Fuel Cells - Kinetics

19/05/200819/05/2008

FUEL CELL REACTION

KINETICS

M. OLIVIER

[email protected]

22

INTRODUCTIONINTRODUCTION

Each electrochemical reaction event results in the transfer of one or more electrons, the current produced by a fuel cell (number of electrons per time) depends on the rate of the electrochemical reaction (number of reactions per time).

Increasing the rate of the electrochemical reaction is therefore crucial to improve fuel cell performance.

- Catalysis;

- Electrode design….

33


Electrochemical processes are heterogeneous.

Electrochemical reactions, like the HOR:

−+ +↔ eHH 222

take place at the interface between an electrode and an electrolyte.

44


Current expressed the rate of charge transfer

dt

dN

[ ]Adt

dNnF

dt

dQi ==

= the rate of the electrochemical reaction (mol/s)

Charge is the total amount of electricity produced

nFNQdti

t

==∫0

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Because electrochemical reactions only occur at interfaces, the current produced is usually directly proportional to the area at the interface. Therefore, current density (current per unit area) is more fundamental than current.

[ ]2cmA

A

ij =

The rate of the electrochemical reaction per unit area:

[ ]211 −−=== cmsmolnF

j

AnF

i

dt

dN

Av

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� ACTIVATION ENERGY

In order for reactants to be converted into products, they must first make it over the activation energy.

The probability that reactant species can make over this barrier determines the rate at which the reaction occurs.

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ACTIVATION ENERGYACTIVATION ENERGY

1) Mass transport of H2 gas to the electrode:

( ))(2)(2 electrodenearbulk HH →

−+ +↔ eHH 222

( )2)(2 HMMH electrodenear K→+

2) Adsorption of H2 onto the electrode surface:

3) Separation of the H2 molecule into two individually bound (chemisorbed) hydrogen atoms on the electrode surface:

( )HMMHM KK 22 →+

88


4) Transfer of electrons from the chemisorbed hydrogen atoms to the electrode, releasing H+ ions into the electrolyte

( ) ( )[ ]+− ++→× electrodenearHeMHM K2

( ) ( )[ ]++ →× eelectrolytbulkelectrodenear HH2

5) Mass transport of H+ ions away from the electrode :

The overall reaction rate will be limited by the slowest step in the series.

Suppose that the overall reaction is limited by the electron transfer step between chemisorbed hydrogen and the metal electrode surface.

99


1010


The slowest step can be represented as:

( ) +− ++↔ HeMHM K

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Curve 1: free energy of the reactant state as a function of the distance separation between the H atom and the metal surface

Curve 2: free energy of the product state as a function of the distance the H+ ion and the metal surface

Dark line = the minimum energy path for the conversion of [M…H] to [(M + e-) + H+]

a = the activated state

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Only species in the activated state can undergo the transition from reactant to product.

The probability of finding species in the activated state is exponentially dependent on the size of the activation barrier.

RTG

act eP*1∆−

=

The reaction rate in the forward direction (reactantsproducts)

( )RTG

R efcv*1

1

*

1

∆−=

cR* = the reactant surface concentration (mol/cm2)

f1 = the decay rate to products

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The net rate is given by the difference in rates between the forward and reverse reactions.

( )( ) +−

+−

++←

++→

HeMHM

HeMHM

K

K

The net reaction rate v is defined as:

*

2

*

1

2

*

1

*

21

*2

*1

GGG

efcefcv

vvv

rxn

RTG

P

RTG

R

∆−∆=∆

−=

−=

∆−∆−

� NET RATE OF A REACTION

Forward reaction

Reverse reaction

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The net rate of a reaction is given by the difference in rates between the forward and reverse reactions, both of which are exponentially dependent on an activation barrier, ∆G1

*.

( ) RTGG

P

RTG

Rrxnefcefcv

∆−∆−∆−−=

*1

*1

2

*

1

*

� NET RATE OF A REACTION

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( ) RTGG

P

RTG

R

rxnefcFnj

efcFnj

∆−∆−

∆−

=

=*1

*1

2

*

2

1

*

1

� EXCHANGE CURRENT DENSITY

At thermodynamic equilibrium, the forward and reverse current density must balance, there is no net current density (j=0).

021 jjj ==

j0 = exchange current density

Although at equilibrium the net reaction is zero, both forward and reverse reactions are taking place at a rate which is characterized by j0.

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� GALVANI POTENTIAL

Before the build-up of the interfacial potential (∆Φ), the forward rate was much faster than the reverse rate.

The build-up of an interfacial potential equalises the situation by increasing the forward activation barrier from ∆G1

* to ∆G* while decreasing the reverse reaction barrier from ∆G2

*to

∆G*.

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� BUTLER-VOLMER EQUATION

Electrochemical reactions = ability to manipulate the size of the activation barrier by varying the cell potential

If the Galvani potential across a reaction interface is reduced, the free energy of the forward reaction will be favoured over the reverse reaction. While the chemical energy system is the same as before, changing the electrical potential (b) upsets the balance between the forward and reverse activation barriers.

Reducing the Galvani potential by η reduces the forward activation barrier (∆G1

*<∆G*) and increases the reverse activation barrier (∆G2

*>∆G*).

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The forward activation barrier isdecreased by αnFη while the reverse activation barrier isincreased by (1-α)nFη.

The value of α depends on the symmetry of the activation barrier called the transfercoefficient.

For most electrochemicalreactions, α ranges from about 0,2 to 0,5.

