Fuel Cell-Electrochemistry and Reaction Kinetics

Special Topics ( Fuel Cell Fundamentals and Technology) Fuel Cell Principle: Electrochemistry &

Reaction Kinetics Dr.-Eng. Zayed Al-Hamamre

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Chemical Engineering Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

Content Overview Faraday’s Laws Fuel Cell Performance and Irreversibility Electrod Elect rodee – Electr Electrolyte olyte Interface Interface Electrochemical Kinetics Butler–Volmer Equation Polarization Losses

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Chemical Engineering Department Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

Overview Electrochemical Electrochemical reactions results in the transfer of electrons between an electrode surface and a chemical species adjacent to the electrode surface (heterogeneous reaction). For an electrochemical reaction to take place, there are several necessary components: 1.

Anode and and Cathode Cathode Electr Electrode: ode: The The electr electrochemi ochemical cal reacti reactions ons occur occur on the

. cathode 2.

Electrol Electrolyte yte The The main main function function of the elect electrol rolyte yte is is to conduct conduct ions from from one

electrode to the other. other. It is also serves to physically separate the fuel and the oxidizer and prevent electron short-circuiting between the electrodes. 3.

External External Connecti Connection on between between Electr Electrodes odes for for Current Current Flow: Flow: If this this connectio connection n is broken, the continuous circulation of current cannot flow and the circuit is 3

open. Chemical Engineering Department Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

Overview The H2 gas and protons can not exist inside the electrode, while free electrons can not exist in the electrolyte 2eElectrode

- + - +

H2

- + 2H+ - +Electrolyte

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

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

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 4


Overview Electrochemical Electrochemical reactions results in the transfer of electrons between an electrode surface and a chemical species adjacent to the electrode surface (heterogeneous reaction). For an electrochemical reaction to take place, there are several necessary components: 1.

Anode and and Cathode Cathode Electr Electrode: ode: The The electr electrochemi ochemical cal reacti reactions ons occur occur on the

. cathode 2.

Electrol Electrolyte yte The The main main function function of the elect electrol rolyte yte is is to conduct conduct ions from from one

electrode to the other. other. It is also serves to physically separate the fuel and the oxidizer and prevent electron short-circuiting between the electrodes. 3.

External External Connecti Connection on between between Electr Electrodes odes for for Current Current Flow: Flow: If this this connectio connection n is broken, the continuous circulation of current cannot flow and the circuit is 3

open. Chemical Engineering Department Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

Overview The H2 gas and protons can not exist inside the electrode, while free electrons can not exist in the electrolyte 2eElectrode

- + - +

H2

- + 2H+ - +Electrolyte

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

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

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 4


Overview 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

Where A is the area

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Overview

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

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

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

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

The equivalent electrons (eq) is very important. Many electrochemical reactions do not exchange 1 mol of electrons for 1 mol of reactant. For the reaction

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Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

FARADAY’S LAWS: CONSUMPTION AND PRODUCTION OF SPECIES

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 ? The fundamental relationships should be based on conservation of mass and charge The charge transfer per mole of species of interest is nF. In the reaction

,, electrons are transfer per mole of

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

n simply permits determination of the relationship between charge passed and

reactant consumption (or product generation) of any species chosen. 8


FARADAY’S LAWS: CONSUMPTION AND PRODUCTION OF SPECIES

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. 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

J

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Example 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?

2.

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

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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.

5.

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

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Potential Control Electron Energy Potential Control Electron Energy The reaction direction can be controlled by controlling the electrode potential OX + e- → Re The electron energy is measured by Fermi Level. If the electrode potential is made more negative than the equilibrium one, the react on w

e

ase towar t e ormat on o

e, .e. e ectro e s ess osp ta e

to electron. 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.

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Potential Control Electron Energy

Electrode Electrolyte



ee-

Fermi Level.

Fermi Level. Fermi Level.

Potential is made

Equilibrium

more negative

Potential is made more positive

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Fuel Cell Performance and Irreversibility Many fundamental physical, chemical & electrochemical mechanisms involved in in electrode reactions in actual FC operation Reactant transport, reactant dissolution, double layer penetration/ transport, preelectrochemical reaction kinetics, adsorption, surface migration, electrochemical charge transfer, post-electrochemical surface migration, desorption, post-electrochemical reaction, product transport, product evolution, …

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Fuel Cell Performance and Irreversibility The actual useful voltage V obtained from a fuel cell with the load is different from the theoretical/ideal voltage E from thermodynamics. Fuel Cell Losses (‘polarizations’, ‘overpotentials’, ‘overvoltages’) gives Polarization Curve” No losses voltage

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Fuel Cell Performance and Irreversibility 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. 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. 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. 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. 16


Electrode – Electrolyte Interface Activation polarization

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 Activation polarization represents the voltage loss required to initiate the reaction

What is the physical nature of the activation polarization an

ow exact y oes t e c arge trans er react on procee

Between an electrode and the electrolyte, there exists a complex structure known as the electrical (charge) double layer. At the electrode surface and in the adjacent electrolyte, a buildup of charge occurs. 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.

