Download fuel cell charge transport

FUEL CELL CHARGE
TRANSPORT
M. OLIVIER
[email protected]
19/05/2008
19/05/2008
INTRODUCTION
Charge transport completes the circuit in an electrochemical
system, moving charges from the electrode where they are
produced to the electrode where they are consumed.
They are two major types of charges species: electrons and
ions. The transport of electrons versus ions is fundamentally
different, primarily due to the large difference in mass
between the two. In most fuel cells, ion charge transport is
far more difficult than electron charge transport.
Resistance to charge transport results in a voltage loss
(given by Ohm’s law) = ohmic, or IR, loss.
These losses are minimized by making electrolytes as thin as
possible and employing high-conductivity materials.
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INTRODUCTION
Flux J measures how much of a given quantity (ex: moles)
flows through a material per unit area per unit of time.
Charge flux j measures the amount of charge that flows
through a material per unit area per unit of time.
Typical units:
C
A
= 2
2
cm s cm
Charge flux = current density
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INTRODUCTION
j = zi F J
J i = ∑ M ik Fk
k
Ji = flux of species i
Fk = the k different forces acting on i
Mik = coupling coefficients which reflect the relative ability of
a species to respond to a given force with movement as well
as the effective strength of the driving force itself
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INTRODUCTION
If charge transport is dominated by electrical driving forces:
dV
j =σ
dx
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CHARGE TRANSPORT : VOLTAGE LOSS
Why does charge transport result in a voltage loss?
Because fuel cell conductors are not perfect – they have an
intrinsic resistance to charge flow.
L
V = j 
σ 
 L 
 = i R
V = i 
 Aσ 
V
j =σ
L
L
Aσ
Resistance of our conductor
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CHARGE TRANSPORT : VOLTAGE LOSS
V is the voltage which must be applied in order to transport
charge at a rate given by i.
This voltage represents a loss (Ohmic loss)= voltage which
was expended or sacrificed in order to accomplish charge
transport.
η ohmic = i Rohmic = i (Relec + Rionic )
Often small compared to Rionic
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CHARGE TRANSPORT : VOLTAGE LOSS
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TRANSPORT RESISTANCE
Fuel cell resistance scales with area and with thickness: for
this reason fuel cell electrolytes are generally made as thin
as possible.
Fuel cell resistances are additive.
Performance
improvements may
be won by the
development of
better ion
conductors.
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TRANSPORT RESISTANCE
RESISTANCE SCALES WITH AREA
Area-normalised resistance known as area-specific
resistance (ASR):
η ohmic = i Rohmic = j ( ASRohmic )
ASRohmic = A fuel Cell Rohmic
ASRohmic =
10
10
L
σ
[A cm ]
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TRANSPORT RESISTANCE
RESISTANCE SCALES WITH THICKNESS
The shorter the conductor length L, the lower the resistance.
ASRohmic =
L
σ
Fuel cell electrolytes are designed to be as thin as possible.
The most important limitations are:
- Mechanical Integrity : Ex: membrane failure can result in
catastrophic mixing of the fuel and oxidant.
- Nonuniformities: Thin electrolyte areas may become “hot
spots” that are subject to rapid deterioration or failure.
- Shorting: Especially when the electrolyte is on the same
order of magnitude as the electrode roughness.
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TRANSPORT RESISTANCE
RESISTANCE SCALES WITH THICKNESS
The shorter the conductor length L, the lower the resistance.
ASRohmic =
L
σ
Fuel cell electrolytes are designed to be as thin as possible.
The most important limitations are:
- Fuel crossover : As the electrolyte thickness is reduced, the
crossover of reactants may increase.
- Contact resistance : Resistance associated with the interface
between the electrolyte and the electrode.
- Dielectric breakdown: When the electrolyte is so thin that the
electric field across the membrane exceeds the dielectric
breakdown field for the material.
