Lecture 4-Fuel Cell-Electrochemistry & Reaction Kinetics

Special Topics ( Fuel Cell

Fundamentals and Technology)

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan

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Dr.-Eng. Zayed Al-Hamamre

Fuel Cell Principle: Electrochemistry &

Reaction Kinetics

Content

Ø Overview

Ø Faraday’s Laws

Ø Fuel Cell Performance and Irreversibility

Ø Electrode – Electrolyte Interface


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Ø Electrochemical Kinetics

Ø Butler–Volmer Equation

Ø Polarization Losses

Ø Electrochemical reactions results in the transfer of electrons between an electrode

surface and a chemical species adjacent to the electrode surface (heterogeneous

reaction).

Ø For an electrochemical reaction to take place, there are several necessary

components:

1. Anode and Cathode Electrode: The electrochemical reactions occur on the

electrode surfaces. Oxidation occurs at the anode and reduction at the

Overview


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electrode surfaces. Oxidation occurs at the anode and reduction at the

cathode

2. Electrolyte The main function of the electrolyte is to conduct ions from one

electrode to the other. It is also serves to physically separate the fuel and the

oxidizer and prevent electron short-circuiting between the electrodes.

3. External Connection between Electrodes for Current Flow: If this connection

is broken, the continuous circulation of current cannot flow and the circuit is

open.

Ø The H2 gas and protons can not exist inside the electrode, while free electrons can

not exist in the electrolyte

Ø The current produced by fuel cell (number of electron per time) depends on the rate

Overview

+

+

+

+

-

-

-

-

2e-

H2

2H+

Electrode Electrolyte


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of electrochemical reactions.

Q Charge in C, t is time, n No. of electron, dN\dt is the rate of electrochemical reaction

Ø Although the anode and cathode reactions are independent, they are clearly coupled

to each other by the necessity to balance the overall reaction, so that the electrons

produced in the HOR are consumed in the ORR

Ø Current produced by the cell is directly proportional to the area of the interface,

therefore, current density (current per unit area, A or mA\cm2) is used

Overview

Where A is the area

Ø Electrochemical reaction rate can be expressed per unit area base:


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Ø Electrochemical reaction rate can be expressed per unit area base:

Overview

Ø The total charge passed by the flow of an ampere of electrons in one second

Ø Voltage A volt (V) is a measure of the potential to do electrical work.


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Ø Thus, it is a measure of the work required to conduct one coulomb of charge.

Overview

Ø Faraday’s constant F represents the charge per mole of equivalent electrons

Ø The equivalent electrons (eq) is very important. Many electrochemical reactions do

not exchange 1 mol of electrons for 1 mol of reactant.


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Ø For the reaction

FARADAY’S LAWS:

CONSUMPTION AND PRODUCTION OF SPECIES

Ø How much mass of a given reactant is required to produce a given amount of

current? Conversely, how much current is required to produce a certain amount of

product ?

Ø The fundamental relationships should be based on conservation of mass and charge

Ø The charge transfer per mole of species of interest is nF.


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Ø In the reaction ,, electrons are transfer per mole of

oxygen, thus the charge passing is 4F (coulombs/mole)

Ø n simply permits determination of the relationship between charge passed and

reactant consumption (or product generation) of any species chosen.

FARADAY’S LAWS:

CONSUMPTION AND PRODUCTION OF SPECIES

Ø Considering water produced as the species of interest, the value of n is 2, and there

are 2F coulombs passed per mole of H2O produced.

Ø Faraday’s Laws establish a link between the flow of charge and mass

The amount of product formed or reactant consumed is directly proportional to the

charge passed. J


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J

Example

Ø Consider a single hydrogen fuel cell at 4 A current output:

Anode oxidation:

Cathode reduction:

Global reaction:

1. What is the molar rate of H2 consumed for the electrochemical reaction?


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2. What is the molar rate of O2 consumed for the electrochemical reaction?

Example

3. What is the minimum molar flow rate of air required for the electrochemical

reaction?

4. What is the maximum molar flow rate of air delivered for the electrochemical

reaction?

There is no maximum of reactant supplied.


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5. What is the rate of water generation at the cathode in grams per hour?

