1. Dr. Akshaya Jena and Dr. Krishna Gupta
Characterization of Pore Structure of Fuel Cell Components for Enhancing Performance
Dr. Akshaya Jena and Dr. Krishna Gupta
Porous Materials, Inc.,
Ithaca, New York, USA

2. Outline
Introduction
Through pore throat diameter, distribution, gas permeability & surface area by:
Capillary Flow Porometry
Capillary Condensation Flow Porometry
Hydrophobic through and blind pore volume & distribution by:
Vacuapore
Through pore volume, diameter, distribution & liquid permeability by:
Liquid Extrusion Porosimetry
Summary and Conclusion

3. Introduction
Pore structure governs kinetics of physicochemical processes & Flows of reactants and products in fuel cells.
Quantitative measurement of pore structure is essential for Design, development and performance evaluation.
Technologies for pore structure measurement are currently being developed to characterize the complex pore structure of fuel cell components.
We will discuss several innovative techniques successfully developed and applied for evaluation of pore structure of fuel cell components.

4. Importance of Such Properties
Through Pore Throat Diameters, Distribution, Gas Permeability and Surface Area
Importance of Such Properties
Through Pores:
Fluid flow
Pore Diameters:
Capillary forces for liquid movement
Throat diameters:
Separation of undesirable particles
Gas permeability:
Overall rate of the processes
Through pore surface area:
Physicochemical processes
Effects of stress, chemical environments & temperature:
Influence of operating conditions

5. Through Pore Throat Diameters, Distribution, Gas Permeability and Surface Area
Suitable Characterization Techniques
Advanced Capillary Flow Porometry
Capillary Condensation Flow Porometry

6. Advanced Capillary Flow Porometry
Basic Principle
For wetting liquid:
Wetting Liquids fill pores spontaneously
Cannot come out spontaneously
A pressurized inert gas can displace liquid from pores provided:
Work done by Gas = Increase in Interfacial Free Energy

7. Advanced Capillary Flow Porometry
Pressure needed to displace liquid from a pore:
p = 4 γ cos θ / D
p = differential gas pressure
γ = surface tension of wetting liquid
θ = contact angle of the liquid
D = pore diameter
Pore diameter is defined for all pore cross-sections

8. Advanced Capillary Flow Porometry
(Perimeter/Area)pore = (Perimeter/Area)cylindrical opening
Pore Diameter = Diameter of Cylindrical Opening
SKETCH

9. Advanced Capillary Flow Porometry
Measured differential pressure & gas flow through dry & wet sample yield pore structure

10. Advanced Flow Porometers
The Technique
Advanced Flow Porometers
Accurate
Pressure transducers
Flow transducers
Regulators
Controllers
Sophisticated sample sealing mechanisms to direct flow in desired directions
Internal computers
To control sequential operations
To execute automated tests

11. Advanced Flow Porometers
The Technique
Advanced Flow Porometers
Proper algorithms
To detect stable pressure and flow
To acquire data
Software
To convert acquired data to pore structure characteristics
To present data in tabular, graphical and excel formats

12. The PMI Advanced Capillary Flow Porometer
An Example:
The PMI Advanced Capillary Flow Porometer

13. The PMI Advanced Capillary Flow Porometer
Features:
Sealing with uniform pressure by pneumatic piston-cylinder device
Automatic addition of measured amount of wetting liquid at appropriate time

14. The PMI Advanced Capillary Flow Porometer
Appropriate design & strategic location of transducers to minimize pressure drop in the instrument
Minimal operator involvement
Use of samples without cutting and damaging the bulk product

15. Analysis of Experimental Data
Dry Flow, Wet Flow & Differential Pressure
Flow rate and differential pressure measured in a solid oxide micro fuel cell component

16. Analysis of Experimental Data
Through Pore Throat Diameter
Pore diameter computed from pressure to start flow = Through Pore Throat Diameter

17. Analysis of Experimental Data
The Largest Through Pore Throat Diameter
(Bubble Point Pore Diameter)
Computed from pressure to initiate gas through wet sample
The largest pore size in a solid oxide micro fuel cell component

18. Analysis of Experimental Data
The Mean Flow Through Pore Throat Diameter
50% of flow is through pores larger than the mean flow through pore throat diameter
MFPD computed using pressure when wet flow is half of dry flow
Mean flow pore diameter of a solid oxide micro fuel cell component

19. Analysis of Experimental Data
The Smallest Through Pore Throat Diameter
& The Pore Diameter Range
Smallest pore is computed using pressure at which wet and dry curves meet
Pore diameter range measured in a solid oxide micro fuel cell component

20. Analysis of Experimental Data
Flow Distribution
The flow distribution is given by the distribution function, fF
fF = -d [(Fw / Fd)p × 100] / d D
Fw = wet flow, Fd = dry flow
Flow distribution in a membrane

21. Analysis of Experimental Data
Flow Distribution
Area under distribution function in any diameter range = % flow through pores in that range

