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

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Presentation on theme: "Characterization of Pore Structure: Foundation Dr. Akshaya Jena Director of Research Porous Materials, Inc., USA."— Presentation transcript:

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

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

3 Topics ê Vapor Adsorption ê Vapor Condensation F Conclusions ê Nonmercury Intrusion Porosimetry

4 Pore Structure Typical Pore Structure

5 Pore Structure Three Different Kinds of Pores

6 Characteristics of Pore Structure Characteristics

7 Characteristics of Pore Structure

8 Effects of application environment on pore structure characteristics

9 Characterization Techniques

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

11 Extrusion Flow Porometry (Capillary Flow Porometry)  For displacement of wetting (g s/l { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/4142327/13/slides/slide_10.jpg", "name": "Extrusion Flow Porometry (Capillary Flow Porometry)  For displacement of wetting (g s/l

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

13 Extrusion Flow Porometry (Capillary Flow Porometry) F For a wetting liquid: p = g l/g cos q (dS s/g /dV) (dS s/g /dV) = measure of pore size p d V = g s/g dS s/g + g s/l dS s/l + g l/g dS l/g p = differential pressure dV = infinitesimal increase in volume of the gas in the pore dS s/g = infinitesimal increase in interfacial area

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

15 Extrusion Flow Porometry (Capillary Flow Porometry) = [dS/dV](cylindrical opening of diameter, D) = 4/D D = [4g l/g cos q]/p Definition of pore diameter, D [dS/dV](pore)

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

17 Extrusion Flow Porometry (Capillary Flow Porometry) Test Method F For viscous flow F = [  /(256m l p s )]  i N i D i 4 ][p i + p o ]p  = a constant m = viscosity of gas l = thickness p s = standard pressure N i = number of pores of diameter D i p = differential pressure, inlet pressure, p i minus outlet pressure, p o

18 Extrusion Flow Porometry (Capillary Flow Porometry) F Dry curve normally concave upward Membranes showing three different ways in which flow rate may vary with differential pressure

19 Extrusion Flow Porometry (Capillary Flow Porometry) F Nonviscous flow F Tortuous paths for flow F High flow rate F Pore diameter F Interaction of sample with liquid Others possible shape of dry curve because of: F High pressure

20 Extrusion Flow Porometry (Capillary Flow Porometry) F The largest pore is emptied first and gas flow begins F With increase in differential pressure smaller pores are emptied and gas flow increases F When all pores are empty wet curve converges with the dry curve with the dry curve F Initially there is no gas flow Wet Curve F F versus p for a wet sample

21 Extrusion Flow Porometry (Capillary Flow Porometry) F Equipment The PMI Capillary Flow Porometer

22 Extrusion Flow Porometry (Capillary Flow Porometry) Measurable Characteristics Through pore Throat Diameter F The technique measured only the throat diameter Variation of pore size along pore path and the measured pore diameter

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

24 Extrusion Flow Porometry (Capillary Flow Porometry)

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

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

27 Extrusion Flow Porometry (Capillary Flow Porometry) F (F w,j / F d,j ) = [g(D,N, …)] w,j /[g(D,N,…)] d,j F Cumulative filter flow F [(F w,j / F d,j )x100] Distribution: F F = [  / (256  l p s )] [  i N i D i 4 ][p i +p o ]p

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

29 F  [(F w /F d )x100] = D1  D2 [-f F dD] Extrusion Flow Porometry (Capillary Flow Porometry) F f F = - d[F w /F d )x100]/dD Flow distribution over pore diameter F Area in a pore size range = % flow in that size range

30 Extrusion Flow Porometry (Capillary Flow Porometry) F Fractional pore number = N i /   i N i Fractional pore number distribution

31 Extrusion Flow Porometry (Capillary Flow Porometry)  F = k (A/ml)(p i -p o ) Liquid permeability F Computed from flow rate at average pressure using Darcy’s law Change of flow rate of water through paper as a function of differential pressure

32 Extrusion Flow Porometry (Capillary Flow Porometry)  F = k (A/2mlp s )(p i +p o )[p i -p o ] F Can be expressed in any unit: Darcy Gurley Frazier Rayls Gas permeability F Computed from flow rate at STP Flow of air through a filter

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 F Based on Kozeny-Carman relation  [F l /p A] = {P 3 /[K(1-P) 2 S 2 m]} + [ZP 2 p]/[(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-(r b /r a )] Envelope Surface Area F = gas flow rate in volume at average pressure, p per unit time

35 Extrusion Flow Porometry (Capillary Flow Porometry) 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). Envelope Surface Area r b = bulk density of sample r a = true density of sample

36 Extrusion Flow Porometry (Capillary Flow Porometry) F Results particularly relevant for filtration media F Toxic materials, high pressures & subzero temperatures not used F A highly versatile technique Summary F Flow Porometry measures a large variety of important pore structure characteristics.

