Electrochemistry for Engineers 0581.5271 Electrochemistry for Engineers LECTURE 5 Lecturer: Dr. Brian Rosen Office: 128 Wolfson Office Hours: Sun 16:00

Forced Convection

Ideally polarizable electrodes Double layer charging (if R ≠ infinity)

Kinetically controlled current flow - Reaction rate constant, k - Reaction rate law, (ex. r = kCO) - Exchange current (iO) - symmetry factor, α

Mass transport controlled - 1D diffusion model - Cottrell experiment - Mass transport limiting current

Mass transport + kinetic control

Separate Contributions When in the “mixed control” regime, it is sometimes possible to separate the “activation” parameters from the “transport” parameters by operating with a system with well defined transport properties = Rotating electrodes

Rotating Disc Electrodes insulator

Laminar Flow at Electrode Velocity (cm/s) Rotation Rate (s-1) Kinematic viscosity (cm2/s)

Diffusion-Convection Layer Systems with convection form diffusion-convection layers of constant thickness adjacent to the electrode surface. This is due to the drag created at the interface. The thickness is function of convection rate and form. Coexistence of diffusion and convection when x < δO

How to model Steady State Mass-Transport Limiting Current Density At the limiting current, the concentration of “O” at the electrode surface is zero (in a reduction) and the rate of convection and rate of diffusion are equal.

separate and integrate Recall.. Levich Equation

PEM Fuel Cells

Oxygen Reduction in Acid Mass transport limiting current density at 3000 rpm

Linear Sweep Under Rotation Kinetic current >> mass transport limit MASS TRANSPORT LIMITED Current estimated by Levich Equation Dependence on ω Kinetic current << mass transport limit KINETIC LIMIT Current estimated by BUTLER-VOLMER No dependence on ω

Levich Plots Mixed control as kinetic limitations set in at high ω Limiting current (plateau) Mass transport control At exceptionally high speeds (generally >2500 rpm), reactions with slow kinetics cannot keep up with the increasing speed of mass transport. These kinetic limitations cause the limiting current to fall BELOW the current predicted by the Levich equation

Modeling Mixed Control Measured current under mixed control Mass transport limited current Kinetically limiting current in the absence of mass transfer limitations

Kouteckỳ-Levich Equation

Kouteckỳ-Levich Equation Where E2 < E1 (reduction) E2>E1 (oxidation) As expected, iK grows larger (1/iK grows smaller) as the overpotentials is increased.

Plotting Mixed Control – f(E) Oxygen Reduction 1/iK (-)

Mixed Control Visualized Pt 1 Kinetic Control Mixed Control Mass transport controlled

Mixed Control Visualized Pt 2 iK ilim i

Mechanistic Data on O2 Reduction

Mechanistic Information ▪ ● ▲ Data from Eliran Hamo (EML-TAU)

Rotating Ring-Disc Electrodes (RRDE) Recall convection pattern v(x,r) Ring and disc are both WORKING ELECTRODES and are INDEPENDENTLY CONTROLLED

Operation RO OR O Scanning E  (-) Constant E (+) DISC RING r OR RO O One can measure the extent a specific product is made at the disc by reversing the reaction at the ring

Recall… To what extent does the 2e- reaction occur at various potentials?

Example Operation or RRDE Scanning E  (-) Constant E (+) DISC RING r O2 + 2H+ + 2e- H2O2 H2O2  O2 + 2H+ + 2e- O2 + 4H+ + 2e- H2O O2 What is the practical limit for selecting the potential of the ring in this case?

Ficks 2nd Law - RRDE RDE: (from before) RRDE: Concentration is a function of radius due to depletion! RRDE: DISC RING r

Solving as before we get: ……

RRDE Collection Efficiency x = fraction of R that makes it to the ring electrode y = fraction of R that is flung back into solution 1-x-y = fraction of R that is subjected to other processes (decomposition, conversion to non- electroactive species.