Potential Control Electron Energy

Ø The reaction direction can be controlled by controlling the electrode potential

OX + e-→ Re

Ø The electron energy is measured by Fermi Level.


Ø If the electrode potential is made more negative than the equilibrium one, the

reaction will be biased toward the formation of Re, i.e. electrode is less hospitable


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reaction will be biased toward the formation of Re, i.e. electrode is less hospitable

to electron.

Ø If the electrode potential is made relatively more positive than equilibrium

potential, the reaction will be biased toward the formation of Ox, the electrode

attracts electron.



Fermi

Level.


Fermi

Level.

e-


Fermi

e-


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Equilibrium

Level.

Potential is made

more negative

Potential is made

more positive

Fermi

Level.

Ø Many fundamental physical, chemical & electrochemical mechanisms involved in in

electrode reactions in actual FC operation

Reactant transport, reactant dissolution, double layer penetration/ transport, pre-

electrochemical reaction kinetics, adsorption, surface migration, electrochemical charge

transfer, post-electrochemical surface migration, desorption, post-electrochemical reaction,

product transport, product evolution, …

Fuel Cell Performance and Irreversibility


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Ø The actual useful voltage V obtained from a fuel cell with the load is different from

the theoretical/ideal voltage E from thermodynamics.

No losses voltage

Ø Fuel Cell Losses (‘polarizations’, ‘overpotentials’, ‘overvoltages’) gives

Polarization Curve”


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Ø Activation losses: These are caused by the slowness of the reactions taking place on

the surface of the electrodes. A proportion of the voltage generated is lost in driving

the chemical reaction that transfers the electrons to or from the electrode.

Ø Fuel crossover and internal currents: This energy loss results from the waste of

fuel passing through the electrolyte, and, to a lesser extent, from electron conduction

through the electrolyte. However, a certain amount of fuel diffusion and electron

flow will always be possible.


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flow will always be possible.

Ø Ohmic losses: This voltage drop is the straightforward resistance to the flow of

electrons through the material of the electrodes and the various interconnections,

This voltage drop is essentially proportional to current density, linear, and so is

called ohmic losses.

Ø Mass transport or concentration losses: These result from the change in

concentration of the reactants at the surface of the electrodes as the fuel is used.

Ø Activation polarization, dominates losses at low current density, is the voltage

overpotential required to overcome the activation energy of the electrochemical

reaction on the catalytic surface

Ø Activation polarization represents the voltage loss required to initiate the reaction

What is the physical nature of the activation polarization

and how exactly does the charge transfer reaction proceed?

Electrode – Electrolyte Interface

Activation polarization


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and how exactly does the charge transfer reaction proceed?

Ø Between an electrode and the electrolyte, there exists a complex structure known as

the electrical (charge) double layer.

Ø At the electrode surface and in the adjacent electrolyte, a buildup of charge occurs.

Ø At the anode, the potential is lower than the surrounding electrolyte, so the there is a

buildup of negative charge along the surface of the catalyst and a positive charge in

the surrounding electrolyte forming the double-layer structure.


The Charge Double Layer

Ø Is a complex and electrode phenomenon

Ø Important in understanding the dynamic electrical behavior of fuel cells

Ø Whenever two different materials are in contact, there is a build-up of charge on the

surfaces or a charge transfer from one to the other across the interface (charge

separation occurs in the interfacial region).


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Ø The charge double layer forms:

• Due to electron diffusion effects,

• Because of the reactions between the

electrons in the electrodes and the

ions in the electrolyte, and also

• As a result of applied voltages

At the cathode of an acid electrolyte fuel cell:

Ø Electrons will collect at the surface of the

electrode and

Ø H+ ions will be attracted to the surface of the

electrolyte.

Ø These electrons and ions, together with the O2



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2

supplied to the cathode will take part in the

cathode reaction.

O2 + 4e− + 4H+ → 2H2O

The charge double layer at the surface

the cathode in an acidic electrolyte fuel

cell .

Ø The probability of the reaction taking place obviously depends on:

• The density of the charges,

• Electrons, and

• H+ ions on the electrode and electrolyte surfaces.

Ø The more the charge, the greater is the current.

