pore water in polymer electrolyte fuel cell

ObjectiveMassoud Kaviany University of Michigan
[email protected]
Reactive Heat Transfer in Porous Media, EUROTHERM 81 Ecole des Mines d'Albi, France, June 4 – 6, 2007
Outline
1. Background 2. Objectives 3. Pore Water in Polymer Electrolyte (PE) (Concentration of Talk) 4. Pore Water in Catalyst Layer (CL) 5. Pore Water in Diffusion Layer (DL) 6. Water Droplets in Cathode Gas Channel (GC) 7. Summary-Outlook Acknowledgement
1. Background
PEFC is a layered structure, using a proton-
conducting polymer electrolyte membrane (e.g., Nafion)
–
–
–
–
•
Water in PE –
Water is inherent in the fuel cell, although its role is both positive and negative
Figure 1. Schematic of polymer electrolyte fuel cell (PEFC), showing the reactions, and water/hydrogen/air gas streams [1].
OH2e2HO 2 1:Cathode
→++
+→
−+
−+
[1] M. Eikerling, Water in Polymer Electrolyte Fuel Cells: Friend or Foe?, Physics Today, October 2006.
Pore Size and Layer Thickness Distributions (Figure 2)
Figure 2. Pore size and layer thickness in PEFC.
Continuum and statistical treatment regions are also shown.
Liquid Saturation Distribution in Fuel Cell
–
–
–
–
At the catalyst layer of the cathode (3), the liquid saturation is lower than the cathode side of the membrane, since it should have a triple-
phase boundary for the oxygen reduction.
–
–
Low current density allows for less water production and less electro-osmotic drag.
Figure 3. Anticipated liquid water saturation profile (high/low current density) throughout PEFC [2].
[2] A.Z. Weber and J. Newman, Effects of Microporous
Layers in Polymer Electrolyte Fuel Cells, Journal of the Electrochemical Society, Vol. 152, pp. A677-A688, 2005.
Liquid Pressure Distribution in Fuel Cell
–
–
–
–
At high current density je
more water is produced and condenses, causing higher water pressure at the catalyst layer and its adjacent diffusion layer.
Figure 4. Predicted water pressure distribution (high/low current density) throughout PEFC [3].
[3] D.M. Bernardi
and M.W. Verbrugge, A Mathematical Model of the Solid-Polymer-Electrolyte Fuel Cell, Journal of the Electrochemical Society, Vol. 139, pp. 2477-2491, 1992.
Role of Water in PEFC
Component Flooded Dry
Covering triple phase boundaries (TPBs), ηa
, ηc -
flow initiated from channel, ηo
, ηc -
-
Catalyst Layer (CL) - Low proton conductivity
(Electro-osmosis),
ηo
, ηa
, ηc
•
State of water control electrochemical transport and reaction kinetics in PEFC
2 2
o e e t e a c
e
j p

o e a
η η η Δ
[4] J. Larminie, and A. Dicks, Fuel Cell Systems Explained, Wiley, New York, 2003.
2. Objectives
Water management is essential in PEFC performance. •
There is need further understanding of the state of water and its role in proton/water transport and electrochemical
reactions, a molecular dynamics (MD) perspective
would be helpful.
•
•
•
Throughout the pore ranges and water states, i.e., membrane-catalyst (nano-pores, adsorbed-
capillary water) to the gas diffusion medium (micro-pores, capillary water) to the milli-channel (droplet water), the water pressure distribution is continuous through the assembly.
3. Pore Water in Polymer Electrolyte
•
•
•
•
•
•
Here, we will emphasize on understanding a thermodynamic state of pore water in Nafion.
Nafion Proton Conductivity and Its Relation to Water State •
Nafion structure and pore water –
Tetrafluoroethylene (TFE) backbone (hydrophobic) where no water/proton penetrate.
–
•
–
–
•
Water should be well managed to optimize chemical reaction at the catalyst layers.
Figure 5. Proton/water transport in hydrated Nafion.
Electrochemical reaction is also shown [5].
[5] Pyoungho
Datta, Sorption in Proton-
Exchange Membranes, Journal of the Electrochemical Society, Vol. 150, No. 12, pp. E601-E607, 2003.
Proton Conduction Mechanisms in Water
•
•
In liquid water, the solvation of the excess proton is idealized
by two forms; the H9
O4 +
–
→ Eigen Mechanism might be a more probable candidate [8].