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Electrode – Electrolyte Interface The Charge Double Layer Is a complex and electrode phenomenon Important in understanding the dynamic electrical behavior of fuel cells 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). 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 18


Electrode – Electrolyte Interface At the cathode of an acid electrolyte fuel cell: Electrons will collect at the surface of the electrode and H+ ions will be attracted to the surface of the electrolyte. These electrons and ions, together with the O2 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 .

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Electrode – Electrolyte Interface 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.

The more the charge, the greater is the current. , electrical voltage (activation overvoltage). 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). 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. 20


Electrode – Electrolyte Interface 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). The discontinuity of charge physically behaves like a capacitor. Simple approximate models have been proposed to describe the properties of the electrified interface

e m o z compac ayer mo e •

Gouy-Chapman diffuse layer model

•

Stern modification

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

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Electrode – Electrolyte Interface Helmholtz compact layer model (parallel-plate condenser) Two layers of charge of opposite sign are separated by a fixed distance Assume counter-charge essentially within one ion’s depth

potential drop across the interface will be linear

Capacitance dielectric constant Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

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Electrode – Electrolyte Interface Gouy-Chapman Diffuse Double Layer Model

Ions in the electric double layer are subjected to electrical and thermal fields With certain electrolytes (especially weak solutions), charge may need to build up over greater depth

Diffuse char e

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.

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Electrode – Electrolyte Interface Stern Double Layer Model

Combine features of Helmoholtz and Gouy-Chapman to capture real physics of DL Ions are considered to have a finite size and are located at a finite distance from the electrode. The charge distribution in the electrolyte is divided into two contributions: i. As in the Helmholtz model immobilized close to the electrode, and ii. As in the Gouy-Chapman model, diffusely spread out in solution The Capacitance across this electrode/electrolyte interface

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Electrode – Electrolyte Interface Stern Double Layer Model

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Electrochemical Kinetics Equilibrium:

Measurements of redox potentials (and voltage potentials) Gives a quantitative estimate of the reaction tendency to proceed (equilibrium) No kinetic information is derived from these measurements Kinetics:

Concerned the mechanism b which electron transfer rocess occur. Need to know if the reactions (electron transfer) will proceed fast enough to make them useful We desire the rate of electron transfer (ET) that occurs at the electrode electrolyte interface for given conditions How can kinetic information about ET processes be derived? Increasing the rates of fuel-cell reactions is central to developing highly efficient commercial fuel cells. Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

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Electrochemical Kinetics Basic Kinetic Concepts for Interfacial ET process: Current flow is proportional to reaction flux (rate) Reaction rate is proportional to interface reactant concentration Similar to homogeneous reaction chemical kinetics: constant o f proportionality between reaction rate σ (mol/cm2 /s) and reactant concentration c (mol/cm3) is the rate constant k (cm/s) 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 27


Electrochemical Kinetics

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 An applied potential acts as a driving force for the ET reaction Expect that current should increase with increasing driving force Catalysts act to reduce the magnitude of the activation energy barrier .

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The reaction is thermodynamically favorable, and the reaction will generate

current, a flow of electrons or ions.

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Electrochemical Kinetics The rate of electrochemical reaction is finite because the energy barrier (activation Energy) impedes the conversion of reactants into products.

For reaction to take place, the activation energy must be over come

The current produced by the electrochemical reaction is limited.

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Electrochemical Kinetics Electron Transfer and Mass Transport We know that both mass transport (reactants and products) and the electron transfer process itself contribute to kinetics Let us ONLY consider the kinetics of interfacial electron transfer from a classical, macroscopic and phenomenological (non quantum) viewpoint This approach is based on classical Transition State Theory, and results in the ButlerVolmer Equation Transition State Theory Quantitative study of the transition state that molecules pass through during reaction (chemical, electrochemical)

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Electrochemical Kinetics Transition State Theory

Transition State molecules exist for 10-12

Reaction driving force voltage over potential at the electrode Elementary charge transfer reaction step Fuel /Oxidizer Partially converted y p l a h t n e r o y g r e n e e e r F

constant

reactants

Plank’s constant Products


Boltzmann

Rate constant 36

Electrochemical Kinetics Eyring and Arrhenius Equations The Eyring equation is valid for many types of dynamic rate processes (gases, liquids, in solution, and on surfaces) Consider the transition state (*) of an activated process

Pre-exponential factor

Activation energy term

(entropy, temp. dependence)

(enthalpy dependence) 37


Electrochemical Kinetics Activation energy of charge transfer reactions

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)

M: represents the nonreacting catalyst

2.

