fuel cell charge transport(natha) - umons · 22 introduction charge transport completes the circuit...

19/05/200819/05/2008

FUEL CELL CHARGE

TRANSPORT

M. OLIVIER

[email protected]

22

INTRODUCTIONINTRODUCTION

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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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:22

cm

A

scm

C=

Charge flux = current density

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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

∑=

=

k

kiki

i

FMJ

JFzj

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If charge transport is dominated by electrical driving forces:

dx

dVj σ=

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CHARGE TRANSPORT : VOLTAGE LOSSCHARGE 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.

σ

σ

σσ

A

L

RiA

LiV

LjV

L

Vj

=

=

==

Resistance of our conductor

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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.

( )ionicelecohmicohmic RRiRi +==η

Often small compared to Rionic

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99

TRANSPORT RESISTANCETRANSPORT 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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Area-normalised resistance known as area-specific resistance (ASR):

RESISTANCE SCALES WITH AREA

( )

[ ]

σ

η

LASR

cmARAASR

ASRjRi

ohmic

ohmicCellfuelohmic

ohmicohmicohmic

=

=

==2

1111


The shorter the conductor length L, the lower the resistance.

RESISTANCE SCALES WITH THICKNESS

σ

LASRohmic =

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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The shorter the conductor length L, the lower the resistance.


σ

LASRohmic =

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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Practical limitations :

Limit achievable thickness : 10 – 100 µm

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FUEL CELL RESISTANCES ARE ADDITIVE

It is extremely very difficult to distinguish between all the various sources of resistance loss.

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IONIC RESISTANCE USUALLY DOMINATES

The best electrolytes employed in fuel cell:

111.0 −−Ω≈ cmσ

21,005,0 cmASR Ω−≈At a thickness of 50 µm:

A 50-µm-thick porous carbon cloth electrode:

26105 cmASR Ω×< −

This example illustrates how electrolyte resistance usually dominates fuel cells.

Developing satisfactory ionic conductors is challenging.

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PHYSICAL MEANING OF CONDUCTIVITYPHYSICAL 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.

( ) iii ucFz=σ

A material’s conductivity is determined by carrier concentration Ci and carrier mobility ui.

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PHYSICAL MEANING OF CONDUCTIVITYPHYSICAL MEANING OF CONDUCTIVITY

ELECTRONIC VERSUS IONIC CONDUCTORS

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REVIEW OF FUEL CELL ELECTROLYTESREVIEW 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 CLASSESREVIEW OF FUEL CELL CLASSES

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 immobilizedin a supporting matrix.

IN AQUEOUS ELECTROLYTES/IONIC LIQUIDS

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IN AQUEOUS ELECTROLYTES/IONIC LIQUIDS

( ) iii ucFz=σ

Selected Ionic Mobilities at Infinite Dilution in Aqueous Solutions at 25°C.

2121


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.

2222


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.

2323


IN POLYMER ELECTROLYTES: Ionic Transport in Nafion

Teflon backbone = mechanical strength

Sulfonic acid functional groups:charge sites for proton transport

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In the presence of water, the protons (H+) in the pores form hydronium complexes (H3O

+) and detach from the sulfonicacid 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.

2525



The water content λ in Nafion = the ratio of the number of water molecules to the number of charged (SO3

-H+) sites

220 << λCompletely

dehydrated NafionFull saturation

2626



Water content versus water activity for Nafion 117 at 303 K

2727



Ionic conductivity of Nafion versus water content λ at 303 K

2828



Ionic conductivity of Nafion versus temperature when λ= 22

( ) ( )

−=

TT K

1

303

11268exp, 303 λσλσ

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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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Charge compensation effects in YSZ lead to creation of oxygenvacancies

The addition of 8% (molar) yttria to zirconia causes about 4% of the oxygen sites to be vacant.

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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.

A material’s conductivity is determined by the combination of carrier concentration c and carrier mobility u:

( ) ( )RT

DzFcucFz

2

==σ

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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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The carrier diffusivity in SOFC electrolytes is exponentially temperature dependent:

( )RTGacteDD∆−= 0

D0 = constant (cm2/s)

∆Gact= the activation barrier for the diffusion process (J/mol)

( ) ( )

RT

eDzFcRTGact∆−

= 0

2

σ

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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:

( ) ( ) ( )

RT

eeDzFcRTGkTh

sitesactv ∆−∆−

=2

0

2

σ

fuel cell charge transport(natha) - umons · 22 introduction charge transport completes the circuit...

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