Ø Any collection of charge, at the electrode/electrolyte interface will generate an



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Ø Any collection of charge, at the electrode/electrolyte interface will generate an

electrical voltage (activation overvoltage).

Ø The overvoltage opposes and reduces the reversible ideal voltage (Voltage lost in

driving the chemical reaction that transfers the electrons to or from the electrode).

Ø charge double layer needs to be present for a reaction to occur, that more charge is

needed if the current is higher, and so the overvoltage is higher if the current is

greater.

Ø The use of catalytic effect of the electrode by increasing the probability of a

reaction – so that a higher current can flow without such a build-up of charge

(enable reaction to occur with a low buildup of charge).

Ø The discontinuity of charge physically behaves like a capacitor.

Simple approximate models have been proposed to describe the properties of the

electrified interface

• Helmholtz compact layer model



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• Helmholtz compact layer model

• Gouy-Chapman diffuse layer model

• Stern modification

Ø The layer of charge on or near the electrode–electrolyte interface is a store of

electrical charge and energy (a single capacitor or series of capacitors)

A useful conceptualization involves representing the interfacial structure

as an electrical equivalent circuit

Helmholtz compact layer model (parallel-plate condenser)

Ø Two layers of charge of opposite sign are separated by a fixed distance

Ø Assume counter-charge essentially within one ion’s depth


potential drop

across the


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interface will

be linear

Capacitance

dielectric constant


Gouy-Chapman Diffuse Double Layer Model

Ø Ions in the electric double layer are subjected to electrical and thermal fields

Ø With certain electrolytes (especially weak solutions), charge may need to build up

over greater depth

Diffuse charge


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Diffuse charge

The Capacity,n0 NO. of ions per unit volume in the bulk of

the electrolyte , V is the potential drop from

the metal to the bulk of the electrolyte.

Stern Double Layer Model

Ø Combine features of Helmoholtz and Gouy-Chapman to capture real physics of DL

Ø Ions are considered to have a finite size and are located at a finite distance from the

electrode.

Ø The charge distribution in the electrolyte is divided into two contributions:

i. As in the Helmholtz model immobilized close to the electrode, and



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i. As in the Helmholtz model immobilized close to the electrode, and

ii. As in the Gouy-Chapman model, diffusely spread out in solution

Ø The Capacitance across this electrode/electrolyte interface

Stern Double Layer Model



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Electrochemical KineticsEquilibrium:

Ø Measurements of redox potentials (and voltage potentials)

Ø Gives a quantitative estimate of the reaction tendency to proceed (equilibrium)

Ø No kinetic information is derived from these measurements

Kinetics:

Ø Concerned the mechanism by which electron transfer process occur.


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Ø Concerned the mechanism by which electron transfer process occur.

Ø Need to know if the reactions (electron transfer) will proceed fast enough to make

them useful

Ø We desire the rate of electron transfer (ET) that occurs at the electrode electrolyte

interface for given conditions

Ø How can kinetic information about ET processes be derived?

Ø Increasing the rates of fuel-cell reactions is central to developing highly efficient

commercial fuel cells.

Basic Kinetic Concepts for Interfacial ET process:

Ø Current flow is proportional to reaction flux (rate)

Ø Reaction rate is proportional to interface reactant concentration

Ø Similar to homogeneous reaction chemical kinetics: constant of proportionality

between reaction rate σ (mol/cm2/s) and reactant concentration c (mol/cm3) is the

rate constant k (cm/s)

Electrochemical Kinetics


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Ø All chemical and electrochemical reactions are activated processes

• Activation energy barrier that must be overcome for reactions to proceed

• Energy must be supplied to surmount the activation energy barrier

• Energy may be supplied thermally or also (for ET processes at electrodes) via

application of a potential to the electrodes

Ø Applying a potential to an electrode generates an electric field at the

electrode/electrolyte interface that reduces the magnitude of the activation energy

barrier increasing the ET reaction rate, Electrolysis works on this principle

Ø An applied potential acts as a driving force for the ET reaction



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Ø Expect that current should increase with increasing driving force

Ø Catalysts act to reduce the magnitude of the activation energy barrier .



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Ø The reaction is thermodynamically favorable, and the reaction will generate

current, a flow of electrons or ions.



