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Previous class • EEC fit • Using Rt and Rp to guess initial values • RMA • Simple Reaction Today • RMA • Two step reac...

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Previous class • EEC fit • Using Rt and Rp to guess initial values

• RMA • Simple Reaction

Today • RMA • Two step reaction

RMA – Electron Transfer  Fe  CN 6 

4

3

 Fe CN 6   e

• Experimental and simulation results

k1  M   M ads  e

Two step reaction

k2   M ads   M sol

Metal Atom

M

Metal Ion in solution

Electrode Solution

Solution

 M ads

 M sol

Surface atoms

Surface atoms

Electrode

Electrode ek1  M   M ads  e

k1dc 1  SS   k2SS  0

iF  Fk1dc 1   SS 

Adsorbed metal Ion  sol

d  k1 1     k2 dt

k1dc  SS  k1dc  k2

Solution Surface atoms



Newly exposed Surface atom k2   M ads   M sol

Two step reaction

k1  M   M ads  e

k2   M ads   M sol



d  k1 1     k2 dt

k1dc 1  SS   k2SS  0

k1dc  SS  k1dc  k2 iF  Fk1dc 1   SS 

iF  Fk1 1   

• Linearization Eac = Eac0 sin(wt) k1

k1dc 1  b1Eac 

Fk1dc 1  b1Eac 1   

k1  M   M ads  e

Two step reaction



k2   M ads   M sol

    ss  E 

 ss 

Edc

1  2 Eac  2! E 2

iF

• Linearization

k1

k1dc 1  b1Eac 

iF

k1dc  SS  k1dc  k2

Eac2  ... Edc

iF  Fk1dc 1   SS 

Fk1dc 1  b1Eac 1   

  Fk1dc 1  b1Eac   1   ss   E     Fk1dc    E 

Eac = Eac0 sin(wt)

k1dc 1  SS   k2SS  0

 Eac E Vdc

iF  Fk1 1   

d  k1 1     k2 dt

Edc

    Eac  b1Fk1dc   Edc   E

 Eac     2  Eac Edc 

  Fk1dc 1   ss   b1Fk1dc 1   ss  Eac  Fk1dc    E 

  Eac Edc 

k1  M   M ads  e

Two step reaction

k2   M ads   M sol

 E

Edc

jwt dE d  Edc  Eac 0e    jw Eac 0e jwt  jw Eac dt dt

d   k1 1     k2 dt





  d    E dt 

 E  Edc  t

k1 1     k2

dE d  Edc  Eac sin wt     w Eac 0 cos wt   w Eac 0 sin wt   2 dt dt





  d  jw   E dt 



  Eac Edc 

     Eac    k1dc 1  b1Eac  1   ss  E Edc             k2   ss  Eac    E Edc    



dE  w Eac 0 sin wt    jw Eac 0 sin wt   jw Eac 2 dt

E   Edc  Eac 0e jwt 

iF

  Fk1dc 1   ss   b1Fk1dc 1   ss  Eac  Fk1dc    E 

  Eac Edc 