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## Characterization of Pore Structure: Foundation

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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**Topics**• Vapor Adsorption • Vapor Condensation • Conclusions • Nonmercury Intrusion Porosimetry**Typical Pore Structure**Pore Structure**Three Different Kinds of Pores**Pore Structure**Characteristics**Characteristics of Pore Structure**Effects of application environment on pore structure**characteristics Characteristics of 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**Types of pore cross-section**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**The PMI Capillary Flow Porometer**Extrusion Flow Porometry (Capillary Flow Porometry) • Equipment**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**Cumulative filter flow**Extrusion Flow Porometry (Capillary Flow Porometry)**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**Flow of air through a filter**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**PMI Liquid Extrusion Porosimeter**Extrusion Porosimetry Equipment**Pore volume plotted against differential pressure**Extrusion Porosimetry Measurable Characteristics Through pore volume**Measured pore volume plotted against pore diameter**Extrusion Porosimetry Through pore diameter**Pore Volume distribution function**Extrusion Porosimetry Through 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 Porosimetry Liquid 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