Post on 20-Dec-2015
Potential waveform:
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E = E i + ωt for 0 ≥ t ≥ λ
E = E i + ωλ −ωt for λ > t
⎧ ⎨ ⎩
0
Ei
E
A New WaveformA New Waveform
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∂Co(x, t)
∂t= Do
∂ 2Co(x, t)
∂x 2
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New Condition :
CO (0, t)
CR (0, t)= θ(t) = exp
nF
RTE i ± ωt − E o
( ) ⎡ ⎣ ⎢
⎤ ⎦ ⎥
Trouble : C o(t) ≠ θ C R (t) because θ(t)
For the reversible case have the standard Semi-infinite diffusion conditions plus:
Diffusion ConditionDiffusion Condition
SolutionSolution1948
Sevick, “Oscillographic Polarography with Periodic Triangular Voltage”, Collection of Czech. Chem. Comm., 13, 349 (1948).
Randles, “A Cathode Ray Polarograph”, Faraday Society, 44, 327 (1948).
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Let θ(t) = θS(t)
θ = expnF
RT(E i − E o)
⎡ ⎣ ⎢
⎤ ⎦ ⎥
S(t) = exp −σt( ) where σ =nF
RTω
ProblemProblem
There is no analytical solution to Fick’s second law when the boundary is time dependent. Sevick and Randles solutions was to approximate the integral with a series. While this works for the reversible case, it is not very pragmatic for more complex mechanisms.
New Solution:
Wait for a high speed computer (IBM main frame -1964- University of Wisconsin at Madison)
Nicholson and Shain, “Theory of Stationary Electrode Polarography”, Analytical Chemistry, 36, 706 (1964)
Reversible CV ContinuedReversible CV Continued
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i = nFAC o*(Doσ )1/ 2 π χ (σt)( )
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ip = 0.443nFAD o1/ 2Co
* nF
RT
⎛
⎝ ⎜
⎞
⎠ ⎟
1/ 2
ω1/ 2
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where : σ =nF
RTω
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E p − E1/ 2 = E p − E o +RT
nFln
Do
DR
⎛
⎝ ⎜
⎞
⎠ ⎟
1/ 2
≈28.5mV
n
Myth: A reversible wave will have a 60mV peak to peak separation.
Don’t Miss this TableDon’t Miss this Table
Two KEY PointsTwo KEY Points
1. Should use all three diagnostics 2. MUST go over three orders in magnitude in scan rate
to reliably use a diagnostic!
Implication: A single CV scan doesn’t tell you much, don’t over interpret it!
The Baseline IssueThe Baseline Issue
Nicholson, Anal. Chem. 38, 1406 (1966)
Three solutions
•Guess
•Record i-t over i-V
•Nicholson:
An EC An EC MechanismMechanism
ClRe(CO)3phen in acetonitrile (CH3CN)
+ tetrabutylammonium
perchlorate
Luong, Nadjo and Wrighton, JACS, 100, 5790 (1978)