fuel cell-electrochemistry and reaction kinetics
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Special Topics ( Fuel Cell
Fundamentals and Technology)
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Dr.-Eng. Zayed Al-Hamamre
Fuel Cell Principle: Electrochemistry &
Reaction Kinetics
Content
Overview Faradays Laws Fuel Cell Performance and Irreversibility Electrode Electrolyte Interface
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Electrochemical Kinetics ButlerVolmer Equation
Polarization Losses
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Electrochemical reactions results in the transfer of electrons between an electrodesurface and a chemical species adjacent to the electrode surface (heterogeneous
reaction).
For an electrochemical reaction to take place, there are several necessarycomponents:
1. Anode and Cathode Electrode: The electrochemical reactions occur on the
Overview
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.
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 connectionis broken, the continuous circulation of current cannot flow and the circuit is
open.
The H2 gas and protons can not exist inside the electrode, while free electrons cannot exist in the electrolyte
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, tis time, n No. of electron, dN\dtis the rate of electrochemical reaction
Although the anode and cathode reactions are independent, they are clearly coupledto each other by the necessity to balance the overall reaction, so that the electrons
produced in the HOR are consumed in the ORR
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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
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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.
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Thus, it is a measure of the work required to conduct one coulomb of charge.
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Overview
Faradays constant Frepresents the charge per mole of equivalent electrons
The equivalent electrons (eq) is very important. Many electrochemical reactions donot exchange 1 mol of electrons for 1 mol of reactant.
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For the reaction
FARADAYS LAWS:
CONSUMPTION AND PRODUCTION OF SPECIES
How much mass of a given reactant is required to produce a given amount ofcurrent? 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.
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In the reaction ,, electrons are transfer per mole ofoxygen, thus the charge passing is 4F(coulombs/mole)
n simply permits determination of the relationship between charge passed andreactant consumption (or product generation) of any species chosen.
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FARADAYS LAWS:
CONSUMPTION AND PRODUCTION OF SPECIES
Considering water produced as the species of interest, the value ofn is 2, and thereare 2Fcoulombs passed per mole of H2O produced.
Faradays 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
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?
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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.
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5. What is the rate of water generation at the cathode in grams per hour?
Potential Control Electron Energy
The reaction direction can be controlled by controlling the electrode potentialOX + e- Re
The electron energy is measured by Fermi Level.
Potential Control Electron Energy
If the electrode potential is made more negative than the equilibrium one, the
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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 equilibriumpotential, the reaction will be biased toward the formation of Ox, the electrode
attracts electron.
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Fuel Cell Performance and Irreversibility
The actual useful voltage V obtained from a fuel cell with the load is different fromthe theoretical/ideal voltageEfrom thermodynamics.
No losses voltage
Fuel Cell Losses (polarizations, overpotentials, overvoltages) givesPolarization Curve
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Fuel Cell Performance and Irreversibility Activation losses: These are caused by the slowness of the reactions taking place onthe 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 offuel 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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Ohmic losses: This voltage drop is the straightforward resistance to the flow ofelectrons 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 inconcentration of the reactants at the surface of the electrodes as the fuel is used.
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Activation polarization, dominates losses at low current density, is the voltageoverpotential required to overcome the activation energy of the electrochemical
reaction on the catalytic surface
Activation polarization represents the voltage loss required to initiate the reactionWhat is the physical nature of the activation polarization
Electrode Electrolyte Interface
Activation polarization
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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 asthe 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.
Electrode Electrolyte InterfaceThe 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).
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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
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At the cathode of an acid electrolyte fuel cell:
Electrons will collect at the surface of theelectrode and
H+ ions will be attracted to the surface of theelectrolyte.
These electrons and ions, together with the O2
Electrode Electrolyte Interface
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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 .
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.
Electrode Electrolyte Interface
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,electrical voltage (activation overvoltage). The overvoltage opposes and reduces the reversible ideal voltage (Voltage lost indriving 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 isneeded if the current is higher, and so the overvoltage is higher if the current is
greater.
