How does rotation speed on an RDE impact half-wave potential shifts? Key insights for EC reactions

Increasing the RDE rotation speed generally shifts the half-wave potential negatively for an EC mechanism. At low rotation rates, a homogeneous chemical reaction rapidly consumes the species generated at the electrode, producing a chemically perturbed half-wave potential, (E'_{1/2}), shifted in the positive direction. As rotation increases, convective mass transport becomes faster and competes more effectively with the follow-up chemical reaction, moving the wave back toward its kinetically unperturbed potential by approximately 30/n mV for every tenfold increase in rotation rate at 25 °C, where (n) is the number of transferred electrons.

The key point is that rotation changes the competition between homogeneous chemical reaction and mass transport. For a coupled EC reaction, higher rotation reduces the time available for the electrogenerated intermediate to react chemically near the electrode, so the observed half-wave potential shifts negatively toward its unperturbed value.

Why Rotation Changes the Observed Potential

Rotation increases convective mass transfer

For an RDE, the convective mass-transfer coefficient follows:

[ m_R = 0.62D_R^{2/3}\nu^{-1/6}\omega^{1/2} ]

Here, (D_R) is the diffusion coefficient, (\nu) is the kinematic viscosity, and (\omega) is the angular rotation rate.

Because (m_R) is proportional to (\omega^{1/2}), increasing the rotation rate improves mass transport, but with diminishing returns. A 100-fold increase in rotation rate produces a 10-fold increase in the mass-transfer coefficient.

The diffusion layer becomes thinner

The steady-state diffusion layer thickness decreases approximately as:

[ \delta_O = 1.61D_O^{1/3}\omega^{-1/2}\nu^{1/6} ]

A faster-spinning disk therefore creates a thinner concentration boundary layer. Electroactive species reach the electrode more rapidly, and products or intermediates are transported away more efficiently.

The limiting current increases

The Levich relationship describes the convective limiting current:

[ i_{l,c}=0.62nFAD_O^{2/3}\omega^{1/2}\nu^{-1/6}C_O^* ]

Thus, the limiting current increases with the square root of rotation speed. This current change is an important diagnostic because it confirms that hydrodynamic mass transport is being varied in a controlled way.

How Coupled Chemical Reactions Shift the Half-Wave Potential

Low rotation favors the follow-up reaction

In an EC mechanism, an electron-transfer step first generates an intermediate, followed by a homogeneous chemical reaction. At low rotation rates, transport is relatively slow, so the intermediate remains near the electrode longer.

The chemical reaction can then consume a substantial fraction of that intermediate before it is transported away. The resulting voltammetric wave is shifted from the potential expected for the electron-transfer step alone.

Higher rotation suppresses chemical perturbation

Increasing rotation accelerates transport through the diffusion layer and reduces the residence time of species near the electrode. Physical transport consequently becomes more competitive with the homogeneous reaction.

The chemical reaction has less opportunity to deplete the electrogenerated species at the surface. The observed half-wave potential therefore shifts in the negative direction, back toward the kinetically unperturbed value.

The shift scales with electron number

At 25 °C, the characteristic shift is approximately:

[ \Delta E'_{1/2}\approx -\frac{30}{n}\text{ mV per decade increase in rotation rate} ]

The negative sign describes the usual direction for the EC behavior described here. The magnitude decreases as the number of transferred electrons, (n), increases.

Interpreting the Rotation-Rate Dependence

A positive shift at low rotation indicates chemical involvement

If the half-wave potential is more positive at low rotation and moves negatively as rotation increases, the data are consistent with a follow-up chemical reaction that consumes the electrode-generated intermediate.

The size and trend of the shift provide information about the relative rates of chemical reaction and mass transport.

Rotation creates a kinetic-transport competition

The relevant comparison is between the homogeneous chemical rate and the rate at which the intermediate is removed from the interfacial region. Slow rotation gives the chemical step more influence; fast rotation gives mass transport more influence.

This makes RDE measurements useful for distinguishing an intrinsic electron-transfer response from a response altered by coupled solution chemistry.

Limiting current and potential should be evaluated together

The increase in limiting current with (\omega^{1/2}) primarily reflects improved mass transport. The accompanying half-wave-potential shift reveals how that transport change affects the coupled chemical mechanism.

Considering both observables is more informative than interpreting either one in isolation.

Understanding the Trade-offs

Higher rotation does not eliminate the chemical reaction

Increasing rotation reduces the influence of a follow-up reaction near the electrode, but it does not necessarily stop the reaction throughout the solution. A sufficiently fast homogeneous reaction may still dominate even at high rotation rates.

The direction of the shift depends on the mechanism

The negative shift described here applies to the stated EC case, where the chemical reaction consumes the electrogenerated species and low rotation produces a positive perturbation. Different mechanisms, such as catalytic or reversible chemical steps, can produce different potential and current trends.

Hydrodynamic assumptions must remain controlled

The standard relationships assume a well-behaved rotating disk, appropriate fluid properties, steady rotation, and sufficiently uniform mass transport. Surface roughness, catalyst-film porosity, bubble formation, or uncontrolled convection can make the apparent rotation dependence deviate from ideal RDE behavior.

Mass transport and kinetics can be confused

A change in current with rotation does not by itself prove that intrinsic electron-transfer kinetics have changed. The purpose of controlled hydrodynamic measurements is to separate transport effects from homogeneous and heterogeneous rate constants.

How to Apply This to Your Analysis

Use a series of rotation rates and examine both the Levich current response and the half-wave-potential trend.

• If your primary focus is identifying a follow-up chemical reaction: Look for a positive low-rotation potential shift that moves negatively toward the unperturbed value as rotation increases.
• If your primary focus is measuring mass-transfer behavior: Confirm that the limiting current is approximately proportional to (\omega^{1/2}) while accounting for diffusion coefficient, viscosity, area, concentration, and electron number.
• If your primary focus is extracting kinetic constants: Use rotation-dependent data to model the competition between homogeneous reaction and transport rather than assigning the entire potential shift to electron-transfer kinetics.
• If your primary focus is comparing catalysts or materials: Keep electrolyte properties, electrode area, concentration, temperature, and surface preparation controlled so that rotation remains the principal changing variable.

By varying rotation systematically, an RDE reveals whether a half-wave potential is governed primarily by intrinsic electron transfer, mass transport, or a coupled chemical reaction.

Summary Table:

Key Relationship: ΔE'₁/₂ ≈ -(30/n) mV per decade increase in rotation rate at 25°C

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