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( )

( ) ( )

( ) ( ) ( )( )RTnFRTnF

RTnF

RTnF

eejj

ejj

ejj

ηαηα

ηα

ηα

−−

−−

−=

=

=

1

0

1

02

01

Butler-Volmer Equation

The current produced by an electrochemical reaction increases exponentially with activation overvoltage.

2020



Activation overvoltage ηact = voltage which is sacrificed (lost) to overcome the activation barrier associated with electrochemical reaction

The Butler-Volmerequation tells us that if you want more electricity (current) from our fuel cell, we must pay a price in terms of lost voltage.

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Having a high j0 is absolutely critical to good fuel cell performance. They are several ways to increase j0.

2222

HOW TO IMPROVE KINETIC PERFORMANCEHOW TO IMPROVE KINETIC PERFORMANCE

RTG

R efcFnj*1

1

*

0

∆−=

We have four ways to increase j0:

- Increase the reactant concentration CR*

- Decrease the activation barrier ∆G1*

- Increase the temperature T

- Increase the number of possible reaction sites (increase the reaction interface roughness)

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� INCREASE REACTANT CONCENTRATION

The thermodynamic benefit is minor, due to the logarithmic form of the Nernst Equation.

In contrast, the kinetic benefit is significant, with a linear impact.

Kinetic reactant concentration effects generally work against us for several reasons:

-most fuel cells use air instead of pure oxygen at the cathode

-reactant concentrations tend to decrease at fuel cell electrodes during high-current-density operation (mass transport) : further kinetic penalties

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� DECREASE ACTIVATION BARRIER

Highly catalytic electrode dramatically increases j0.

A catalytic electrode lowers the activation barrier. The free-energy curves depend on the nature of the electrode metal.

For the case of the hydrogen charge transfer:

-If the [M…H] bond is too weak, it is difficult for hydrogen to bond to electrode surface and to transfer charge from the hydrogen to the electrode;

-If the [M…H] bond is too strong, the hydrogen bonds too well to the electrode surface and it is difficult to liberate H+.

The optimal compromise between bonding and reactivity occurs for intermediate-strengh [M…H] bonds: Pt, Pd, Ir and Rh.

2525

10-9AcidPlatinumOxygen

10-3

10-4

AcidAlkaline

PlatinumHydrogen

j0 (A cm-2)MediumCatalyst

electrode


� DECREASE ACTIVATION BARRIER

2626


� INCREASE TEMPERATURE

Like changing the activation barrier, changing temperature has an exponential effect on j0.

2727


� INCREASE REACTION SITES

Increasing the number of available reaction sites per unit area

If an electrode surface is extremely rough, the true electrode surface area can be orders of magnitude larger than the geometric (smooth) electrode area and provides many more sites for reaction.

'

'

00A

Ajj =

j0’ = the intrinsic exchange current density of a perfectly

smooth electrode surface

= an intrinsic property of an electrode for a specific electrochemical reaction

2828

SIMPLIFIED ACTIVATION KINETICSSIMPLIFIED ACTIVATION KINETICS

� POLARISATION RESISTANCE

When ηact Is Very Small

ηact<15mV

A Taylor series expansion of the exponential terms can be performed with powers higher than 1 neglected.

( ) ( ) ( )( )RTnFRTnFeejj

ηαηα −−−= 1

0

RT

nFjj actη0=

The current and overvoltage are linearly related for small deviations from equilibrium and are independent of α.

jRjnFj

RTtact ==

0

η

Rt = Polarisation resistance

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� TAFEL EQUATION

When ηact Is Very Large

ηact> 50-100 mV

The second exponential term in the Butler-Volmer equation becomes negligible. On other words, the forward-reaction direction dominates, corresponding to a completely irreversible reaction process.

( )

jba

jnF

RTj

nF

RT

ejj

act

act

RTnF act

log

lnln 0

0

+=

+−=

=

η

ααη

ηα

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� TAFEL EQUATION

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DIFFERENT FUEL CELL REACTIONS PRODUCE DIFFERENT DIFFERENT FUEL CELL REACTIONS PRODUCE DIFFERENT

KINETICSKINETICS

The HOR kinetics are extremely fast, while the ORR kinetics are extremely slow. Completion of the ORR requires many individual steps and significant molecular reorganization.

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DIFFERENT FUEL CELL REACTIONS PRODUCE DIFFERENT DIFFERENT FUEL CELL REACTIONS PRODUCE DIFFERENT

KINETICSKINETICS

V

3333

DIFFERENT DIFFERENT

FUEL CELL FUEL CELL

REACTIONS REACTIONS

PRODUCE PRODUCE

DIFFERENT DIFFERENT

KINETICSKINETICS

HORHOR

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DIFFERENT DIFFERENT

FUEL CELL FUEL CELL

REACTIONS REACTIONS

PRODUCE PRODUCE

DIFFERENT DIFFERENT

KINETICSKINETICS

ORRORR

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CATALYSTCATALYST--ELECTRODE DESIGNELECTRODE DESIGN

- Maximize reaction surface areaMaximize reaction surface area, highly porous, nanostructuredelectrodes to achieve intimate contact between gas phases pores, the electrically conductive electrode, and the ion-conductive electrolyte.

Reaction sites : triple phase zones or triple phase boundaries (TPBs)

Reaction can only occur where the three important phases : electrolyte, gas, and electrically connected catalyst regions are in contact.

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-- Optimal catalyst material:Optimal catalyst material:

- High mechanical strength

- High electrical conductivity

- Low corrosion

- High porosity

- Ease of manufacturability

- High catalytic activity (high j0)

For PEMFC: platinum is currently the best known catalyst

For higher temperature fuel cells, nickel- or ceramic-based catalysts are often used.

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Gas diffusion layer

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Fuel Cells - Kinetics

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