Figure 6. The protonic defect migrates through the hydrogen bond network through a series of
covalent bond cleavage/formation. http://en.wikipedia.org/wiki/Grotthuss_mechanism
[6] Noam Agmon, The Grotthus
Mechanism, Chem. Phys. Lett., Vol. 244, pp. 456-462, 1995. [7] M. Tuckerman and et. al., Ab-Initio Molecular-Dynamics Simulation of the Solvation and
Transport of H3O+ and OH-
Ions in Water, Journal of Physical Chemistry, Vol. 99, No. 16, pp. 5749-5752, 1995.
[8] O. Markovitch
and N. Agmon, Structure and Energetics
of the Hydronium Hydration Shells, The Journal of Physical Chemistry A, Vol. 111, pp. 2253-2256, 2007.
•
ion). •
O+ at the center of an H9
O4 + complex in where the hydronium is strongly
•
H5
O2 +
•
(a) Proton is solvated on the center of Eigen H9
O4 + cation having
(b) fluctuation between hydronium and adjacent water allows for Eundel
cation, and proton is shared by two water molecules, and –
(c) finally, proton is localized again on the other water molecule as a form of eigen cation.
Figure 7. The protonic defect migrates through the hydrogen bond network through a series of covalent
bond cleavage/formation [6, 7].
Mechanism –
(d) Proton is solvated as a form of hydronium, and hydronium and
water allow for Zundel
ion, and –
(e) Proton is transported toward an adjacent water, and repeating as (f).
[9] M. Eigen, Proton Transfer, Acid-Base Catalysis, and Enzymatic Hydrolysis, Angewandte
Chemie
International Edition, Vol. 3, No. 1, 1-72, 1964. [10] G. Zundel, Hydration Structure and Intermolecular Interaction in Polyelectrolytes, Angew. Chem. Internati. Edit., Vol. 8, No. 7, 499-509, 1969.
Pore Water States (Phase) in Nafion and Proton Conductivity (Proposed Hypothesis) •
•
•
λ
•
λ
•
λ
•
6 < λ
•
•
the membrane (Schroeder paradox).
The electrical/mechanical properties are strongly dependant on the state (phase) of water and its pore coverage.
Figure 8. Water state as a function of water content λ
in hydrated Nafion
[11]. [11] T. Thampan, S. Malhotra, H. Tang, and R. Dattaa, Modeling of Conductive
Transport in Proton-Exchange Membranes for Fuel Cells, Journal of the Electrochemical Society, Vol. 147, No. 9, pp. 3242-3250, 2000.
Gas/Condensed-Phase Transition
•
•
•
•
The grand potential functional of solid (s) and fluid (f) system is
where Fh
is Helmholtz free energy density of a uniform hard sphere fluid of density ρ,
where φff
where φsf
is the chemical potential.
( ) 1dH HE F rρ= ∫
( ) ( ) ( )12 1 2 2 1 1 d d 2ff ffE r r r r r ρ ρ= ∫
( ) ( )1 1dsf sfE r r μ ρ= −∫
[12] B.K. Peterson et.al., Fluid Behavior in Narrow Pores, J. Chem. Soc., Faraday Trans., Vol. 82, pp. 1789-1800, 1986.
Minimizing grand potential functional with respect to ρ(r), we have
where µh
is the chemical potential for the uniform hard-sphere fluid density. •
From the Percus-Yevick
•
( ) ( ) ( ) ( )0 1 1 1 h
h ff sf F
r r r ρ
∂ = = − − ∂
( ) ( )
− + = + − −
( ) ( ) ( )1 12 2 2dff ffr r r rμ ρ= ∫ ( ) ( )1 12 2dsf sfr r rμ ρ = ∫
12 6 , ,2 2
R R r r
,0 ,
2 2 2 2 4 2 (2 )
0
m sf m sf ff ff m sf
m sf m sf m sf m sf sf ff m sf c
c c
r r r r
Minimizing the grand potential function, we calculate for the Ar
(fluid)-CO2 (solid) system, and cylindrical pore structure.
•
•
•
In Figure 9(b) shows variation of the normalized fluid density distribution for Ar
on CO2
pores, for several pore radii, at given pressure. The gas-liquid transition occurs at R/Rm
= 5.07 (pore radius to equilibrium separation distance).
•
We propose the same physics can be applied the water-Nafion
system, then the water state is determined by surface force and pore size.
Figure 9. Gas/condensed-phase transition (Ar-CO2
system) (a) phase stability diagram (b) normalized density distribution [12].