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TRANSPORT RESISTANCE
RESISTANCE SCALES WITH THICKNESS
Practical limitations :
Limit achievable thickness : 10 – 100 µm
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TRANSPORT RESISTANCE
FUEL CELL RESISTANCES ARE ADDITIVE
It is extremely very difficult to distinguish between all the various
sources of resistance loss.
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TRANSPORT RESISTANCE
IONIC RESISTANCE USUALLY DOMINATES
The best electrolytes employed in fuel cell:
σ ≈ 0.1 Ω −1 cm −1
At a thickness of 50 µm:
ASR ≈ 0,05 − 0,1 Ω cm 2
A 50-µm-thick porous carbon cloth electrode:
ASR < 5 ×10 −6 Ω cm 2
This example illustrates how electrolyte resistance usually
dominates fuel cells.
Developing satisfactory ionic conductors is challenging.
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PHYSICAL MEANING OF CONDUCTIVITY
Conductivity quantifies the ability of a material to permit the
flow of charge when driven by an electric field.
Two major factors: how many carriers are available to
transport charge and the mobility of those carriers within
the material.
σ = ( zi F )ci ui
A material’s conductivity is determined by carrier
concentration Ci and carrier mobility ui.
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PHYSICAL MEANING OF CONDUCTIVITY
ELECTRONIC VERSUS IONIC CONDUCTORS
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REVIEW OF FUEL CELL ELECTROLYTES
Three major candidate materials classes for fuel cells:
aqueous, polymer, and ceramic electrolytes
Any fuel cell electrolyte must meet the following
requirements:
- High ionic conductivity
- Low electronic conductivity
- High stability (in both oxidizing and reducing environments)
- Low fuel crossover
- Reasonable mechanical strength (if solid)
- Ease of manufacturability
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REVIEW OF FUEL CELL CLASSES
IN AQUEOUS ELECTROLYTES/IONIC LIQUIDS
Almost all aqueous/liquid electrolyte fuel cells use a matrix
material to support or immobilize the electrolyte.
1. Provides mechanical strength to the electrolyte
2. Minimizes the distance between the electrodes while
preventing shorts
3. Prevents crossover of reactant gases through the
electrolyte
Examples: Alkaline fuel cells use concentrated aqueous
KOH electrolytes; phosphoric acid fuel cells use either
concentrated H3PO4 electrolytes or pure H3PO4. Molten
carbonate fuel cells use molten (K/Li)2CO3 immobilized
in a supporting matrix.
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REVIEW OF FUEL CELL CLASSES
IN AQUEOUS ELECTROLYTES/IONIC LIQUIDS
σ = ( zi F )ci ui
Selected Ionic Mobilities at Infinite Dilution in Aqueous Solutions at 25°C.
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REVIEW OF FUEL CELL CLASSES
IN POLYMER ELECTROLYTES
For a polymer to be good ion conductor, at a minimum it
should possess the following structural properties:
1) The presence of fixed charges sites;
2) The presence of free volume (“open space”).
The fixed charge sites should be opposite charge compared to
the moving ions.
In a polymer structure maximizing the concentration of these
charge sites is critical to ensure high conductivity.
Excessive addition of ionically charged side chains will
significantly degrade the mechanical stability of the polymer.
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REVIEW OF FUEL CELL CLASSES
IN POLYMER ELECTROLYTES
Schematic of ion transport between polymer chains: Polymer
segments can move or vibrate in the free volume, thus
inducing physical transfer of ions from one charged site to one
another.
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REVIEW OF FUEL CELL CLASSES
IN POLYMER ELECTROLYTES: Ionic Transport in Nafion
Teflon backbone = mechanical
strength
Sulfonic acid functional groups:
charge sites for proton
transport
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REVIEW OF FUEL CELL CLASSES
IN POLYMER ELECTROLYTES: Ionic Transport in Nafion
In the presence of water, the protons (H+) in the pores form
hydronium complexes (H3O+) and detach from the sulfonic
acid side chains. When sufficient water exists in the pores,
the hydronium ions can transport in the aqueous phase.