37 Extrusion Porosimetry F Largest pore of membrane { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/4142327/13/slides/slide_36.jpg", "name": "Extrusion Porosimetry F Largest pore of membrane

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

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

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

41 Extrusion Porosimetry Equipment PMI Liquid Extrusion Porosimeter

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

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

44 Extrusion Porosimetry Through pore volume distribution F Distribution function F Area in any pore size range = volume of pores in that range Pore Volume distribution function F f v = -(dV/d logD)

45 Extrusion Porosimetry S =  p dV/(g l/g cos q) F Not very accurate F Sensitive to pore configuration F Over estimates volume of pore throat Through pore surface area  Integration of Equation: p = g l/g cos q (dS s/g /dV)

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

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

48 Mercury Intrusion Porosimetry Principle Intrusion of a non-wetting liquid in to pore F Non-wetting liquid cannot enter pores spontaneously  g s/l >g s/g

49 Mercury Intrusion Porosimetry F Work done by the liquid = Increase in interfacial free energy  (p-pg) dV = (gs/l -gs/g) ds  P = (-g l/g cos q) (dS/dV) F 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/D p = -4g l/g cos q/D

51 Test Method F Measured intrusion pressure yields pore diameter Mercury Intrusion Porosimetry F Measured intrusion volume of mercury yields pore volume

52 Mercury Intrusion Porosimetry F Equipment The PMI Mercury Intrusion Porosimeter

53 Mercury Intrusion Porosimeter Measurable Characteristics Through and blind pore volume Intrusion volume with pressure

54 Mercury Intrusion Porosimetry Through and blind pore diameter Measurable pore diameters

55 Mercury Intrusion Porosimetry Through and blind pore diameter Cumulative pore volume with pore diameter

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

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

58 Mercury Intrusion Porosimetry Through and blind pore surface are Cumulative surface area  S = [1/(-g l/g cos q)]  p dV

59 Mercury Intrusion Porosimetry Surface area not very accurate F Wide parts of ink-bottle pores measured as pores with neck diameter Inkbottle pore

60 Mercury Intrusion Porosimetry F At high pressures, correction terms in the small volume of small pores is appreciable F For very small pores, large pressure increases cause small increases in volume. The integral is less accurate. Surface area not very accurate

61 Mercury Intrusion Porosiemtry Extrusion volume and hysteresis Hysteresis in the intrusion-extrusion cycle

62 Mercury Intrusion Porosimetry Inkbottle pore

63 Mercury Intrusion Porosimetry F No flow characteristics are measurable F Uses toxic materials and high pressures Summary F Almost any material can be tested - mercury in non-wetting to most materials

64 Non-Mercury Intrusion Porosimetry F Non-wetting intrusion liquid is NOT MERCURY Water Oil Application liquid Principle F Exactly same as mercury intrusion porosimetry

65 Non-Mercury Intrusion Porosimetry Measurable Characteristics F All characteristics measurable by mercury intrusion porosimetry - measurable

66 Non-Mercury Intrusion Porosimetry F Smaller pores measurable F Can measure one kind of pores in a mixture like the mixture of hydrophobic and hydrophilic pores Measurable Characteristics F An order of magnitude low pressures used F Advantages over Mercury Intrusion Porosimetry F No toxic material used

67 Non-Mercury Intrusion Porosimetry F Can detect one kind of pore in a mixture Summary F Can measure all characteristics measurable by Mercury Intrusion without using any toxic material or high pressures

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

69 Vapor Adsorption F W = amount of adsorbed gas F W m = amount of gas that can form a monomolecular layer F C = a dimensionless constant F = (A 1 v 2 /A 2 v 1 ) exp [(E-L)/RT] F BET theory of physical adsorption [p/(p o -p)W] = [1/(W m C)] + [(c-1)/W m C](p/p o )

70 Vapor Adsorption W m = 1/[(intercept)+(slope)] F Surface area: S = W m N o a N o = Avogadro’s number a = cross-sectional area of the adsorbed gas molecule F [p/p o -p)W]versus(p/p o )-linear

71 Vapor Adsorption F Only one layer of molecules gets bonded to the material Chemisorption F Chemical interaction between the gas and the surface