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Ø The rate of electrochemical reaction is finite because the energy barrier (activation

Energy) impedes the conversion of reactants into products.


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For reaction to take

place, the activation

energy must be over

come



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Electron Transfer and Mass Transport

Ø We know that both mass transport (reactants and products) and the electron transfer

process itself contribute to kinetics

Ø Let us ONLY consider the kinetics of interfacial electron transfer from a classical,

macroscopic and phenomenological (non quantum) viewpoint

Ø This approach is based on classical Transition State Theory, and results in the Butler-

Volmer Equation



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Volmer Equation

Transition State Theory

Ø Quantitative study of the transition state that molecules pass through during reaction

(chemical, electrochemical)

Transition State

molecules exist for 10-12Transition State Theory

Fuel /Oxidizer

Reaction driving force

voltage over potential

at the electrode

Elementary charge

transfer reaction step


Boltzmann


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Fuel /OxidizerPartially converted

reactants

transfer reaction step

Products

Fre

e en

erg

y o

r en

tha

lpy

Rate constant

Plank’s

constant

constant

Eyring and Arrhenius Equations

Ø The Eyring equation is valid for many types of dynamic rate processes (gases,

liquids, in solution, and on surfaces)

Ø Consider the transition state (*) of an activated process



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Pre-exponential factor

(entropy, temp. dependence)

Activation energy term

(enthalpy dependence)


Activation energy of charge transfer reactions

Ø For the H2 → 2H+ + 2e-, the following series of steps are being followed:

1. Mass transport of H2 onto the electrode

H2 (bulk) → H2 (near electrode)

2. Absorption of H2 onto the electrode surface

H2 (near electrode) + M → M… H2

M: represents the

nonreacting catalyst

surface


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H2 (near electrode) + M → M… H2

3. Separation of the H2 molecules into two individual bond (chemisorbed)

Hydrogen atoms on the electrode surface

M… H2 + M → 2M…H

4. Transfer of electrons from the chemisorbed hydrogen atoms to the electrode

releasing H+ ions into the electrolyte (limiting step)

2 [M…H → (M + e-) + H+ (near electrode)

5. Mass transport of the H+ away from the electrode

2 [H+ (near electrode) → H+ (bulk electrolyte)


Ø The overall reaction rate will be determined by the slowest step in the series

12

Fre

e en

erg

y

∆G*1

∆G*2

a

Activation energy

Ø 1 increase with the distance

from metal surface (stability

improves with absorption to

the electrode surface).

Free energy of the

Chemisorbed HFree energy H+


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Distance from interface

(M + e-) + H+

M…H

∆Grxn

∆G*2

the electrode surface).

Ø 2 energy is required to bring

H+ to the electrode surface

to over come the repulsive

force (unfavorable for the

H+ to be at the surface of

electrode)

Ø The red line represent the min. energy path for

the conversion (conversion involves an over

come of energy max. (a: activated state)


Ø Overall rate of reaction:

Ø For the case where the activation energy of the product state lower than the reactants


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Ø For the case where the activation energy of the product state lower than the reactants

state, then the forward reaction proceeds faster than the backward reaction rate.

Ø The unequal rates results in a build up of charge (e- accumulating at the electrode and

H+ in the electrolyte) .

Ø The charge accumulation continues until the resultant potential across the reaction

interface counter balance the free energy difference between reactants and products.

(electro-chemical equilibrium)


Exchange current density

Ø Defined as the rate of the forward or reverse reaction under equilibrium conditions.

Ø Since

Then, the forward current density:


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Ø The reverse current density:


Ø At equilibrium:

and

Where j0 is the exchange current density

Reactant conc. at Equ.


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Ø The free energy of charge species are sensitive to voltage. Therefore, changing the

cell voltage changes the free energy of the charged species taking part in the reaction.

Ø The size of the activation barrier can be manipulated by varying the cell potential.

Ø Rate constant, k, varies with applied potential, E, because ∆G* varies with applied

potential.



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Ø Application of a finite “overpotential,” η = E - ENernst, lowers the activation energy

barrier for an electrochemical reaction by a fixed amount, β (Symmetry factor, β, or

the electron transfer coefficient, determines how much of the electrical energy input

affects the activation energy barrier of the redox process (0 < β < 1)).

