Cyclic Voltammetry. Current-Potential-Time Space Reversible System Time.

Cyclic Cyclic VoltammetryVoltammetry

Current-Potential-Time Current-Potential-Time SpaceSpace

t

E

i

E1/2

Reversible System

Time

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

N&S DiagnosticsN&S Diagnostics

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:

Cyclic Voltammetry. Current-Potential-Time Space Reversible System Time.

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