number distribution Fractional pore number = Ni/iNi Fractional pore number distribution

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

Liquid permeability Computed from flow rate at average pressure using Darcy’s law F = k (A/ml)(pi-po) Change of flow rate of water through paper as a function of differential pressure

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**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 of air through a filter

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

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

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**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)]

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**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 (48/13p).

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**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

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**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

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**Extrusion Porosimetry**

Principle of extrusion porosimetry Displaced liquid flows through membrane & measured

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**Extrusion Porosimetry**

Principle of extrusion porosimetry Gas that displaces liquid in sample pores does not pass through membrane

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**Extrusion Porosimetry**

Test method Differential pressure yields pore diameter Extruded liquid (weight or volume) gives pore volume

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**Extrusion Porosimetry**

Equipment PMI Liquid Extrusion Porosimeter

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**Extrusion Porosimetry**

Measurable Characteristics Through pore volume Pore volume plotted against differential pressure

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**Extrusion Porosimetry**

Through pore diameter Measured pore volume plotted against pore diameter

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**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

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**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

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**Extrusion Porosimetry**

Liquid permeability From liquid flow rate Liquid flow rate as a function of differential pressure

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**Extrusion Porosimetry**

Summary Only technique that permits measurement of through pore volume Does not use toxic materials, high pressures and subzero temperatures.

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**Mercury Intrusion Porosimetry**

Principle Intrusion of a non-wetting liquid in to pore Non-wetting liquid cannot enter pores spontaneously gs/l >gs/g

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**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)

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**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

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**Mercury Intrusion Porosimetry**

Test Method Measured intrusion pressure yields pore diameter Measured intrusion volume of mercury yields pore volume

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**Mercury Intrusion Porosimetry**

Equipment The PMI Mercury Intrusion Porosimeter

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**Mercury Intrusion Porosimeter**

Measurable Characteristics Through and blind pore volume Intrusion volume with pressure

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**Mercury Intrusion Porosimetry**

Through and blind pore diameter Measurable pore diameters

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**Mercury Intrusion Porosimetry**

Through and blind pore diameter Cumulative pore volume with pore diameter

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**Mercury Intrusion Porosimetry**

Through and blind pore diameter Examples of pore configurations in which some of the diameters are not measurable

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**Mercury Intrusion Porosimetry**

Pore Volume distribution fv = -(dV/d log D) Pore size distribution Area in a size range = Pore volume in that range

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**Mercury Intrusion Porosimetry**

Through and blind pore surface are S = [1/(-gl/g cos q)] p dV Cumulative surface area

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**Mercury Intrusion Porosimetry**

Surface area not very accurate Wide parts of ink-bottle pores measured as pores with neck diameter Inkbottle pore

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**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

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**Mercury Intrusion Porosiemtry**

Extrusion volume and hysteresis Hysteresis in the intrusion-extrusion cycle

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**Mercury Intrusion Porosimetry**

Inkbottle pore

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**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

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**Non-Mercury Intrusion Porosimetry**

Principle Exactly same as mercury intrusion porosimetry Non-wetting intrusion liquid is NOT MERCURY Water Oil Application liquid

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**Non-Mercury Intrusion Porosimetry**

Measurable Characteristics All characteristics measurable by mercury intrusion porosimetry - measurable

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**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

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**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

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**Adsorbed layers of molecules on a surface**

Vapor Adsorption Principle Physical Adsorption Weak van der Waal’s type interaction with surface Multi-layer adsorption Adsorbed layers of molecules on a surface

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**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]

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**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

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**Vapor Adsorption Chemisorption**

Chemical interaction between the gas and the surface Only one layer of molecules gets bonded to the material

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**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

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**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

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**Vapor Adsorption Test Method Gravimetric method**

Weight gain of sample in the sample chamber is measured

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Vapor Adsorption Equipment The PMI Sorptometer

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**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)

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

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

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**Vapor Adsorption Single point surface area**

Assuming large C, Wm, is computed from a single measurement Good approximation for large C

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**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

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

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

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**Vapor Adsorption Summary Technique determines surface area accurately**

Both through pore and blind pore surface areas are measured.

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**Vapor Condensation Principle Condensation of vapor in pore**

Condensation in pore

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**Vapor Condensation G[v(p)l (pore)]**

dV({G[v(p)l(bulk)]}/V) +dSGs[s/vs/l] = 0 dV = volume of condensed liquid V = molar volume of liquid dS = solid/liquid interfacial area

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**Vapor Condensation dV({G[v(p)l(bulk) = G[v(p)v(po)] = RT ln (po/p)**

Gs[s/vs/l] = (gs/l - gs/v) ln(p/po) = -[4Vgl/v cos q/RT]/D

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**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

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**Vapor Condensation Test method Measures relative vapor pressure (p/po)**

Measures amount of condensed vapor At a given pressure

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Vapor Condensation Equipment The PMI Sorptometer

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**Variation of cumulative pore volume with relative pressure**

Vapor Condensation Measurable Characteristics Through and blind pore volume Condensation occurs in through & blind pores Variation of cumulative pore volume with relative pressure

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**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

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**Variation of cumulative pore volume with pore diameter**

Vapor Condensation Variation of cumulative pore volume with pore diameter

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**Vapor Condensation Pore Volume Distribution**

Distribution function fv: fv = -(dV/dD) Pore size distribution by gas adsorption Area in any pore diameter range = volume of pores in that range

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Vapor Condensation Pore structure of materials containing very small pores Type of pores Macropores: >0.05mm Mesopores: mm Micropores: <0.002mm

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Vapor Condensation Pore structure of materials containing very small pores Capability Technique: mm Validity of relations: mm For micropores data need to be analyzed using other models

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**Adsorption and desorption isotherms**

Vapor Condensation Adsorption and desorption isotherms and hystersis Adsorption and desorption isotherms

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**Adsorption/desorption isotherms for chemisorption of ammonia at 25C**

Vapor Condensation Adsorption/desorption isotherms for chemisorption of ammonia at 25C

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**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

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**Examples of a few different type of adsorption curves**

Vapor Condensation Examples of a few different type of adsorption curves

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**Vapor Condensation Summary**

Measure volume and diameter of very small through and blind pores No other technique can measure such characteristics

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**Conclusions Extrusion Techniques**

Two recent techniques Extrusion Flow Porometry & Liquid Extrusion Porosimetry have been discussed in detail

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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

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Conclusion All characteristics particularly relevant for filtration are measurable The techniques do not use toxic materials, high pressures or subzero temperatures

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**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

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**Conclusion Fluid flow characteristics cannot be measured**

Uses very high pressures and mercury, which is toxic

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**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

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

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**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

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**Conclusion Flow properties are not measurable**

Many require subzero temperatures

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Thank You

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