72 Vapor Adsorption F p/W = [1(KW m )]+p[1/W m ] F p = pressure of gas F W = amount of adsorbed gas F K = K o exp(E/RT) F W m = amount of adsorbed gas for a completed monomolecular layer F Model for chemisorption (Langmuir)

73 Vapor Adsorption F Volumetric method: F A known amount of gas is introduced in to the sample chamber of known volume F Amount of gas left in the sample chamber is computed from change in gas pressure Test Method F Sample maintained at constant temperature

74 Vapor Adsorption F Weight gain of sample in the sample chamber is measured Test Method F Gravimetric method

75 Vapor Adsorption F Equipment The PMI Sorptometer

76 Vapor Adsorption F [p/(p o -p)W]versus(p/p o )linear in the range 0.05< (p/p o )<0.35 F Plot of [p/(p o -p)W]versus (p/p o ) Measurable Characteristics Through and blind pore surface area F Multipoint surface area

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

78 Vapor Adsorption Single point surface area F Assuming large C, Wm, is computed from a single measurement F Good approximation for large C

79 Vapor Adsorption ê Water ê Carbon monoxide ê Carbon dioxide ê Poisonous chemicals ê Many others F Over a wide range of temperature and pressure Chemisorption F Chemisorption of many chemicals measurable

80 Vapor Adsorption Chemisorption of ammonia at 25  C plotted after p/W = [1/KW m )]+p[1/W m ] /

81 Vapor Adsorption F Both through pore and blind pore surface areas are measured. Summary F Technique determines surface area accurately

82 Vapor Condensation Principle F Condensation of vapor in pore Condensation in pore

83 Vapor Condensation F dV = volume of condensed liquid F V = molar volume of liquid F dS = solid/liquid interfacial area  G[v(p)  l (pore)] dV({  G[v(p)  l(bulk)]}/V) +dS  G s [s/v  s/l] = 0

84 Vapor Condensation dV({  G[v(p)  l(bulk) =  G[v(p)  v(p o )] = RT ln (p o /p)  G s [s/v  s/l] = (g s/l - g s/v ) ln(p/p o ) = -[4Vg l/v cos q/RT]/D

85 Vapor Condensation F Definition of pore diameter (dS/dV) Pore = (dS/dV)Cyliderical opening of diameter, D = 4/D ln(p/p o ) = -[4Vg l/v cos q/RT]/D

86 Vapor Condensation F Measures amount of condensed vapor At a given pressure Test method F Measures relative vapor pressure (p/p o )

87 Vapor Condensation F Equipment The PMI Sorptometer

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

89 Vapor Condensation F Prior to condensation, pores contain adsorbed films ê True pore radius, r p r p = (D/2)+t t = thickness of adsorbed layer Through and blind diameter F Diameter of pore from condensation ln(p/po) = -[4V g l/v cos q/RT]D

90 Vapor Condensation Variation of cumulative pore volume with pore diameter

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

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

93 Vapor Condensation  Validity of relations:  0.0015mm F For micropores data need to be analyzed using other models F Capability  Technique: 0.2-0.00035mm Pore structure of materials containing very small pores

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

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

96 Vapor Condensation F Large number of larger pores  High adsorption at high pressure F Large number of small pores  saturation F Strong interaction of adsorbate with the adsorbed  increasing adsorption F Shape of adsorption curve  many factors

97 Vapor Condensation Examples of a few different type of adsorption curves

98 Vapor Condensation F No other technique can measure such characteristics Summary F Measure volume and diameter of very small through and blind pores

99 Conclusions Extrusion Techniques F Two recent techniques Extrusion Flow Porometry & Liquid Extrusion Porosimetry have been discussed in detail

100 Conclusions F 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

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

102 Conclusion F This technique can measure pore volume and pore diameters of through and blind pores in almost any material Mercury Intrusion Techniques F The widely used mercury intrusion porosimetry has been briefly discussed

103 Conclusion F Uses very high pressures and mercury, which is toxic F Fluid flow characteristics cannot be measured

104 Conclusion F This technique can measure pore volume and diameter of through and blind pores like mercury intrusion porosimetry Non- Mercury Intrusion Techniques F The novel technique non-mercury intrusion porosimetry has been discussed

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

106 Conclusion F These techniques can measure surface area, pore diameter and pore volume of through and blind pores F Characteristics of very small pores are measurable Gas adsorption & condensation techniques F The widely used gas adsorption and condensation techniques were discussed briefly

107 Conclusion F Flow properties are not measurable F Many require subzero temperatures

108 Thank You


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