(a)
(b)
•
•
•
•
The van der
•
•
For a liquid film inside a cylinder, we use Ra
= R
δ
•
•
In turn, this gives
( )0 0 , (2 )g lp T Hδμ μ μ υ σ= + −
( ) ( )0 0 , l g l
a p T f
υ σμ μ υ σ δ ∂ ∂ ∂ ∂
= − = − + ≥ ≥ ∂ ∂ ∂ ∂
[13] W.F. Saam
and M.W. Cole, Excitation and Thermodynamics for Liquid-Helium Films, Phys. Rev. B, Vol. 11, pp. 1086-1105, 1975. [14] M. Kaviany, Principles of Heat Transfer in Porous Media, Srpinger-Verlag, New York, 1995.
Adsorption/Capillary Transition
•
At a threshold pore water content, the water interatomic interaction with Nafion
surface forms thin adsorbed layer.
•
As the adsorbed-layer thickness increases, the thin film reaches unstable (r → rca
) and transits to capillary condensate water occurs.
•
•
The smaller pores show earlier transition due to the confinement effect (Figure 10).
Figure 10. Adsorbed/capillary water state transition in hydrated Nafion (cylinderical
pore)
[13].
5 22 2 2 22 1 3 2 2 22 2 21 1 1ca ca ca ca
o
− = − + −
Schroeder Paradox –
•
In Nafion-water system, surface wetting mechanism in the pores of Nafion is different for different water states. In the vapor state, the hydrophobicity hinders water condensing in pores, while in the capillary state the surface tension dominates the hydrophobicity and water contacts the surface.
Figure 11. Water activity on Nafion, as a function of the membrane hydration [16].
[15] P. Schroeder, Uber
von Gelatine, Z. Phys. Chem., Vol. 45, pp. 57, 1903.
[16] T.A. Zawodzinski
and et. al., Water Uptake By and Transport Through Nafion 117 Membranes, , J. Elec. Soc., Vol. 140, pp. 1041-1047, 1993.
[17] A.Z. Weber and J. Newman, Transport in Polymer-Electrolyte Membranes, J. Elec. Soc., Vol. 150, pp. A1008-A1015, 2003.
Existing Continuous Activity Model for Schroeder Paradox
•
Using the non-ionic gels to describe the sorption isotherm of the binary polymer-
solvent system, we have
υ
: polymer-solvent interaction parameter
( )2
φ φ υ
G G n n
[18] C. Vallieres
and et. al., On Schroeder’s Paradox, Journal of Membrane Science, Vol. 278, pp. 357-364, 2006.
Figure 12. Propanol/RTV 141 experimental swelling data at 40oC, and binary solution of volume fraction at a unit
activity [18].
•
The membrane water equilibrium isotherms balance among water activity outside the membrane aout
, water activity aw
, water pressure pw
, as given by isotherm model
–
Schroeder paradox arises via the jump in liquid pressure which occurs when the hydrophilic meniscus is removed (that is, pc
= 0).
•
•
Considering the mechanical pressure from swelling membrane from water, the shear modulus G
is related to Young modulus E
and Poisson ratio v
+ + =
+ where r
is the ratio of partial molar volume of polymer membrane and solvent
[21] P. J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953
( ) ( )21ln ln 1 1 1wa r
ε ε χ ε = + − − + −
( )2 1E v G= +
[19] I. nazarov
and K. Promislow, The Impact of membrane Constraint on PEM Fuel Cell Water Management, J. Electrochem. Soc., Vol. 154, pp. B623-B630, 2007 [20] P. Choi, N.H. Jalani, and R. Datta, Thermodynamics and Proton Transport in Nafion, Journal of The Electrochemical Society, Vol. 152, No. 3, E123-E130, 2005
Continuous Water Activity Model for Schroeder Paradox
•
The final form of the water adsorption isotherm for Nafion is
2
V rS RT
λ χ
− + + − + +
+ + − + = − − + +
+ +
Figure 13. Experimental data and prediction of water content and water activity for Nafion [18].
Here S
is the specific pore surface area (pore surface area /volume).
Observation of Water on Nafion Surface
•
•
•
•
•
Figure 14. Observation of water condensation on the Nafion
surface.
Water on the Nafion Surface with ESEM
•
•
•
These observations supports that water surface droplets form at hydrophilic sites and move toward hydrophobic regions.
Figure 15. Water condensate grows on hydrophilic site on Nafion
surface.
Water Condensation and Transitions on Nafion Surface
•
Initially, the water vapor
•
•
shows hydrophobicity.
This observation supports droplets forming at hydrophilic sites and moving towards hydrophobic regions.
Figure 16. Observations of condensate nucleation and transition from nucleate condensation to droplet formation on the Nafion
surface.
•
Another time observation at a different location on the Nafion
surface.
