Electrochemistry for Engineers LECTURE 4 Lecturer: Dr. Brian Rosen Office: 128 Wolfson Office Hours: Sun 16:00

Cyclic Voltammetry

Sweep rate (generally in mV/sec) ϴ=ϴ= Since ϴ is a function of time, we can no longer take the Laplace transform of the Nernst Equation as we did when we solved for the current-time relationship for an arbitrary step

Solution to the Linear Sweep Problem (Reversible systems only!) (τ is a dummy variable) No analytical solution exists – the solution to this problem must be obtained numerically Laplace transforms can be taken of C O and C R as usual, BUT The boundary condition is now a function of TIME!

Numeric Solution to Sweep Problem (Reversible systems only!) Defining… Where the χ-function is dimensionless and acquired numerically We now have a generalized (dimensionless) version of the current As a function of time and sweep rate!

The Solution (Reversible systems only!)

ipip EpEp

Peak Current, i p (Reversible systems only!)

E i – potential where only R is present

E is scanned positive and an ANODIC current is measured due to the oxidation of “R” into “O” (remember we can see oxidation current below E 0 because O was not present until now. Therefore, although the reduction reaction is thermodynamically favored below E 0, we only see the oxidation because of the small concentration of “O”

The anodic current increases as E is scanned even more positive because the driving force for oxidation increases as E is scanned in the positive direction.

The driving force for oxidation is consuming “R” at the maximum rate that diffusion can bring “R” to the surface and the current reaches a maximum. In a 1 electron reversible system this peak comes mV past E 0

Beyond the peak, the concentration of “R” near the electrode drops significantly causing the measured current to drop even though the driving force for reaction is increasing.

What If We Have Convection? With convection the current continues to increase until the consumption of “R” on the surface once again becomes limited by the mass transfer. (EVEN WITH CONVECTION, YOU WILL HIT A LIMIT EVENTUALLY)

The Idea CV for n=1, Reversible 57 mV for completely reversible system

Non-symmetric Reversal

Multiple Species O, O’, R, R’

Charging During CV’s Charging Current for Potential Step Charging Current for Potential Sweep (assuming Cd is not a function of E)

Charging During CV’s i p varies with υ 1/2 i chrg varies with υ 1 High scan rates and low concentrations of “O” (or “R”) can make it very difficult to see the faradaic wave

Quasi/Non Reversible Systems -i c Where the dashed line is the reversible system and the kinetics get slower as we move from II, to III, to IV

Applications in Energy Fig. 10 Cyclic voltammetry in 0.5 M H 2 SO 4 –argon purged solution with a potential scan rate of 50 mV s −1 recorded at CNT/CeO 2 (black curve) and CNT/CeO 2 /Pt (blue curve) electrodes.

Applications in Energy