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Voltammetry A variety of electroanalytical methods rely on the application of a potential function to an electrode with the measurement of the resulting current in the cell. In contrast with bulk electrolysis methods, the objective is not to engage all of the analyte in reaction. Furthermore, voltammetric methods generally require achievement of polarization whereas it is ordinarily desirable to avoid polarization in bulk electrolysis methods. Bulk electrolysis: relatively large electrodes (on the order of cm2) Voltammetry: relatively small electrodes (on the order of μm2-mm2) In both cases, relatively high concentrations of bulk electrolytes (that do not engage in electrochemical reactions under the conditions used) are used to avoid migration. Various excitation waveforms are used for different purposes. Linear sweep voltammetry: Potential of working electrode changed at a rate of mV/s Excess of nonreactive supporting electrolyte to minimize migration (motion of analyte ions due to external field). Reference electrode connected via a high impedance voltmeter. Current flows primarily between working electrode and counter electrode. Typical working electrodes are a disk electrode (left) and a mercury electrode (right). Voltage ranges associated with Pt, Hg, and C based working electrodes. Limits established by oxidation and reduction of water. (Hg gives lower negative voltages due to large overvoltage of H2 on mercury.) Current versus applied potential referred to as a voltammogram: By convention, reduction (cathodic) currents are positive and oxidation (anodic) currents are negative. A + ne- ' P ∫-shaped curve is referred to as a voltammetric wave. Point Z – limiting current, il – current limited by polarization il = kc A k is a constant, cA = analyte concentration The point at which i = il/2, E1/2, is referred to as the half-wave potential and it is approximately equal to the standard potential for the half-reaction. This value can be used for identification purposes. Hence linear sweep voltammetry can be both a qualitative and quantitative technique. Two types: 1. High convection: hydrodynamic voltammetry 2. Low convection: polarography We will discuss only hydrodynamic voltammetry… Convection supplied by i) vigorous stirring of the solution in contact with the electrode, ii) rapid rotation of the electrode, or iii) flowing analyte solution over the electrode. In all cases, an excess of supporting electrolyte is used to minimize migration of the analyte. Near the electrode: A + ne- ' P Eappl cP0 0.059 =E − log 0 − Eref n cA 0 A where EA0 is the standard electrode potential for the half-reaction, cP0 is the product concentration in the Nernst diffusion layer, δ, and cA0 is the analyte concentration in the Nernst diffusion layer. δ is typically 0.01-0.001 cm, depending upon stirring rate and solvent viscosity. Current at the electrode is determined by the rate at which A arrives at the electrode, which is given by: δcA/δx where x is the distance from the electrode ⎛ ∂c ⎞ i = nFAD A ⎜ A ⎟ where n is the number of e ∂ x ⎝ ⎠ transferred, F is Faraday’s constant, A is the electrode surface area (cm2), DA is the diffusion coefficient for A (cm2/s), and cA is concentration (mol/cm3). ⎛ ∂c A ⎞ i = nFAD A ⎜ ⎟ ⎝ ∂x ⎠ i= (c nFADA δ ) ( 0 0 − c = k c − c A A A A A ) At the point where cA0 → 0, i becomes il and il = nFAD A δ c A = k Ac A 0 plugging il = kAcA into i = k A (c A − c A ) and rearranging il − i c = kA 0 A i=− i=− c P0 = nFADP δ nFADP i kP δ (c ) ( 0 0 − c = k c − c P P P P P cP0 = k P cP0 ) Plugging c A0 = il − i i c P0 = k A and k P into 0 c 0 . 059 = E A0 − log P0 − Eref gives n cA Eappl Eappl = E A0 − k i 0.059 0.059 log A − log − Eref n kP n il − i At E1/2, i = il/2, and E1 / 2 kA 0.059 =E − log − Eref n kP 0 A solving for EA0 and plugging into the equation for Eappl yields: Eappl 0.059 i = E1 / 2 − log n il − i this is the equation for the ∫-shaped curve if DA and DP are similar, kA/kP ≈ 1 such that E1/2 ≈ EA0 - Eref Linear sweep voltammetry can provide qualitative (via E1/2) and quantitative (via il) information. Provided E1/2 values are sufficiently different (i.e., they can be resolved) species present in mixtures can be determined in a single expt. Mixtures of the same species in different oxidation states can also be determined Curve C: 10-4 M Fe3+ Curve B: 0.5 x 10-4 M Fe3+, 0.5 x 10-4 M Fe2+ Curve A: 10-4 M Fe2+ Uses of linear sweep hydrodynamic voltammetry: 1.) For oxidizable or reducible species in flowing streams, as in the outlet of a liquid chromatograph: e.g., LC/EC – BAS 2.) Sensors – cells established to be selective for particular species (e.g., oxygen, glucose) usually a fixed V msmt (amperometry) Cyclic voltammetry: msmt of current as working electrode potential is swept first in one direction and then in the other forward scan: scan in direction of more negative potential reverse scan: scan in direction of more positive potential switching potentials: voltages at which scan reversal occurs Uses: primarily qualitative study of redox reactions identification of reaction intermediates observation of rapid sequential (follow-up) rxns e.g.: Fe(CN)63- + e- ' Fe(CN)646 mM in Fe(CN)63-, 1 M in KNO3 Points: A: beginning of scan, small anodic current due to oxidation of water B: beginning of reduction of Fe(CN)63- to Fe(CN)64C: rapid increase in current with applied V D: maximum cathodic current (see equation) E: current decays due to extension of diffusion layer (unstirred solution) F: scan reversal point F-J: reoxidation of Fe(CN)64- to Fe(CN)63For a rapidly reversible redox reaction ip = 2.686x105AcD½υ½ where ip = peak current (either cathodic or anodic), A = electrode area, c is concentration, D = diffusion coefficient, υ = scan rate (volts/s) |Epa-Epc| = ΔEp = 0.059/n if ΔEp > 0.059/n, rate of electron transfer is slow relative to scan rate, kinetics of electron transfer can be determined via measurements taken as a function of scan rate. Stripping methods: voltammetry experiments involving a bulk electrolysis preconcentration step followed by the removal of the analyte via a potential sweep while measuring current Step 1: a fixed electrolysis time during which analyte is deposited onto an electrode (allows for orders of magnitude in preconcentration) Step 2: evolution of the analyte via a voltage sweep of the electrode (concentrations as low as nano-molar can be determined)