Liquid Water Saturation
•
•
With the identical liquid water pressure among pores
(assuming that the liquid water clusters interconnect with each other), the contact angles on the surfaces, saturation, effective pore radius are different, as given by the capillary pressure model of Leverett-
Melrose [22]
•
( ) ( )
K
ε =
Figure 18. Capillary pressure and water saturation in the pores in the hydrated Nafion
may be modeled by Leverett-Melrose model
[22].
[22] J.A Rogers and M. Kaviany, Funicular and evaporative-front regimes in convective drying of granular beds, International Journal of Heat and Mass Transfer, Vol. 35, pp. 469-480, 1992.
Molecular Dynamics Simulation in Hydrated Nafion
•
where ε
is the the
•
where t, V, kB
•
where N
is the number of molecules in the simulation system.
[23] S. Cui et. al., A Molecular Dynamics Study of a Nafion Polyelectrolyte Membrane and the Aqueous Phase Structure for Proton Transport, Journal of Physical Chemistry, Vol. 111, pp. 2208-2218, 2007.
[24] F. Müller-Plathe, Permeation of polymers -
a computational approach, Acta
Figure 19. (a) Water-hydronium
molecular structure [23].
= −
=
= − ∑
( ) ( )+
i
σ = − ∑
( ) ( ) ( ) ( ) 2
B
2 0 0 6 i j i i j j
j i
+ − −
∑
Figure 20(a). Proton conductivity of Nafion
117 at 303 K as a function of membrane hydration [25]. Figure 20(b). Water activity of Nafion 117 in water as a
function of membrane hydration [16].
[25] T.A. Zawodzinski
and et. al., A Comparative Study of Water Uptake By and Transport Through Ionomeric
Fuel Cell Membranes, Journal of the Electrochemical Society, Vol. 140, pp. 1981-1985, 1993.
Water Uptake through Nafion 117 Membrane •
Water content λ
High hydration is favorable for proton conductivity
–
A possible explanations for water state (vapor, adsorbed, and capillary water) and water state/morphology transitions including shroeder
paradox as a function of water content are shown in Figures 20(a) and (b).
Water Diffusion through Nafion 117 Membrane
•
High water content allows for increased water diffusivity. –
•
due to effective surface force change.
Figure 21(c). Water diffusion coefficient of Nafion
117 in water as a function of membrane hydration [16].
Figure 21(d). Chemical shift of the hydrated Nafion
117 as a function of membrane hydration [26].
[26] J. Kawamura and et. al., Microscopic states of water and methanol in Nafion membrane observed by NMR micro imaging, Solid State Ionics, Vol. 176, pp. 2451-
2456, 2005.
•
).
•
–
–
•
–
•
Water state is also critical in determining the reaction rate. Figure 22. Schematic of geometry and water state in the pores of the
catalyst layer. Active/passive TPBs
are also shown [27].
[27] M. Eikerling
and A.A. Kornyshev, Electrochemical Impedance of the Cathode Catalyst Layer in Polymer Electrolyte Fuel Cells, Journal of Electroanalytical
Chemistry, Vol. 475, pp. 107-123, 1999.
Reaction Rate in Catalyst Layer
•
Electrochemical reaction rate on the TPB of a porous media with the specific surface area Asg
/V
•
At given temperature and activation energy, an increase in the specific surface area Asg
/V
•
•
should be maximized.
[28] P.B. Weisz, Zeolites-New Horizons in Catalysis, Chmitec, pp. 498, 1973.
Figure 23. Effect of the specific surface area Asg
/V on the required activation energy for reaction [28].
where <lTPB
( ) 1 22
r i sg
A V ρ Δ
r i sg
A V ρ Δ
•
•
–
–
–
•
.
the hydrate catalyst layer
connecting to carbon paper
[29].[29] E.J. Lamas, P.B. Balbuena, Molecular Dynamics Studies of a Model Polymer-Catalyst-Carbon Interface, Electrochimica
Acta, Vol. 51, pp. 5904-
5911, 2006.
•
•
and macro-
transport occurr
simultaneously. The micro-droplets are formed near the catalyst layer, and agglomerate to make pore-filling water droplets which in turn is transported towards the low liquid pressure region by capillarity.
[30] J.H. Nam and M. Kaviany, Effective Diffusivity and Water-Saturation Distribution in Single-
and Two-layer PEMFC Diffusion Medium, International Journal of Heat and Mass Transfer, Vol. 46, pp. 4595-4611, 2003.
Figure 25. Two consecutive micrographs using environmental scanning electron microscopy (ESEM) of a diffusion
medium [30].
