Chapter 5 Mechanism of complex electrode reaction

5.1.1 B-V equation for multi-electron process For a di-electron reaction Ox + 2e  Red Its mechanism can be described by At stable state

If

Therefore

5.1.2 important consideration Consider a multi-step electrochemical process proceeding via the following mechanism Net result of steps preceding rds (r.d.s.) Net result of steps following rds Note: n’+n’’+1 = n

Since preceding step is in equilibrium, one can write Similarly, the succeeding reaction is also assumed to be fast, i.e., at equilibrium

Replacing above

After very laborious algebra, one can show that This equation correctly accounts for influence of redox pre-equilibrium on measured value of Tafel slop for the reaction scheme. Tafel slope is not Tafel slope of rate determining step, , rather it is (n’+)

without considering concentration effects By making comparison with The effect of potential change on activation energy of the cathodic and anodic reaction differ from that of simple electrochemical reaction

At small overpotentials, i.e., in the linear regime: The exchange current is n times that of the current of the r.d.s. Therefore, charge transfer resistance for multi-step is: At higher negative polarization At higher negative polarization

For a multi-electron reaction Ox + ne  Red Its mechanism can be described by Steps before rds, with higher i0 at equilibrium Steps after rds, with higher i0 at equilibrium

Therefore At small overpotential

At higher overpotential For cathodic current For anodic current

5.1.3 Stoichiometric number multi-electron process

Ob Os O* R* Rb Rs 5.2 surface transitions reactions: Surface region Bulk solution Os Mass transfer O* Chem. rxn Desorption/ adsorption R* EC rxn Rb Rs

5.2 Homogeneous proceding surface reactions place homogeneous ( region close to electrode surface) heterogeneous ( adsorption, desorption, new phase formation ) time Foregoing / preceding Post, succeeding parallel Electrochemical -chemical (EC) Chemical-Electrochemical (CE)

Classification of couple electrode  homogeneous : Mechanism with single electrochemical step (1) CE – preceding reaction e.g. Reduction of formaldehyde on mercury Dominant, no EC rxn. A difficult to be reduced CE

Mechanism with single electrochemical step (2) EC – following reaction H2O EC

For evolution of hydrogen EC 2 M  H  2M + H2  H+ + M +e  M  H H+ + M  H + e  M + H2  EE Possible proceeding/succeeding reactions: dissociation, complexities, dimerization, isomerization , formation of new phase (gas bubble, metal plating, conversion layer).

Mechanism with single electrochemical step (3) ECcat – catalytic reaction

5.2 Reaction mechanism-proceeding reaction For CreEre reaction as If K <1, then O is the main reactant which can be reduced at potential 2, while O* is easier to be reduced at potential 1 than O. This means at 2, both O and O* can be reduced. At 1, For slow chemical kinetics: At 1, For fast chemical kinetics, O* can be replenished in time: 1 2 Limiting kinetic current Ik

At 2, For slow chemical kinetics: Curves I and II can be described by normal diffusion current when O and O* become totally depleted, respectively. Curve III is different.

At electrode surface, the concentration gradient of O and O At electrode surface, the concentration gradient of O and O* can be described as: At stable state: Very small At 1 If: No concentration polarization of O at electrode surface.

For O* at complete concentration polarization, its boundary conditions are: At x = , At x = 0, surface concentration: Therefore, the concentration gradient at electrode surface is:

The thickness of reaction region

Less than the effective thickness diffusion layer, why? At incomplete polarization: The limiting current resulted for CE mechanism is usually much larger than that of merely diffusion control kinetics, Why?

Cyclic voltammograms for the CE case. A  B; B + e -  C When  = 0 V, c0 = 1 mM , A= 1cm2, DA = DB = DC = 10-5 cm2 /s, K =103, kf = 10-2 s-1, kb =10 s-1, T =25 ℃, at scan rates ,v of (1) 10 V/s; (2) 1 V/s; (3) 0.1 V/s; (4) 0.01 V/s.

Depends on cre not on diffusion When K=10-3, kf =10-2 s-1 kb = 10 s-1, v=0.01~10 V s-1,  = 26 ~ 0.026. v / Vs-1 lg control effect of preceding 10 -1.6 DP Less effect (1) 1 -0.6 KI 0.01 1.6 KP Depends on cre not on diffusion

v Some diagnostic criteria for a CE situation . 1) ip /v1/2 will decrease as v increases 2) ipa /ipc will become large for small K or for large v 2 4 6 8 10 0.5 1.0 1.5 2.0 v

Both O and O* can be reduced The first wave corresponds the reduction of Cd2+ which is governed electrochemically, while the second wave corresponds to reduction of CdX-. Wave III is oxidation of Cd(Hg) which is governed by diffusion.

