lecture 4-fuel cell-electrochemistry & reaction kinetics
TRANSCRIPT
Special Topics ( Fuel Cell
Fundamentals and Technology)
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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.
Potential Control Electron Energy
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.
Potential Control Electron Energy
Electrode Electrolyte
Fermi
Level.
Electrode Electrolyte
Fermi
Level.
e-
Electrode Electrolyte
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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Fuel Cell Performance and Irreversibility
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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Fuel Cell Performance and Irreversibility
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.
Electrode – Electrolyte Interface
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
Electrode – Electrolyte Interface
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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
Electrode – Electrolyte Interface
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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
Electrode – Electrolyte Interface
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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
Electrode – Electrolyte Interface
potential drop
across the
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interface will
be linear
Capacitance
dielectric constant
Electrode – Electrolyte Interface
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
Electrode – Electrolyte Interface
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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
Electrode – Electrolyte Interface
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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
Electrochemical Kinetics
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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 .
Electrochemical Kinetics
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Ø The reaction is thermodynamically favorable, and the reaction will generate
current, a flow of electrons or ions.
Electrochemical Kinetics
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Electrochemical Kinetics
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
Electrochemical Kinetics
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Electrochemical Kinetics
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Electrochemical Kinetics
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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
Electrochemical Kinetics
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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
Electrochemical Kinetics
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
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
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)
Electrochemical Kinetics
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)
Electrochemical Kinetics
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)
Electrochemical Kinetics
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:
Electrochemical Kinetics
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.
Electrochemical Kinetics
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Electrochemical Kinetics
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)
Electrochemical Kinetics
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
Electrochemical Kinetics
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)
Electrochemical Kinetics
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
Electrochemical Kinetics
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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Electrochemical Kinetics
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
Electrochemical Kinetics
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Electrochemical Kinetics
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.
Electrochemical Kinetics
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
Electrochemical Kinetics
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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Electrochemical Kinetics
Butler–Volmer Equation with Identical Charge Transfer Coefficients–sinh
Simplification
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Apply the Eyring equation to electron transfer (ET) process
Electrochemical Kinetics
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
Electrochemical Kinetics
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.
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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