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Characterization of Pore Structure: Foundation

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 .

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Characterization of Pore Structure: Foundation

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  1. Characterization of Pore Structure: Foundation Dr. Akshaya Jena Director of Research Porous Materials, Inc., USA

  2. Topics • Characteristics of pore structure • Characterization techniques • Extrusion Flow Porometry • Liquid Extrusion Porosimetry • Mercury Intrusion Porosimetry • Pore structure

  3. Topics • Vapor Adsorption • Vapor Condensation • Conclusions • Nonmercury Intrusion Porosimetry

  4. Typical Pore Structure Pore Structure

  5. Three Different Kinds of Pores Pore Structure

  6. Characteristics Characteristics of Pore Structure

  7. Characteristics of Pore Structure

  8. Effects of application environment on pore structure characteristics Characteristics of Pore Structure

  9. Characterization Techniques

  10. Extrusion Flow Porometry (Capillary Flow Porometry) • Flows spontaneously into pores Principle Displacement of a wetting liquid from a pore • Wetting liquid:

  11. 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

  12. Extrusion Flow Porometry (Capillary Flow Porometry) • For all small displacement of liquid

  13. 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

  14. Types of pore cross-section Extrusion Flow Porometry (Capillary Flow Porometry) • For most pores size not defined

  15. 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)

  16. Extrusion Flow Porometry (Capillary Flow Porometry) Test Method Dry Curve • Flow rate, F versus p for a dry sample

  17. 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

  18. 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

  19. 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

  20. 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

  21. The PMI Capillary Flow Porometer Extrusion Flow Porometry (Capillary Flow Porometry) • Equipment

  22. 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

  23. Extrusion Flow Porometry (Capillary Flow Porometry) • Bubble point pressure in F vs p plot. • The largest pore diameter (Bubble Point Pore Diameter)

  24. Extrusion Flow Porometry (Capillary Flow Porometry)

  25. Dry, wet and half-dry curves for a filter and the mean flow pressure Extrusion Flow Porometry (Capillary Flow Porometry) • Mean flow pore diameter

  26. Extrusion Flow Porometry (Capillary Flow Porometry) • Pore diameter range Largest - Bubble point pressure Lowest - pressure at which wet and dry curves meet

  27. 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

  28. Cumulative filter flow Extrusion Flow Porometry (Capillary Flow Porometry)

  29. 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] = D1D2[-fFdD] • Area in a pore size range = % flow in that size range

  30. Fractional pore number distribution Extrusion Flow Porometry (Capillary Flow Porometry) • Fractional pore number = Ni/iNi Fractional pore number distribution

  31. 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

  32. 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

  33. 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

  34. 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

  35. 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

  36. 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.

  37. 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

  38. Principle of extrusion porosimetry Extrusion Porosimetry • Displaced liquid flows through membrane & measured

  39. Principle of extrusion porosimetry Extrusion Porosimetry • Gas that displaces liquid in sample pores does not pass through membrane

  40. Extrusion Porosimetry • Extruded liquid (weight or volume) gives pore volume Test method • Differential pressure yields pore diameter

  41. PMI Liquid Extrusion Porosimeter Extrusion Porosimetry Equipment

  42. Pore volume plotted against differential pressure Extrusion Porosimetry Measurable Characteristics Through pore volume

  43. Measured pore volume plotted against pore diameter Extrusion Porosimetry Through pore diameter

  44. 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

  45. 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)

  46. Liquid flow rate as a function of differential pressure Extrusion Porosimetry Liquid permeability • From liquid flow rate

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

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

  49. Mercury Intrusion Porosimetry • 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) • Pressurized liquid can enter pores

  50. 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

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