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
k1dc 1 SS k2SS 0
iF Fk1dc 1 SS
Adsorbed metal Ion sol
d k1 1 k2 dt
k1dc SS k1dc 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
k1dc 1 SS k2SS 0
k1dc SS k1dc k2 iF Fk1dc 1 SS
iF Fk1 1
• Linearization Eac = Eac0 sin(wt) k1
k1dc 1 b1Eac
Fk1dc 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
k1dc 1 b1Eac
iF
k1dc SS k1dc k2
Eac2 ... Edc
iF Fk1dc 1 SS
Fk1dc 1 b1Eac 1
Fk1dc 1 b1Eac 1 ss E Fk1dc E
Eac = Eac0 sin(wt)
k1dc 1 SS k2SS 0
Eac E Vdc
iF Fk1 1
d k1 1 k2 dt
Edc
Eac b1Fk1dc Edc E
Eac 2 Eac Edc
Fk1dc 1 ss b1Fk1dc 1 ss Eac Fk1dc 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 k1dc 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
Fk1dc 1 ss b1Fk1dc 1 ss Eac Fk1dc E
Eac Edc