22. Analysis of Experimental Data
Pore Fraction Distribution
Pore Fraction
Nj = the number of through pores of throat diameter Dj
Fj = [1/(4 γ cos θ / pj)4] [(Fw,j / F d,j) – (Fw,j-1 / Fd,j-1)]
pj = differential pressure to remove wetting liquid from pore of diameter Dj

23. Analysis of Experimental Data
Pore Fraction Distribution
Flow fraction distribution of a membrane

24. Analysis of Experimental Data
Gas Permeability
From Darcy’s Law:
F = k (A / 2μ l ps) (Ts / T) (pi + po) [pi – po]
F = gas flow rate in volume at STP
ps = standard pressure
Ts = standard temperature
k = permeability
A = area
μ = viscosity
l = thickness
T = test temperature in Kelvin
pi= inlet gas pressure
po = outlet gas pressure

25. Analysis of Experimental Data
Gas Permeability
Permeability computed from dry flow
Flow rate through a dry sample

26. Analysis of Experimental Data
Through Pore Surface Area
Kozeny-Carman equation relates through pore surface area to flow
[F l / p A] = {P3 / [K(1 - P)2 S2 μ]}
+ [Z P2 π] / [1 - P) S (2 π p ρ) ½]
F = flow rate in volume at average pressure
p (p = [pi + po / 2]),
and test temperature
P = porosity
S = surface area per unit volume of solid
ρ = density of gas at average pressure
K = 5
Z = (48/13 π)
Flow rate through a dry sample

27. Analysis of Experimental Data
Through Pore Surface Area
Change of envelope surface
area with flow rate

28. Enhanced Capability
Advanced Porometers with special attachments can test samples under a variety of conditions

29. Enhanced Capability Compression & Cyclic Compression Porometry
Sample under compressive stress or cyclic compressive stress
Effects of compressive stress on gas permeability of GDL

30. Enhanced Capability
Controlled Thermal & Chemical Environment Porometry
Sample under desired controlled humidity and temperature
The PMI Fuel Cell Porometer

31. Enhanced Capability Microflow Porometry
Samples exhibiting very low flow rates
Fuel cell components
Membranes
Dense ceramics
Tightly woven fabrics
Tiny parts
Silicon wafers
Storage materials
Small flow rates through a fuel cell component measured in the microflow porometer

32. Enhanced Capability In-Plane Porometry (Directional Porometry)
In-Plane pore structure of sample or pore structure of each layer of multilayer components
Fuel cell components
Battery separators
Nonwoven filters
Felts
Paper
Pore structure of each layer of a ceramic component

33. Capillary Condensation Flow Porometry
Basic Principle
Capillary Condensation Flow Porometry is a recently patented novel technique
Condensation of Vapor of a Wetting Liquid in Pores
Vapor at p<po cannot condense
Vapor at p<po can condense in pores
p = pressure of vapor, po = eq. vapor pressure

34. Capillary Condensation Flow Porometry
Basic Principle
Free Energy Balance shows → condensation occures in pores smaller than Dc
Dc = - [4 V γl/v cos θ / RT] / [ ln (p/po)]
V = molar volume of condensed liquid R = gas constant
γl/v = surface tension T= test temperature
θ = contact angle Dc = pore diameter

35. Capillary Condensation Flow Porometry
Basic Principle
Flow of Vapor through Empty Pores
A small imposed vapor pressure gradient causes flow through empty pores greater than Dc

36. The Technique
Measured vapor pressure in equilibrium with the sample yields Dc
Measured rate of pressure change in the downstream side yields flow rate

37. The PMI Capillary Condensation Flow Porometer
An Example:
The PMI Capillary Condensation Flow Porometer

38. Analysis of Experimental Data
Through Pore Throat Diameter
Condensation starts at the throat of a through pore and prevents gas flow
Dc = through pore throat diameter

39. Analysis of Experimental Data
Change of Vapor Flow Rate
Measured Flow Rate = Flow through all pores > Dc
Molecular flow is applicable to flow through such small pores
(F/AΔp)cumulative = (Ts/T) (π/12τpsl)(8RT/πM)½
[ΣD Dmax Ni(Di)3]
A = area of sample p = pressure drop across the sample
l = sample thickness T= test temperature in K
M = molecular weight, Ni= number of pores of diameter Di
F= flow rate in volume at STP, ps and Ts
 = average tortuosity of pores and is equal to ( L/l) where L is the length of capillary,
D = pore diameter computed by adding to Dc a small correction term for thickness of adsorbed layer

40. Analysis of Experimental Data
Change of Vapor Flow Rate
Variation of flow rate with pore diameter
Flow rate through a membrane

41. Analysis of Experimental Data
Pore Distribution
Expressed in terms of distribution function, f
f = - d((F/AΔp)cumulative) / dD
Flow distribution in a membrane

42. Analysis of Experimental Data
Number of Pores of Diameter, Di
Number of pores computed using the following relation
f = (Ts/T) (π/12τpsl)(8RT/ πM) ½ [3Ni(Di)2]