Ø In the previous figure, the activation barrier of the forward reaction is decreased by

while the reverse activation barrier is increased by


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Ø The current produced by reaction is:

Ø The reactant flux is (mol/cm2-s):

Heterogeneous ET

rate constant (cm/s)

Interfacial reactant

concentration (mol/cm3)


Ø Gibbs Free Energy: η = overpotential

Ø Interims of the exchange current density:

and

Butler–Volmer equation


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the net current then is

where

Butler–Volmer equation


Butler–Volmer Equation

Ø Increasing the exchange current density can be performed by:

• Increasing the reactant concentration

• Decreasing the activation barrier

• Increasing the temperature T

• Increasing the number of active reaction site (increasing the reaction interface)


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• Increasing the number of active reaction site (increasing the reaction interface)


Butler–Volmer equation, effect of activation overvoltage on fuel cell performance

Ø The curve was constructed by

calculating the ideal cell

potential (Nernst Equation)

then subtracting

Ø Reaction kinetics inflict an

exponential loss on a fuel cell


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exponential loss on a fuel cell

i-V curve (BV equation)

Ø The smaller the j0, the greater

is this voltage drop.

Ø Having a high j0 is critical to

have good fuel cell

performance


Ø The current produced by an electrochemical reaction increases exponentially with the

activation overvoltage (voltage loss to overcome the activation barrier associate with

electrochemical reaction).

Ø The equation state that, to obtain more electricity (current) from the fuel cell, a price

interims of lost voltage must be paid.


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Butler–Volmer Model of Kinetics (More general expression)

Ø To describe activation polarization losses at a given electrode.

Ø The BV model describes an electrochemical process limited by the charge transfer

of electrons (ORR, and in most cases the HOR with pure hydrogen).

Ø The assumption of the BV kinetic model is that the reaction is rate limited by a

single electron transfer step


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Ø The net current density is

For an anode reaction with

positive η, the anodic branch

will exponentially increase,

For a cathodic reaction with

negative η, the cathodic branch

will exponentially increase,

η >> 0 η << 0



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Ø If β = 1 the additional

overpotential at the

electrode goes

completely toward

promoting the

reduction reaction


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reduction reaction

Ø If β = 0 the additional

potential is applied

toward promotion of

the anodic oxidation

reaction.


Butler–Volmer Model: High-Electrode-Loss Region of Butler–Volmer

(Tafel equation)

Ø The overvoltage at the surface of an

electrode followed a similar pattern

in a great variety of electrochemical

reactions.

Ø For high polarization one of the


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Tafel plots for slow and fast electrochemical reactions

Ø For high polarization one of the

branches will dominate, thus the

overvoltage value is given by

For j > j0

n

n


Ø In the low-loss region and using Taylor series expansion and linearization of the BV

equation, then the overvoltage potential can be expressed as:

Butler–Volmer Model: Low-loss (overpotential) region


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Butler–Volmer Equation with Identical Charge Transfer Coefficients–sinh

Simplification


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Apply the Eyring equation to electron transfer (ET) process


Ø Consider the transition state (*) of an activated process

Characteristic ET distance

(molecular diameter)

Ø Let then


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Ø Let then

Ø Using the equation

Important: rate constant for

heterogeneous ET depends

directly on applied electrode

potential


Ø A low-overpotential region where kinetics are

facile and relatively low losses occur

Ø A higher overpotential region, where losses

become much more significant

Ø A very high current region where mass

transport losses dominate

Butler–Volmer Simplifications


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Ø At low current density, the activation

overpotential η required to maintain a net

reaction rate in a given direction is small.

transport losses dominate

Ø Beyond a threshold value in current density related to the equilibrium reaction exchange rate

of the electrode, the additional polarization required for increasing current is greatly

increased.



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Activation Polarization


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Ohmic and Concentration Polarization


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Ohmic Polarization


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Concentration Polarization


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Cell Voltage


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Lecture 4-Fuel Cell-Electrochemistry & Reaction Kinetics

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Transcript of Lecture 4-Fuel Cell-Electrochemistry & Reaction Kinetics