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The use of catalytic effect of the electrode by increasing the probability of areaction 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
Electrode Electrolyte Interface
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e m o z compac ayer mo e
Gouy-Chapman diffuse layer model
Stern modification
The layer of charge on or near the electrodeelectrolyte interface is a store ofelectrical 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)
Two layers of charge of opposite sign are separated by a fixed distance Assume counter-charge essentially within one ions depth
Electrode Electrolyte Interface
potential drop
across the
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interface will
be linear
Capacitance
dielectric constant
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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
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The Capacity,
n0 NO. of ions per unit volume in the bulk of
the electrolyte , Vis the potential drop from
the metal to the bulk of the electrolyte.
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
Electrode Electrolyte Interface
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ii. As in the Gouy-Chapman model, diffusely spread out in solution The Capacitance across this electrode/electrolyte interface
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Stern Double Layer Model
Electrode Electrolyte Interface
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Electrochemical KineticsEquilibrium:
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 measurementsKinetics:
Concerned the mechanism b which electron transfer rocess occur.
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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 electrolyteinterface 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.
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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 of proportionality
between reaction rate (mol/cm2/s) and reactant concentration c (mol/cm3) is the
rate constant k (cm/s)
Electrochemical Kinetics
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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
Applying a potential to an electrode generates an electric field at theelectrode/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
Electrochemical Kinetics
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Expect that current should increase with increasing driving force Catalysts act to reduce the magnitude of the activation energy barrier .
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Electrochemical Kinetics
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The reaction is thermodynamically favorable, and the reaction will generatecurrent, a flow of electrons or ions.
Electrochemical Kinetics
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Electrochemical Kinetics
The rate of electrochemical reaction is finite because the energy barrier (activationEnergy) impedes the conversion of reactants into products.
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For reaction to take
place, the activation
energy must be over
come
Electrochemical Kinetics
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Electrochemical Kinetics
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Electrochemical Kinetics
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Electron Transfer and Mass Transport
We know that both mass transport (reactants and products) and the electron transferprocess 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 Butler-
Electrochemical Kinetics
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Volmer Equation
Transition State Theory
Quantitative study of the transition state that molecules pass through during reaction(chemical, electrochemical)
Transition State
molecules exist for 10-12Transition State Theory
Reaction driving force
voltage over potential
at the electrode
Elementary charge
transfer reaction step
Electrochemical Kinetics
Boltzmann
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Fuel /Oxidizer
Partially convertedreactants
ProductsFreeenergy
orenthalpy
Rate constant
Planks
constant
constant
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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
Electrochemical Kinetics
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Pre-exponential factor
(entropy, temp. dependence)
Activation energy term
(enthalpy dependence)
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)
2. Absorption of H2 onto the electrode surface
H near electrode + M M H
M: represents the
nonreacting catalyst
surface
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3. Separation of the H2 molecules into two individual bond (chemisorbed)Hydrogen atoms on the electrode surface
M H2 + M 2MH
4. Transfer of electrons from the chemisorbed hydrogen atoms to the electrode
releasing H+ ions into the electrolyte (limiting step)
2 [MH (M + e-) + H+ (near electrode)
5. Mass transport of the H+ away from the electrode
2 [H+ (near electrode) H+ (bulk electrolyte)
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Electrochemical Kinetics
The overall reaction rate will be determined by the slowest step in the series1
2
Freeenerg
y
G*1*
a
Activation energy
1 increase with the distancefrom metal surface (stability
improves with absorption to
Free energy of the
Chemisorbed HFree energy H+
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Distance from interface
(M + e-) + H+
MH
Grxn
2.
2 energy is required to bringH+ to the electrode surface
to over come the repulsive
force (unfavorable for the
H+ to be at the surface of
electrode)
The red line represent the min. energy path forthe conversion (conversion involves an overcome of energy max. (a: activated state)
Electrochemical Kinetics
Overall rate of reaction:
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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 andH+ in the electrolyte) .
