Chapter 4 Electrochemical kinetics at electrode / solution · PDF file...

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Transcript of Chapter 4 Electrochemical kinetics at electrode / solution · PDF file...

  • Chapter 4

    Electrochemical kinetics at electrode / solution

    interface and electrochemical overpotential

  • Valid only for reversible cell or for electrode at

    electrochemical reversibility.

    inet =0

    ln ox

    red

    aRT

    nF a   

    (2) Nernst equation:

    ln ii i

    RT a

    nF

       

    Dependent of electrode potential on species activities

    ln c d

    C D

    a b

    A B

    a aRT E E

    nF a a  

    1) Two important empirical relations

    0. Brief introduction

  • (2) Tafel equation:

    The point of intersection of the extrapolation on the

    line  = 0 is log i0.

    A is in fact the  at j = 1 A cm-2.

     = a + b log j

    Valid only for special irreversible process when  > 118 mV.

    1) Two important empirical relations

    0. Brief introduction

  • Effect of potential on electrode reaction

    1. Thermodynamic aspect

    If electrode reaction is fast and electrochemical equilibrium

    remains, i.e., Nernst equation is applicable. Different

    potential corresponds to different surface concentration—

    concentration/diffusion control.

    2. Kinetic aspect

    If electrode reaction is slow and electrochemical equilibrium

    is broken. Different potential corresponds to different

    activation energy—activation/electrochemistry control.

    Chapter 4 Electrochemical kinetics at electrode

  • f f A

    b b B

    net f b f A b B

    r k c

    r k c

    r r r k c k c

       

    Rate expressions

    At equilibrium

    0;

    ( ) ( )

    ( )

    ( )

    net

    b B eq f A eq

    f B eq

    b A eq

    r

    k c k c

    k c K

    k c

     

    4.1.1 basic concepts

    Exchange rate of reaction

    For Elementary unimolecular opposing

    process

    4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

    Kinetic equilibrium

    constant

  • 4.1.1 basic concepts

    4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

    For electrochemical reactions:

    ; f c

    f f A c f Ox

    i i r k c r k c

    nFA nFA     c f Oxi k nFAc

    Rea f di k nFAc

    0 ,0 ,0

    net c a

    c a

    i i i

    i i i

     

     

    At equilibrium conditions:

  • exp a E

    k A RT

        

      Arrhenius equation

    Some important empirical formula:

    According to Transition State Theory:

    exp kT G

    k h RT

     

        

     

    Corresponding to steric factor in

    SCT

    4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

    kT/h term corresponds to the frequency

    factor

    kT k K

    h  

  • Ox e Red f

    b

    k

    k n   

    Potential curve described by Morse empirical equation

    In electrochemistry,

    electrochemical potential

    was used instead of

    chemical potential (Gibbs

    free energy)

    4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

  • 4.1.2 net current and exchange current

    Ox e Red c

    a

    k

    k n   

    Net current:

    Ox (0, )c ci nFAk c t

    Red (0, )a ai nFAk c t

    Ox Red[ (0, ) (0, )]c a c ai i i nFA k c t k c t   

    4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

  • Ox Red[ (0, ) (0, )]c a c ai i i nFA k c t k c t   

    At equilibrium condition

    0 ,0 ,0c ai i i 

    cG

    RT c

    kT k e

    h

    aG

    RT a

    kT k e

    h

    If cOx = cRed = activity = 1 at re

    Then i net = 0 standard exchange current

    4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

  • 4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

    For unequilibrium conditions

  • ir re    Δ ΔG nFE nF    

    0Δ Δ ΔG G nF  

    polarization

    4.1.3 effect of overpotential on activation energy

    transfer coefficient

    4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

  • Fraction of applied potential

    alters activation energy  for

    oxidation and  for reduction

    ΔF 

    ΔF 

    ΔF 

    Δ cG 

    ,0Δ cG 

    Δ aG 

    ,0Δ aG 

    Ox en  Red

    ΔnF 

    ,c re

    ,c ir ,a ir

    ΔnF 

    ΔnF 

    ,0 Δa aG G nF      Anode side

    ,0 Δc cG G nF      cathode side

    4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

  • 

     

    

    

    tantan

    tan

    /)1(tan

    /tan

     

    

    xFE

    xFE

     

     x

    ΔnF 

    ΔnF 

    0 

     

     is usually approximate to 1/2

    4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

  • ,0

    ,0

    ,0

    exp( )

    exp( )exp( )

    exp( )

    cB

    c c

    cB

    c

    c

    G nFk T k

    h RT

    Gk T nF

    h RT RT

    nF k

    RT

       

       

     

      

      

     

    4.1.4 Effect of polarization on reaction rate

    ,0

    ,0

    exp( )

    exp( )

    aB

    a a

    a

    G nFk T k

    h RT

    nF k

    RT

       

     

       

    Marcus theory: transition state theory

    4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

  • Ox Ox ,0(0, ) (0, ) exp( )c c c nF

    i k c t nFc t k RT

        

    ,0 exp( )a a nF

    i i RT

      

    No concentration polarization

    ,0 exp( )c c nF

    i i RT

       

    ,0

    2.3 2.3 lg lgc c

    RT RT i i

    nF nF 

       

    ,0

    2.3 2.3 lg lga a

    RT RT i i

    nF nF 

        

    If initial potential

    is 0, then

    4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

  • ,0

    2.3 2.3 lg lgc re c c

    RT RT i i

    nF nF   

          

    ,0

    2.3 2.3 lg lga re a a

    RT RT i i

    nF nF   

          

    At equilibirum

    ,0 ,0 0a ci i i  0

    2.3 lg cc

    iRT

    nF i 

     

    0

    2.3 lg aa

    iRT

    nF i 

     

    4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

  • lg i

    lg ai

    lg ci

    0lg i

    0 re

    0

    2.3 2.3 lg lgc c

    RT RT i i

    nF nF 

        

    0

    2.3 2.3 lg lga a

    RT RT i i

    nF nF 

        

    4.1 Effect of potential on activation energy

    Chapter 4 Electrochemical kinetics at electrode

  • Ox ,0 Red ,0

    0 Ox Red

    (0, ) exp( ) (0, ) exp( )

    (0, )exp( ) (0, )exp( )

    net c a

    c a

    i i i

    nF nF nFc t k nFc t k

    RT RT

    nF nF nFk c t c t

    RT RT

       

       

     

      

         

     

    Ox ,0(0, ) exp( )c c nF

    i nFc t k RT

       

    Red ,0(0, ) exp( )a a nF

    i nFc t k RT

      

    Master equation

    4.2.1 Master equation

    4.2 Electrochemical polarization

    Chapter 4 Electrochemical kinetics at electrode

  • 0 Ox Red(0, )exp( ) (0, )exp( )net nF nF

    i nFk c t c t RT RT

            

     

    At equilibrium 0neti 

    0 0

    Ox Ox Red Red(0, ) ; (0, )c t c c t c 

    0 0

    Ox Redexp( ) exp( ) nF nF

    c c RT RT

         

    0

    Ox

    0

    Red

    exp( ) c nF

    RTc 