5.3 Reaction mechanism-succeeding/parallel reaction 5.3.1 For EreCcat Electrocatalysis Assuming [S] >> [O] Catalytic decomposition of hydrogen peroxide S is the substrate whose concentration is usually much higher than that of O and R. Therefore, I mainly depends on Id, O.

Assuming [S] >> [O]

Solution is When Concentration of R is very low

Catalytic current at complete concentration polarization Catalytic current at other polarization

Increasing   diffusion ECcat

Here both behaviors going on: we are consuming Red with rate constant k, this will shift the ratio [Red]/[Ox]. So we expect the half wave potential to shift. But, we also are generating Ox with rate k. So we expect the wave to get bigger.

5.3.2 For EreCir reaction For ECir mechanism:

The kinetic current is If is negligible The thickness of the reactive layer

EreCir for the EC reaction when the electron transfer reaction is reversible and the chemical rate constant kEC is extremely large The reduction in size of the reverse peak occurs since much of the R produced electrochemically is destroyed by the chemical step.

Scan rates on voltammograms A/B * = 0 V, c0=1 mM, A =1 cm2, D = 10-5 cm2 /s, and kf = 10 s-1. The vertical scale changes from panel to panel.

Conversion rate constant on voltammograms http://www.nuigalway.ie/chem/Donal/Surfaces11.ppt#274,13,Catalytic

Normalized current for several values of . 180 120 60 60 0.2 0.0 0.2 0.4 (e) Normalized current (   1/2) n / mV  = 10 0.1 0.01 For small , reversible by nature. For large , no reverse current can be observed, i.e., irreversible.

Diagnostic Criteria for EreCir mechanism: 180 120 60 60 0.2 0.0 0.2 0.4 (e) Normalized current (   1/2) n / mV  = 10 0.1 0.01 1) ipa / ipc will approach 1 as v increases 2) ipc proportional to v1/2 3) pc will be displaced in the anodic direction as v decreases (30/n mV per 10  in v) 0.2 0.4 0.6 0.8 1.0 lgv Ip,c/Ip,c

Electrochemical dimerization

5.4.1 Conversion involving adsorption Osol Oads Rads Rsol sol ads rad  10* 0 coverage rde  0* maximum coverage 0* at equilibrium at large negative polarization : rxn, fast

So When make adsorption .id = io

For proceeding reaction, its polarization curves is similar to that of diffusion-control kinetics.

post kinetic : Using similar treatment : so For succeeding reaction, its polarization curves is similar to that of electrochemistry-control kinetics.

5.4.2 Conversion of surface species Since R and O are confined, no diffusion If we use the Langmuir isotherm to describe the coverages of O and R make use of the Nernstian criterion

When bO bR, Reversible, Nernstian, Langmuir, Monolayer

Electrochemistry of LB film

Dynamics of Br electrosorption on single-crystal Ag(100) Journal of Electroanalytical Chemistry Volume 493, Issues 1-2, 10 November 2000, Pages 68-74

If bO >> bR If bR >>bO Pre-wave post-wave Dash line: without adsorption Solid line: with adsorption

5.5 Other mechanisms 5.5.1 EreEre mechanism

When  > 125 mV, two peaks becomes distinguishable Shoulder Changing shapes of cyclic voltammograms for the Er Er reaction scheme at different values of E0 When  > 125 mV, two peaks becomes distinguishable

CVs for the reduction of di-anthrylalkanes (An-(CH2)n-An) in 1:1 benzene/acetonitrile containing 0.1 M tetrabutylammonium perchlorate at a Pt electrode.

5.5.2 EreCreEre mechanism It is much easier for C to be reduced than A

O  R S  T The figure shows the voltammogram for an ECE mechanism where the product (S) is more difficult to reduce than the starting material (O).

If the product (S) is more easy to reduce, slightly different behaviour is seen

0.00 0.60 4.00 3.00 2.00 1.00 3.00 2.00 1.00 Current  = 0 (a) E 0.10 II I Current  = 0.40 (c) III IV Current  = 0.05 (b) 5.00 (d) CVs for the EreCirEre case obtained by digital simulation for E10 = 0.44 V, E20 = 0.20 V for different values of  =(kb/v)(RT/F); n1=n2=1.(a)  =0 (unperturbed Nernstian reaction ); (b) 0.05 ;(c) 0.40 ;(d) 2.

