Chapter 4 Electrochemical kinetics at electrode / solution interface and electrochemical overpotential

Effect of potential on electrode reaction Thermodynamic aspect If electrode reaction is fast and electrochemical equilibrium remains, i.e., Nernst equation is applicable. Different potential corresponds to different surface concentration. 2. Kinetic aspect If electrode reaction is slow and electrochemical equilibrium is broken. Different potential corresponds to different activation energy.

4.1 Effect of potential on activation energy 4.1.1 basic concepts For Elementary unimolecular process Rate expressions Exchange rate of reaction At equilibrium

Some important empirical formula: Arrhenius equation According to Transition State Theory: Corresponding to steric factor in SCT

For electrode reactions For reversible state Nernst equation For irreversible state Tafel equation How to explain these empirical formula?

Potential curve described by Morse empirical equation Activated complex Reactant product Reaction coordinate Standard free energy In electrochemistry, electrochemical potential was used instead of chemical potential (Gibbs free energy) Potential curve described by Morse empirical equation

4.1.2 net current and exchange current Fe3+ Cu Cu2+ Fe2+ Net current: Net current:

If cOx = cRed = activity = 1 at re At equilibrium condition Then i net = 0 standard exchange current

4.1.3 effect of overpotential on activation energy transfer coefficient polarization

Fraction of applied potential alters activation energy  for oxidation and  for reduction Anode side cathode side

 is usually approximate to 1/2    x  is usually approximate to 1/2 deuce

4.1.4 Effect of polarization on reaction rate Marcus theory: transition state theory

No concentration polarization If initial potential is 0, then

At equilibrium

4.2 Electrochemical polarization 4.2.1 Master equation Master equation

Theoretical deduction of Nernst equation from Mater equation At equilibrium Nernst equation

Butler-Volmer equation

4.2.3 discussion of B-V equation 1) Limiting behavior at small overpotentials Current is a linear function of overpotential

Charge transfer resistance False resistance Cathode Anode Net current  / V i / A

2) Limiting behavior at large overpotentials Cathode Anode Net current  / V i / A One term dominates Error is less than 1% At cathodic polarization larger than 118 mV

Taking logarithm of the equation gives: Making comparison with Tafel equation One can obtain

The typical Tafel slope At 25 oC, when n = 1,  = 0.5 The typical Tafel slope -100 -200 -300 300 200 100

log i0 re Tafel plot:   log i plot

4.2.4 determination of kinetic parameters For evolution of hydrogen over Hg electrode

4.2.5 Exchange current density 1) The exchange currents of different electrodes differ a lot Electrode materials solutions Electrode reaction i0 / Acm-2 Hg 0.5 M sulfuric acid H++2e– = H2 510-13 Cu 1.0 M CuSO4 Cu2++2e– = Cu 210-5 Pt 0.1 M sulfuric acid 110-3 110-3 M Hg2(NO3)2 + 2.0M HClO4 Hg22++2e– = 2Hg 510-1

2) Dependence of exchange currents on electrolyte concentration Electrode reaction c (ZnSO4) i0 / Acm-2 Zn2++2e– = Zn 1.0 80.0 0.1 27.6 0.05 14.0 0.025 7.0 High electrolyte concentration is need for electrode to achieve high exchange current.

When i0 is large and i << i0, c is small. When i0 = , c=0, ideal nonpolarizable electrode When i0 is small, c is large. When i0 = 0, c = , ideal polarizable electrode

The common current density used for electrochemical study ranges between 10-6 ~ 1 Acm-2. If exchange current of the electrode i0 > 10~100 Acm-2, it is difficult for the electrode to be polarized. When i0 > 10-8 Acm-2, the electrode will always undergoes sever polarization. For electrode with high exchange current, passing current will affect the equilibrium a little, therefore, the electrode potential is stable, which is suitable for reference electrode.

4.2 potential on electrode kinetics Shift of potential 1 keeps constant The nature of potential -dependence of rate

At equilibrium: cox(0,t)= cox0 i0,c=i0,a=i0 Master equation:

Master equation: At equilibrium Nernst equation

Master equation: Butler-Volmer equation

Butler-Volmer equation at small overpotentials Charge transfer resistance

at large overpotentials Tafel equation

4.3 Diffusion on electrode kinetic When we discuss situations in 4.2, we didn’t take diffusion polarization into consideration When diffusion take effect :

At high cathodic polarization

Taking logarithm yields Therefore: Electrochemical term Diffusion term At this time the total polarization comprises of tow terms: electrochemical term and diffusion term.