The charge accumulation continues until the resultant potential across the reactioninterface counter balance the free energy difference between reactants and products.
(electro-chemical equilibrium)
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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:
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The reverse current density:
Electrochemical Kinetics
At equilibrium:and
Wherej0 is the exchange current density
Reactant conc. at Equ.
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The free energy of charge species are sensitive to voltage. Therefore, changing thecell 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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Rate constant, k, varies with applied potential, E, because G* varies with appliedpotential.
Electrochemical Kinetics
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Electrochemical Kinetics
Application of a finite overpotential, = E - ENernst, lowers the activation energybarrier for an electrochemical reaction by a fixed amount, (Symmetry factor, , or
the electron transfer coefficient, determines how much of the electrical energy input
affects the activation energy barrier of the redox process (0 < < 1)).
In the previous figure, the activation barrier of the forward reaction is decreased bywhile the reverse activation barrier is increased by
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The current produced by reaction is:
The reactant flux is (mol/cm2-s):Heterogeneous ET
rate constant (cm/s)
Interfacial reactant
concentration (mol/cm3)
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Electrochemical Kinetics
Gibbs Free Energy: = overpotential Interims of the exchange current density:
and
ButlerVolmer equation
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the net current then is
where
ButlerVolmer equation
Electrochemical Kinetics
ButlerVolmer Equation
Increasing the exchange current density can be performed by: Increasing the reactant concentration
Decreasing the activation barrier
Increasing the temperature T
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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
ButlerVolmer equation, effect of activation overvoltage on fuel cell performance
The curve was constructed bycalculating the ideal cell
potential (Nernst Equation)then subtracting
Reaction kinetics inflict an
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exponential loss on a fuel cell
i-Vcurve (BV equation)
The smaller thej0, the greateris this voltage drop.
Having a highj0 is critical tohave good fuel cell
performance
Electrochemical Kinetics
The current produced by an electrochemical reaction increases exponentially with theactivation 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 priceinterims of lost voltage must be paid.
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Electrochemical Kinetics
ButlerVolmer 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 asingle electron transfer step
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The net current density is
For an anode reaction with
positive , the anodic branch
will exponentially increase,
For a cathodic reaction with
negative , the cathodic branch
will exponentially increase,>> 0
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Electrochemical Kinetics
If = 1 the additionaloverpotential at the
electrode goes
completely toward
promoting the
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re uc on reac on
If = 0 the additionalpotential is applied
toward promotion of
the anodic oxidation
reaction.
Electrochemical Kinetics
ButlerVolmer Model: High-Electrode-Loss Region of ButlerVolmer
(Tafel equation)
The overvoltage at the surface of anelectrode followed a similar pattern
in a great variety of electrochemical
reactions.
For hi h olarization one of the
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Tafel plots for slow and fast electrochemical reactions
branches will dominate, thus the
overvoltage value is given by
Forj > j0
n
n
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Electrochemical Kinetics
In the low-loss region and using Taylor series expansion and linearization of the BVequation, then the overvoltage potential can be expressed as:
ButlerVolmer Model: Low-loss (overpotential) region
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Electrochemical Kinetics
ButlerVolmer Equation with Identical Charge Transfer Coefficientssinh
Simplification
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Apply the Eyring equation to electron transfer (ET) process
Electrochemical Kinetics
Consider the transition state (*) of an activated processCharacteristic ET distance
(molecular diameter)
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Using the equationImportant: rate constant for
heterogeneous ET depends
directly on applied electrode
potential
Electrochemical Kinetics
A low-overpotential region where kinetics arefacile and relatively low losses occur
A higher overpotential region, where lossesbecome much more significant
A very high current region where mass
ButlerVolmer Simplifications
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At low current density, the activationoverpotential required to maintain a net
reaction rate in a given direction is small.
ranspor osses om na e
Beyond a threshold value in current density related to the equilibrium reaction exchange rateof the electrode, the additional polarization required for increasing current is greatly
increased.
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Electrochemical Kinetics
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Activation Polarization
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Activation Polarization
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Activation Polarization
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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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