-Under these circumstances, ionic conduction in Nafion is
similar to conduction in liquid electrolytes.
-The hydrophobic nature of the Teflon backbone accelerates
water transport through the membrane, since the
hydrophobic pore surfaces tend to repel water.
-To maintain this extraordinary conductivity, Nafion must be
fully hydrated with liquid water.
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REVIEW OF FUEL CELL CLASSES
IN POLYMER ELECTROLYTES: Ionic Transport in Nafion
The water content λ in Nafion = the ratio of the number of
water molecules to the number of charged (SO3-H+) sites
0 < λ < 22
Completely
dehydrated Nafion
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Full saturation
REVIEW OF FUEL CELL CLASSES
IN POLYMER ELECTROLYTES: Ionic Transport in Nafion
Water content versus water activity for Nafion 117 at 303 K
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REVIEW OF FUEL CELL CLASSES
IN POLYMER ELECTROLYTES: Ionic Transport in Nafion
Ionic conductivity of Nafion versus water content λ at 303 K
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REVIEW OF FUEL CELL CLASSES
IN POLYMER ELECTROLYTES: Ionic Transport in Nafion

1 
 1
σ (λ , T ) = σ 303 K (λ ) exp 1268 
− 
 303 T 

Ionic conductivity of Nafion versus temperature when λ= 22
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REVIEW OF FUEL CELL CLASSES
IN CERAMIC ELECTROLYTES
SOFC electrolytes = are solid, crystalline oxide materials that
can conduct ions
The most popular SOFC electrolyte is yttria stabilised
zirconia (YSZ)
Typical YSZ electrolyte contains: 8% yttria mixed with
zirconia
Zirconia = ZrO2 (zirconium oxide)
Yttria = Y2O3 (Yttrium oxide)
Yttria stabilised the zirconia crystal structure in the cubic
phase (where it is most conductive).
Yttria induces high concentrations of oxygen vacancies into
the zirconia crystal structure. High ion conductivity
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REVIEW OF FUEL CELL CLASSES
IN CERAMIC ELECTROLYTES
Charge compensation effects in YSZ lead to creation of oxygen
vacancies
The addition of 8% (molar) yttria to zirconia causes about
4% of the oxygen sites to be vacant.
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REVIEW OF FUEL CELL CLASSES
IN CERAMIC ELECTROLYTES
A material’s conductivity is determined by the combination
of carrier concentration c and carrier mobility u:
c (zF ) D
σ = ( z F )c u =
RT
2
The oxygen vacancies can be considered to be ionic charge
« carriers ».
Carrier mobility is described by D, the diffusivity of the
carrier in the crystal lattice.
Diffusivity describes the ability of a carrier to move, or
diffuse, from site to site within a crystal lattice.
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REVIEW OF FUEL CELL CLASSES
IN CERAMIC ELECTROLYTES
There is an upper limit to doping.
Above a certain dopant or vacancy concentration, defects
start to interact with each other, reducing their ability to
move.
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REVIEW OF FUEL CELL CLASSES
IN CERAMIC ELECTROLYTES
The carrier diffusivity in SOFC electrolytes is exponentially
temperature dependent:
D = D0 e
− ∆Gact ( RT )
D0 = constant (cm2/s)
∆Gact= the activation barrier for the diffusion process (J/mol)
c ( zF ) D0 e − ∆Gact
σ=
RT
2
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( RT )
REVIEW OF FUEL CELL CLASSES
IN CERAMIC ELECTROLYTES
For extrinsic carriers, c is determined by the doping
chemistry of the electrolyte. In this case, c is a constant and
the preceding equation can be used.
For intrinsic carriers, c is exponentially dependent on the
temperature and the equation becomes:
csites ( zF ) D0 e − ∆hv
σ=
RT
2
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( 2 kT )
e − ∆Gact
( RT )