1. id >> i >> i0 Discussion : 1. id >> i >> i0 No diffusion ec polarization At large polarization: At small polarization : c i i 0 c

2. id  i << i0 is invalid diffusion No ec i  id i   log i

3. id  i >> i0 both terms take effect 4. i << i0, id no polarization

diff id When id >>i0 ec  1/2

id diff  ec

Tafel plot under diffusion polarization 400 300 200 100 -100 -200 -300 -400 Tafel plot under diffusion polarization

i0 << i < 0.1 id Tafel plot with diffusion control: Electrochemical polarization i between 0.1id  0.9id mixed control i >0.9 id diffusion control How to overcome mixed / diffusion control? The ways to elevate limiting diffusion current

4.4.1 potential step 4.4 EC methods under EC-diff mixed control Using B-V equation with consideration of diffusion polarization at high polarization . c c  constant it  CO(0,t)

at low polarization : is very small Constant Constant

i(0)= i is the current density at no concentration polarization at  1 2 3 0.5 2 t is the current density at no concentration polarization at  t=0 i(0)= i no concentration polarization

at time right after the potential step : it t1/2 is linear When it at time right after the potential step : it t1/2 is linear Extrapolating the linear part to y axes can obtain Double-layer charge i EC control diff control C

Making potential jump to different  can obtain i at different  Making potential jump to different  can obtain i at different . Then plot i against c can obtain i~c without concentration polarization. The way to eliminate concentration polarization effect c  time constant s it > i due to charge of double layer capacitor

4.4.2 current step 3.8.2 Current step / jump i ic t c at different i0 cathodic current : 0  ic 3.8.2 Current step / jump

 t c c c(0)   transition time when potential step to next rxn. i= i charge

The slope of the linear relationship between c (t) can be used to determine n and . When t0 the second term = 0

4.4.3 cyclic voltammetry (CV) Typical CV diagram for reversible single electrode  I Potential separation

For typical CV diagram of irreversible single electrode  I For typical CV diagram of irreversible single electrode for fast EC reaction : i << i0 controlled by diffusion 0.1 i v 0.0 0.1 0.2 0.2

for the reversible systems , use the forward kinetics only : can be only by numerical method: Nicholson-Shain equation  tramper coefficient n – number of electrons involved in charge transfer step is tabulated x (bt) max =0.4958

For totally irreversible systems, peak potential shift with scan rate 0.1 i v 0.0 0.1 0.2 0.2 for slow EC reaction : ii0 ( quasi reversible, irreversible) in comparison to the same rate, equilibrium can not establish rapidly. Because current takes more time to respond to the applied voltage, Ep shift with scan rate .

per decade of change in scan rate drawn - out ip COx0 lower due to  if =0.5 n= 1

lnip  Ep E0 is linear with S= RT/nF, intercept is linearly proportional to k0

4.4.4 effect of 1 potential on EC rate : x 1  1=0, validate at high concentration or larger polarization nF effect of 1: 1.on concentration 2. =   1

When z0 <0 ( minus ) n  1 large When z0 <0 ( minus ) n  1 large . For anion reduced on cathode , 1 effect is more significant.

1 made c shift positively When z0  n 1 made c shift positively plus >0 minus <0 so: if 1 increases, i decreases +2 +4 2 4 +0.5 0.5 0.01M 0.1M 1M 0.001M -0 without specific adsorption  reduction of +1 cation …… reduction of 1anion 1 accelerates reduction of cations slow reduction of anion lgi

if: n =z0 Cu2+ +2e- = Cu MnO4 +e = MnO42 =0.5 H+ +e- = 1/2 H2 if :z0 =0 adsorption of anion slow reaction

Electrochemistry of LB film

exam: 1.Draw the potential change versus distance away from electrode surface according to Stern electric double-layer and indicate 1 potential 2. When the electrode was positively charged, the surface concentration of action is still more than that of bulk solution. Explain this phenomenon using specific adsorption model 3.The differential double layer capacitance of Cu/H2O surface is 10-5 Fcm-2 while that for Cu/HS(CH2)11CH3 is 10-9Fcm-2 (can be taken as zero). If the differential Cdl for a Cu/HS(CH2)11CH3 system is measured to be 10-7 Fcm-2. Please calculate the coverage of HS(CH2)11CH3 on copper.

4. Electro-capillary curves of Hg in KI and K2S solution are shown in the Figure. Please indicate the PZC of Hg on the curves and explain the difference in PZC. The curves coincide with each other when potential is quite negative but differ a lot when potential is positive, please give explanation.  K2S KI  5.Tell how to determine whether or not a electrode process is governed by diffusion. Given id for RDE can be expressed as id= 0.62 nF Di2/31/2-1/6 ci0

6. This is a water drop with contact angle of  on Pt surface 6.This is a water drop with contact angle of  on Pt surface. When potential shift negatively, plot the change of  with potential, i.e.,  ~ . Pt  7.Deposition of Cu nanowire in microspore of anodic alumina membrane (AAO) can be taken as ideal stable diffusion process. If the thickness of (AAO) is 1m =0.1 mol cm-1, =105cm2 s-1. Please calculate the limiting diffusion current. 8. Convection affects diffusion. If the slope of concentration gradient is ,The effective thickness of diffusion layer E= and the dimity diffusion current id =

9. a typical CV peak is shown in the figure 9.a typical CV peak is shown in the figure. Please Indicate EP, EP/2, Ere, and iP on it. How can you determine whether or not this electrochemical process is electrochemical reversible?