43. Strengths of the Technique
The diameters of pores down to a few nanometers and flow through these small pores are measured
Test pressure on the sample is almost zero
Extreme test conditions are avoided
There is no stress on the sample and structural distortion or damage to the sample is negligible

44. Strengths of the Technique
Only through nanopores are measured and blind pores are ignored unlike the gas adsorption technique
Throat diameters are measured
A wide variety of vapors can be used
Measuring technique is simple

45. Hydrophobic Through and Blind Pore Volume and Distribution
Hydrophobic and hydrophilic pores are relevant for:
Water management
Transport of reactants
Reaction rates
Flow rates of reaction products

46. Work done by water = Increase in surface free energy
Vacuapore
Basic Principle
Hydrophilic pores are spontaneously wetted by water
Hydrophobic pores repel water because
γ (water/solid) > γ (gas/solid)
Pressure on water results in water intrusion
Intrusion volume is pore volume
Pore diameter computed from intrusion pressure
Work done by water = Increase in surface free energy
D = - 4 γ cos θ / p

47. The Technique Recently patented technique Features:
Removal of air from the pores, the sample chamber and water
Application of desired compressive stress on the sample
Optional in-plane intrusion of water

48. The Technique
Vacuapore

49. Analysis of Experimental Data
Only hydrophobic through and blind pore diameters are measured.
Measured pressure yields pore diameter of hydrophobic through and blind pores.
Measured intrusion volume of water = Cumulative pore volume of hydrophobic through and blind pores.

50. Analysis of Experimental Data
Volume distribution is given as function, fv
fv = - dV / d log D
Hydrophobic and hydrophilic pore distributions obtained from results of Vacuapore and Mercury Intrusion Porosimeter.

51. Analysis of Experimental Data
Pore size distribution in GDL of a PEMFC
Hydrophobic pores: 50.3%, MPD = 17.1 m
Hydrophilic pores: 49.7%, MPD = <16.3 m

52. Unique Feature Capable of measuring:
Hydrophobic large and small pore diameters
In-plane pore structure
Influence of compressive stress on pore structure

53. Through Pore Volume, Diameter and Distribution and Liquid Permeability
Important characteristics of flow permitting pores

54. Liquid Extrusion Porosimetry
Basic Principle
Sample supported by membrane
Largest Membrane Pore < Smallest Sample Pore
Pores of sample & membrane filled with wetting liquid
Gas pressure displaced liquid from sample pores flows out through liquid filled pores of membrane
Gas pressure sufficient to remove liquid from sample pores does not remove liquid from membrane pores

55. Liquid Extrusion Porosimetry
Basic Principle
Measured volume of liquid flowing out of membrane yields pore volume
Pressure yields pore diameter
p = 4 γ cos θ / D

56. The Technique
Cylindrical sample chamber holds a support screen and membrane
Chamber below the support screen connected to a container placed on a weighing balance

57. The Technique
O-ring seals against the wall of the sample chamber and the membrane
The pressure of the inert gas on the wet sample is increased to displace liquid from pores.

58. Analysis of Experimental Data
Through Pore Volume
Measured volume is the cumulative through pore volume
Pore volume of five thin layers of a fuel cell component

59. Analysis of Experimental Data
Through Pore Diameter
All diameters between the mouth and the throat are measured
Diameters between the throat and the exit are not measured
Pore diameters measurable by several techniques

60. Analysis of Experimental Data
Through Pore Volume Distribution
Through pore volume distribution function fv
Pore volume distribution of Toray paper
obtained by various techniques

61. Analysis of Experimental Data
Liquid Permeability
Permeability is defined by Darcy’s law:
F = k (A /  l) (pi - po)
F = volume flow rate
k = permeability
A = area
 = Viscosity
(pi - po) = differential pressure
Instrument measures liquid flow rate
Permeability is computed using the equation

62. Unique Features Highly versatile. Tests can be performed:
With sample under compressive stress
At elevated temperatures
Under chemical environments
In variable humid atmospheres
Using a wide variety of liquids
With a wide variety of samples
Complete pore structure can be evaluated by combining various techniques.

63. Unique Features
Pore Structure Characteristics of pores in Toray paper using a number of techniques
Characteristics
Through
Blind
Hydrophobic
Hydrophilic
Pore Volume
75%
25%
29%
71%
Diameter, m 60 40 35 50
Kind of Pore

64. Summary and Conclusions
Recently developed pore structure characterization techniques appropriate for fuel cells have been discussed
Capillary Flow Porometry
Capillary Condensation Flow Porometry
Vacuapore
Liquid Extrusion Porosimetry

65. Summary and Conclusions
These techniques are capable of determining pore structure characteristics of through pores relevant for fuel cell components.
Pore throat diameter
Largest pore diameter
Mean flow pore diameter
Flow distribution
Pore fraction distribution
Gas permeability
Pore diameters of nanopores
Nanopore distribution
Envelope surface area
Pore volume
Pore volume distribution
Liquid permeability

66. Summary and Conclusions
Applications of these techniques have been illustrated with examples of measurements on fuel cell components

67. Thank You