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Cyclic Cyclic Voltammetry Voltammetry
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### Transcript of 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:

E = E i + ωt for 0 ≥ t ≥ λ

E = E i + ωλ −ωt for λ > t

⎧ ⎨ ⎩

0

Ei

E

A New WaveformA New Waveform

∂Co(x, t)

∂t= Do

∂ 2Co(x, t)

∂x 2

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).

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

i = nFAC o*(Doσ )1/ 2 π χ (σt)( )

* nF

RT

⎝ ⎜

⎠ ⎟

1/ 2

ω1/ 2

where : σ =nF

RTω

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:

More On BaselinesMore On Baselines

Hydrazine (NHydrazine (N22HH44)Oxidation)Oxidation

Bpy *

t2g

eg(*)

e–

Bpy *

t2g

eg(*)

An EC An EC MechanismMechanism

ClRe(CO)3phen in acetonitrile (CH3CN)

+ tetrabutylammonium

perchlorate

Luong, Nadjo and Wrighton, JACS, 100, 5790 (1978)

Charge Charge Transfer Transfer

CommunicationCommunication