Chapter 6 Potential Sweep Methods

Transcription

1 Chapter 6 Potential Sweep Methods Linear Sweep Voltammetry E Perturbation signal: E(t) E i + υt E i E f υ = scan rate = ± V/s Time Ox + e - Red i p α C o i 0 /2 i p E (vs. ref) Macroelectrodes: max mv/s Microelectrodes: max V/s

2 E o C o i /2 C i p 0 E (vs. ref) (-) C R Distance (x) Potential reached vicinity of E o and current begins to flow. As potential grows more negative surface concentraion of Ox must drop hence the flux and current increase. Steep C/ x! As potential moves past E o, the surface concentration drops to nearly zero and mass transport of Ox reaches a maximum rate. Current then declines as a depletion effect sets in.

3 E o E 1/2 i /2 i /2 i p i p 0 E (vs. ref) (-) 0 E (vs. ref) (-) Nernstian (Reversible) System C o (0,t)/C R (0,t) = ƒ(t) = exp [nf/rt(e i +υt E o ) ip = (2.69x10 5 )n 3/2 AD o 1/2 C o *υ 1/2

4 Equations for uction half reaction! E 1/2 -E 1/2 = RT/nF = 28.5 mv at 25 o C i /2 i p /2 = E 1/ RT/nF = E 1/ /n mv at 25 o C 0 E (vs. ref) (-) E 1/2 = E o + (RT/nF)ln (D R /D o ) 1/2 /2 = 2.20 RT/nF = 56.5/n mv at 25o C ƒ(υ) i p = ƒ(υ 1/2 ) {i d = ƒ(t -1/2 )} i p /υ 1/2 C o * = current function = constant (can be used to estimate n)

5 Totally Irreversible Systems i E o Larger driving potential E ( vs. ref) (-) i p = (2.99. x 10 5 ) (αn) 1/2 AC o *D o 1/2 υ 1/2 Ox + e - Red k f, k b, k o and α have more of an effect on shape. Hence they can be evaluated! = ƒ(υ) 30/αn for each tenfold inc. in υ i p = ƒ(υ 1/2 ) Plot ln i p vs. -E o at different υ Slope α -αf/rt Y inter α k o = E o RT/αnF[ ln(d o 1/2 /k o ) + ln (αfυ/rt) 1/2 /2 = 1.86RT/αnF = 47.7/αn mv at 25 o C

6 Quasireversible Reactions Ox + e - Red Increasing scan rate tends to shift a uction peak more negative and an idation peak more positive. Shape depends on k o, α and υ! Parameter = k o /(D 0 (1-α) D rα ƒυ) 1/2 Low α, big effect on wave Remember: the perturbation signal is a time dependent potential sweep. Where the wave shows up on the potential axis (time!) depends on the time dependence of the electrode reaction (reaction kinetics). ir effects also shift peak positions in a manner similar to that of kinetic effects! Must correct for this.

7 Effect of Double Layer Charging Current i ch = AC dl υ (A) Faradaic current must always be measu from baseline of the charging current. i ch /i f = C dl υ/(2.69x10 5 )n 3/2 D 1/2 C* The background/faradaic current ratio increases with scan rate. This means uced S/B ratios with increased scan rate! Remember that E true = E appl -ir u Increased scan rates mean increased current and more ir effect!

8 Effect of Potential Sweep Rate on Wave Shape Transition from peak shape to steady state depends on υ and r o. Large υ (short time) and conventional r o planar diffusion or peaks shape. Small υ (long time) and small r o non-planar diffusion or steady state. For υ << RTD/nFr o 2 steady state i-e curve observed.

9 Cyclic Voltammetry Reversal technique Useful for determining k o, concentrations of analyte and studying electrode reaction mechanisms (generate a product at the electrode surface on the forward sweep and probe its fate on the rev. sweep OX E 2 Potential (V) E 1 Time (sec) Current Density (µa/cm 2 ) RED E 1 E Potential (V) 2 i=0

10 Important Diagnostics Current Density (µa/cm 2 ) RED OX E 1 E Potential (V) 2 i=0 and = i p and i p i p /i p ratio Q p and Q p /2 Remember: the perturbation signal is a time dependent potential sweep. Where the wave shows up on the potential axis (time!) depends on the time dependence of the electrode reaction (reaction kinetics).

11 Chapter 6 - Potential Sweep Techniques Reversible or Nernstian Kinetics Current Density (µa/cm 2 ) RED OX i=0 = = 60/n mv Ep ƒ(υ) i p / i p = 1 i p and i p = ƒ(υ 1/2 ) Q p /Q p = 1 -/2 = 2.20 RT/nF = 56.5/n mv E 1 E Potential (V) 2 i p = (2.69 x 10 5 ) n 3/2 AD 1/2 C*υ 1/2

12 i p (corr) (A) 0 0 Slope = (2.69 x 10 5 ) n 3/2 AD 1/2 C* υ 1/2 (V/s) Linearity indicates: Semi-infinite linear diffusion controls the reaction rate. Electrochemical reversibility or irreversibility. Non-complicated reaction (can be reflective of this). i p = (2.69 x 10 5 ) n 3/2 AD 1/2 C*υ 1/2

13 Technique is extremely useful for studying electrode reaction mechanisms! k Red et k Ox + e - ch X (chemical rxn. prod) Current Density (µa/cm 2 ) RED OX i=0 i p /i p Rate of change reflective of k ch 1 E 1 E Potential (V) 2 υ (V/s)

14 20 n = 1, α = 0.5 T = 25 o C A Method for estimating k o in quasireversible systems! 0.2 > k o > 10-5 cm/s Kinetic Parameter Ψ = (D o /D r ) α/2 k o (πd o ƒυ) Peak Potential Separation values are nearly independent of 0.3 < α < 0.7. Nicholson method links kinetic parameter, Ψ, to k o