(a)
(b)Figure 16. Rendering of the water transport model, showing the branching micro-
to macro-
Carbon Paper Structures
[31] V.P. Schultz and et. al., Modeling of Two-Phase Behavior in Gas Diffusion Medium of PEFCs
via Full Morphology Approach, Journal of The Electrochemical Society, Vol. 154, pp. B419-B426, 2007.
Toray 090 SGL 10BA
Length/Width, mm 1.52 3.04
Thickness, µm 190 380
Porosity 0.78 0.88
β 10,000 100
m2
8.3 18 Figure 26. SEM surface images carbon papers (a) and (c) Toray 090 with 30
wt% polytetrafluoroethylene, and (b) and (d) SGL 10BA [31].
(a)
(b)
(c)
(d)
•
•
Water transport by the capillary pressure is modeled, with for example, the Leverett
function
D s
S S S K
[32] M.M. Tomadakis
and S.V. Sotirchos, Ordinary and Transition Regime Diffusion in Random Fiber Structures, AIChE
Journal, Vol. 39, pp. 15-24, 2002.
1 im
− =
−
Figure 27. Variation of the predicted effective diffusivity of fibrous porous diffusion medium with respect to the local water
saturation
[32].
•
•
•
The liquid water flux depends on the condensation rate in catalyst layer.
where γ
is the volumetric condensation coefficient that depends on kinetics of the condensation resistance, the diffusion resistance, and liquid/gas specific interfacial area.
2 2,H O g ,H Oc l lp p p p∇ = ∇ −∇ =∇
2,H O l rl l rl c
l c l l
ρ ρ μ μ
= − ∇ = − ∇
Figure 28. (a) Rendering of the one-dimensional transport in GL, and (b) liquid water flux [30].
(a)
(b)
g gl
R T γ
•
•
•
With given design parameters and the governing equation, the optimal two-layer diffusion medium can be predicted.
2,H O , ,
l f c a
ρ θ μ θ
Some two-layer DL design parameters [30].
Figure 29. (a) Jump in saturation across the interface of porous media I and II. (b) variation of the averaged saturation factor and its maximum
value for enhanced diffusion [30].
(a)
(b)
•
•
•
Figures 30(a) and (b) show water droplets on the DL surface with a groove, for elapsed time, (a) t
= 5.5 min (b) t
= 8.5 min. In the groove, the droplet size is smaller than on the surface showing the branching micro-
to macro-transport [33].
•
Figures 30(c) and (d) show water droplet along the gas channel gas flow stream, (c) is upstream and (d) is further downstream. As the gas flows along the gas channel, the water saturation increases, and more droplets can be observed.
Figure 30. Images of water droplets on interface between gas channel and the diffusion layer [33].
[33] D. Kagaku and et. al., Microscopic Visulatization
of State and Behavior of Liquid Water in a Gas Diffusion Layer of PEFC, Electrochemistry, Vol. 75, pp. 149-151, 2007.
7. Summary
Understanding water state in PEFC is essential in predicting its
performance.
•
•
•
In CL, pore structure of and heterogeneous surface forces determine the water behavior and in turn the effectiveness of TPBs
and reaction kinetics.
An MD view of the water interaction with Nafion
and its effect on proton conductivity is needed. This is challenging, since simulations can only captures part of
the water-surface interactions and transport processes.
•
•
•
It appears the water is initially produced as vapor and dominantly condenses in the DL.
Acknowledgement
This presentation is based on Mr. Gisuk
•
•
I would like to thank the Seminar Organizing Committee, in particular Michel Quintard, for all their efforts and hospitality.
Pore Water in Polymer Electrolyte Fuel Cell
Outline
Liquid Saturation Distribution in Fuel Cell
Liquid Pressure Distribution in Fuel Cell
Role of Water in PEFC
2. Objectives
Nafion Proton Conductivity and Its Relation to Water State
Pore Water States (Phase) in Nafion and Proton Conductivity (Proposed Hypothesis)
Schroeder Paradox
Observation of Water on Nafion Surface
Water on the Nafion Surface with ESEM
Water Condensation and Transitions on Nafion Surface
Water Condensation and Transition on Nafion Surface
Liquid Water Saturation
4. Role of Pore Water in Catalyst Layer
Reaction Rate in Catalyst Layer
Molecular Dynamics Simulations in Catalyst Layer
5. Role of Pore Water in Diffusion Layer
Carbon Paper Structures
6. Role of Water Droplets in Cathode Gas Channel
7. Summary

pore water in polymer electrolyte fuel cell

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