4.1.1. A Deeper Insight into the Meaning of k° and α

Heterogeneous Standard (or conditional) rate constant k° Measures the ability of a species to exchange electrons with the electrode in order to convert to its redox partner large k° : Converting on a short time scale largest values for k°(metre/second) range from 0.01 m s-1 to 0.1 m s-1 redox processes not involved significant molecular reorganizations

small k° : converting on a long time scale smallest values for k° are around 10-11 m s-1 increasing k° by applying a potential value higher than Eo' of the couple more negative for a reduction process more positive for an oxidation process

Transfer Coefficient α An index indicative of the symmetry of the energy barrier for a redox half-reaction

[n . F . (E-E°') - (α. n . F . (E-E°')] Significance of α Applying a potential value E equal to the formal potential E°' of the couple Ox/Red (in equilibrium system) Applying a potential value different from E °',based on ΔG = - n .F.(E- E°') the potential more positive than E°‘, increase the activation barrier for the reduction process by α . n . F . (E - E°') for the oxidation process is lowered by an amount equal to the residual variation of the overall energy [n . F . (E-E°') - (α. n . F . (E-E°')] =(1 -α).n . F. (E-E°'). 1 2

if the slope of the reduction curve equals that of oxidation 1 2 3 θ : slope of the curve of the reduction half-reaction φ : slope of the oxidation half-reaction if the slope of the reduction curve equals that of oxidation (θ =φ) then α = 0.5 between 0.0 and 0.5 , if θ<φ between 0.5 and 1.0 , if θ>φ

4.1.2. Verification of the Theory Under Equilibrium Conditions

Butler - Volmer equation: For a heterogeneous charge transfer validity: if equilibrium potential( Eeq)and zero current condition(i = 0) In bulk: That the same with: Then the relation is valid

4.1.3.The Exchange Current Under equilibrium conditions (i.e. when both forms of a redox couple are present in solution), the faradic current is zero because the cathodic current (ic) equals the anodic current (ia) This current, equal in both directions and exchanged under equilibrium conditions, is defined as the exchange current, i0 It is proportional to the standard rate constant, thus resulting in the common practice of using i0 instead of k° in kinetic equations

substituting in the expression for the exchange current io Under equilibrium condition: Then: Also: substituting in the expression for the exchange current io

often the kinetic equations are written as a function of io rather than k° overvoltage is η = E – Eeq

Current-overvoltage profiles When Ox and Red are in solution, the working electrode will spontaneously find its Eeq (Nernst equation) and there will be no overall current flow. In order for Ox to be reduced or Red oxidized, the system must be moved from equilibrium The solid curve is the sum of the cathodic and anodic components, which are represented by the respective dashed lines At very negative potentials (compared to Eeq) the anodic component is zero, so that the current is due only to the reduction process. The inverse effect occurs for very positive potentials Ox + ne- = Red

i1 , what and why? at high values of η the current reaches a limiting value (i1), beyond which it can rise no more. This happens because the current is limited by the rate of the mass transport of the species Ox or Red from the bulk of the solution to the electrode surface, rather than from the rate of the heterogeneous electron transfer

4.2. Mass Transport Possible Ways to Move a Species from the Bulk of the Solution to the Electrode Surface

Convection Movement of a species under the action of a mechanical force (a gradient of pressure) fortuitous (resulting from collisions or vibrations of the electrochemical cell) intentionally forced (through controlled stirring)

Diffusion movement caused by regions with different concentrations of the active species in solution (a gradient of concentration) randomize the distribution of molecules in a system transporting species from regions of high concentration to regions of low concentration Electrode reactions are an ideal mode to generate diffusive movement In a layer of solution close to the electrode surface (thickness ≈ 0.0001 m) the concentration of Red will be higher and the concentration of Ox lower than that present in the mass of the solution (concentration gradient )

Migration Movement of an ionic solute under the action of an electric field (a gradient of electrical potential) The positive ions are attracted by the negatively charged electrode, while the negative ions are attracted by the positively charged electrode

Supporting Electrolyte Diffusion is the only mode of mass transport for which we possess well known mathematical treatments Adding a supporting electrolyte to minimize the effect of migration by to the solution Produces non-electroactive ions in the potential region of interest In a ratio of at least 100:1 compared to the electroactive species then statistically more probable that, under the effect of an applied potential, the inert ions of the supporting electrolyte migrate to the electrodes rather than those of the electroactive species under study In order to avoid convection, the solution is maintained unstirred (or controlled stirring)