The ECE mechanism

CV of 4-Aminophenol   cyclic voltammograms recorded using a highly doped diamond electrode in an aqueous solution containing 3  10-3 mol dm‑3 4-aminophenol ( C6H4(OH)(NH2) ), and 0.5 mol dm‑3 sulphuric acid (H2SO4).4-aminophenol is an aromatic organic molecule, which may undergo a two step oxidation. The cyclic voltammograms show two oxidation peaks and two reduction peaks per scan Figure 5.5 – CV of sample B67 in 3  10-3 mol dm-3 4-aminophenol & 0.5 mol dm-3 H2SO4 Various scan rates, Ag dag contact, geometric area of working electrode = 20 mm2 http://www.chm.bris.ac.uk/pt/diamond/mattthesis/chapter5.htm

Diffusion equation (all x and t) Summarization Cre Ere (as above) Cre Eir Diffusion equation (all x and t) Reaction Case

(as above, with kb = 0) (equation for cY not required ) Ere Cir Ere Cre

Ere C2ir

CreEre reaction diagram with zones for different types of electrochemical behavior as a function of K and  (defined in the following table). Here, The zones are DP, pure diffusion: DM, diffusion modified by equilibrium constant of preceding reaction: KP pure kinetics: and KI, intermediate kinetics.

Treatment depend on scan rate and on particular technique : Dimensionless Parameters for Voltammetric Methods Technique Time Parameter (s) Dimensionless Kinetic parameter, , for CE EC Chronoamperometry and polarography t (kf +kb ) t k t k Cz* t Linear sweep and cyclic voltammetry 1/ [(kf +kb )/v] (RT/nF) (k/v ) (RT/nF) [(kcz* )/v] Chronopotentiometry  (kf +kb )  k k Cz* Rotating disk electrode 1/ (kf +kb )/  k/  k cz* /

for large kf and kb, p will be displaced as a function of v . (30/n mV per 10 times v)

5.5 Methods for mechanism study Tafel Equation - “Simple” Electron Transfer Assuming that ==0.5 For a simple 1 electron process slope = 1 / 120 mV For a simple 2 electron process slope = 1 / 60 mV

Using the Butler-Volmer and Tafel Equation to Determine Multistep Reaction Mechanisms Mechanism (A): Cu2+ + 2e = Cu or Mechanism (B): Cu2+ + e = Cu+ Cu+ + e = Cu For mechanism (A): n = 2 ,  = 0.5 Plotting logi against  gives a straight line with a gradient of - [60 mV]-1. Similar arguments for reverse reaction: Cu  Cu2+ + 2e, gives a straight line with a gradient of [60 mV]-1.

Mechanism B (Forward Reaction) Cu2+ + e = Cu+ Cu+ + e = Cu assume (1) is rate determining step (r.d.s.): For mechanism (B): n = 1 ,  = 0.5 Hence, for Cu deposition with Cu2+ + e  Cu+ (r.d.s.) Cathodic section of Tafel plot (logi vs. ) gives a slope of - 1 / 120 [mV]

Mechanism B : Reverse Reaction Cu2+ + e = Cu+ Cu+ + e = Cu Reverse: Cu+  Cu2+ + e also r.d.s. rapid step (2) in equilibrium. Can use Nernst eq. to find [Cu+]: Tafel slope = 1 / 40 [mV]

5.7 determination of intermediate Rotating Ring-Disk Electrodes Reversal techniques are obviously not available with the RDE, since the product of the electrode reaction, R, is continuously swept away from the surface of the disk. addition of an independent ring electrode surrounding the disk.

By measuring the current at the ring electrode with the potential maintained at a given value, some knowledge about what is occurring at the disk electrode surface can be obtained. For example, if the potential of the ring is held at a value at the foot of the O+ ne → R wave, product R formed at the disk will be swept over to the ring by the radial flow streams where it will be oxidized back to O (or “collected”).

The theoretical treatment of ring electrodes is more complicated than that of the RDE, since the radial mass transfer term must be included in the convective-diffusion equation. The current at the ring electrode is given by The solution to these equations yields the limiting ring current:

Levich equation for disk electrode: Notice that for given reaction conditions (co0 and ) a ring electrode will produce a larger current than a disk electrode of the same area. Thus the analytical sensitivity of a ring electrode (i.e., the current caused by a mass-transfer-controlled reaction of an electroactive species divided by the residual current) is better than that of a disk electrode, and this is especially true of a thin ring electrode. However, constructing a rotating ring electrode is usually more difficult than an RDE.

RRDE experiments are usually carried out with a bipotentiostat, which allows separate adjustment of ED and ER. Several different types of experiments are possible at the RRDE: Collection experiments, where the disk-generated species is observed at the ring Shielding experiments, where the flow of bulk electroactive species to the ring is perturbed because of the disk reaction, are the most frequent.

Example for a collection experiment: the ring (b) measures the reduction of peroxide produced at the disk (a) during the electroreduction of oxygen.

the ring current is related to the disk current by a quantity N, the collection efficiency ; this can be calculated from the electrode geometry, since it depends only on r1, r2, and r3 and is independent of c, , DR,DO

5.6.3 detection of intermediates using the same electrode (CV) 5.6.4 detection of intermediates using thin-layer cell and spectroscopy