Absorption of H2 onto the electrode surface H near electrode + M → M… H

3.

Separation of the H2 molecules into two individual bond (chemisorbed) Hydrogen atoms on the electrode surface M… H2 + M → 2M…H 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) Mass transport of the H+ away from the electrode 2 [H+ (near electrode) → H+ (bulk electrolyte) 38

4.

5.

surface


Electrochemical Kinetics The overall reaction rate will be determined by the slowest step in the series 1

Activation energy

2

Free energy of the Free energy H+

1 increase with the distance from metal surface (stability improves with absorption to .

y g r e n e e e r F

2 energy is required to bring H+ to the electrode surface to over come the repulsive force (unfavorable for the

Chemisorbed H

a ∆G*1 *

M…H ∆Grxn

2

(M + e -) + H+ Distance from interface

H+ to be at the surface of

The red line represent the min. energy path for

electrode)

the conversion (conversion involves an over come of energy max. (a: activated state)

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Electrochemical Kinetics Overall rate of reaction:

state, then the forward reaction proceeds faster than the backward reaction rate. The unequal rates results in a build up of charge (e- accumulating at the electrode and H+ in the electrolyte) . 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) Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

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Electrochemical Kinetics Exchange current density

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

Then, the forward current density:

The reverse current density:

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Electrochemical Kinetics At equilibrium: and Where j0 is the exchange current density

Reactant conc. at Equ.

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

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Electrochemical Kinetics Rate constant, k, varies with applied potential, E, because ∆G* varies with applied potential.

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Electrochemical Kinetics , lowers the activation energy Application of a finite “overpotential,” η = E - E Nernst

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)). In the previous figure, the activation barrier of the forward reaction is decreased by while the reverse activation barrier is increased by

The current produced by reaction is:

The reactant flux is (mol/cm2-s): Heterogeneous ET

Interfacial reactant

rate constant (cm/s)

concentration (mol/cm3)


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Electrochemical Kinetics Butler–Volmer equation

Gibbs Free Energy:

η = overpotential

Interims of the exchange current density: and

the net current then is

Butler–Volmer equation

where 45


Electrochemical Kinetics Butler–Volmer Equation

Increasing the exchange current density can be performed by: •

Increasing the reactant concentration

•

Decreasing the activation barrier

•

Increasing the temperature T ncreas ng

e num er o ac ve reac on s e ncreas ng

e reac on n er ace

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

The curve was constructed by calculating the ideal cell potential (Nernst Equation) then subtracting Reaction kinetics inflict an exponential loss on a fuel cell i-V curve (BV equation)

The smaller the j0, the greater is this voltage drop. Having a high j0 is critical to have good fuel cell performance

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Electrochemical Kinetics The current produced by an electrochemical reaction increases exponentially with the activation overvoltage (voltage loss to overcome the activation barrier associate with electrochemical reaction). 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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Electrochemical Kinetics Butler–Volmer Model of Kinetics (More general expression)

To describe activation polarization losses at a given electrode. The BV model describes an electrochemical process limited by the charge transfer of electrons (ORR, and in most cases the HOR with pure hydrogen). The assumption of the BV kinetic model is that the reaction is rate limited by a single electron transfer step The net current density is

For an anode reaction with

For a cathodic reaction with

positive η, the anodic branch negative η, the cathodic branch will exponentially increase, will exponentially increase, η >> 0

η << 0

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If β = 1 the additional overpotential at the electrode goes completely toward promoting the re uc on reac on If β = 0 the additional potential is applied toward promotion of the anodic oxidation reaction.

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Electrochemical Kinetics Butler–Volmer Model: High-Electrode-Loss Region of Butler–Volmer (Tafel equation) The overvoltage at the surface of an electrode followed a similar pattern in a great variety of electrochemical reactions. For hi h olarization one of the branches will dominate, thus the overvoltage value is given by

n

n For j > j0

Tafel plots for slow and fast electrochemical reactions


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Electrochemical Kinetics Butler–Volmer Model: Low-loss (overpotential) region In the low-loss region and using Taylor series expansion and linearization of the BV equation, then the overvoltage potential can be expressed as:

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Electrochemical Kinetics Butler–Volmer Equation with Identical Charge Transfer Coefficients–sinh Simplification

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Electrochemical Kinetics Apply the Eyring equation to electron transfer (ET) process

Consider the transition state (*) of an activated process Characteristic ET distance (molecular diameter)

Using the equation Important: rate constant for heterogeneous ET depends directly on applied electrode potential

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Electrochemical Kinetics Butler–Volmer Simplifications A low-overpotential region where kinetics are facile and relatively low losses occur A higher overpotential region, where losses become much more significant A very high current region where mass ranspor osses om na e At low current density, the activation overpotential η required to maintain a net reaction rate in a given direction is small. 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. 56



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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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Fuel Cell-Electrochemistry and Reaction Kinetics

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