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Beyond the Butler-Volmerequation. Curved Tafelslopes from steady-statecurrent voltage curves

[keynote lecture]

This item was submitted to Loughborough University's Institutional Repositoryby the/an author.

Citation: FLETCHER, S. and VARLEY, T.S., 2012. Beyond the Butler-Volmer equation. Curved Tafel slopes from steady-state current voltage curves[keynote lecture]. Electrochem 2012: Electrochemical Horizons, Trinity College,Dublin, 4 September 2012.

Additional Information:

• This is a conference lecture [ c© Stephen Fletcher 2012. All rights reserved].It was a keynote lecture delivered at Electrochem 2012: ElectrochemicalHorizons. Trinity College, Dublin, Tuesday 04 Sept 2012.

Metadata Record: https://dspace.lboro.ac.uk/2134/10316

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Publisher: RSC Faraday Division . c© Stephen Fletcher 2012

Please cite the published version.

https://dspace.lboro.ac.uk/2134/10316

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04 Sept 2012

Electrochem 2012 Trinity College, Dublin S. Fletcher

Stephen Fletcher & Thomas Stephen Varley

Department of Chemistry Loughborough University Leicestershire LE11 3TU

UK

Keynote Lecture Electrochem 2012: Electrochemical Horizons. Trinity College, Dublin, Tuesday 04 Sept 2012.

Beyond the Butler-Volmer equation. Curved Tafel slopes from steady-state current voltage

curves.

PHYS. CHEM. CHEM. PHYS., 13, 5359-5364 (2011)

04 Sept 2012


George Johnstone Stoney (1826-1911) Graduated BA (Trinity College) 1848 Proposed the word “electron” 1894

The Electron is Coming Home!

04 Sept 2012


Early Days

Ludwig Boltzmann d.1906

Paul Drude d.1906

Julius Tafel d.1918

Boltzmann modelled the (non-quantum) distribution of particles in various energy states. Drude modelled the flow of electrons through a metal, and Tafel measured the flow of electrons through a metal/solution interface… then they all committed suicide!

04 Sept 2012


Where are we headed? Materials Molecules Orbitals

19thC 20thC 21stC

Need for control at the single orbital level:

Nanotechnology Catalysis,

Rates, Life.

Today, orbital-level understanding is needed to advance to next-level technologies. Fortunately, quantum mechanics makes this possible.

04 Sept 2012


Life is just one damned electron after another…

Allen Hill (attrib.)

Electron transfer plays a crucial role in photosynthesis, respiration, nitrogen fixation, and in many other biochemical processes (including consciousness). Indeed, more than 10% of the structurally-characterized proteins in the Protein Data Bank are redox proteins, i.e. proteins that participate in, or catalyse, electron transfer. If we want to understand life, then we will first have to understand the role of electrons in living systems. Elsewhere, we have called this field of study “Electronomics”.

04 Sept 2012


Reorganization energy, λ

The reorganization energy is the work needed to convert the stoichiometry and conformation of the reactants into the stoichiometry and conformation of the products, in the absence of electron transfer. Marcus theory asserts that this work is due to the re-orientation of solvent molecules. By contrast, Fletcher theory asserts that this work is due to the electrostatic re-ordering of the entire ionic atmosphere, including co-ions and counter-ions.

04 Sept 2012


Tafel Analysis

Transfer coefficient

Symmetry factor

Traditional theory assumes that the Tafel slope is a straight line, implying that the transfer coefficient is a constant. But more recent work suggests that the Tafel slope may actually be curved due to the weak dependence of the symmetry factor on potential. In particular, the magnitude of this curvature should be reciprocal to the magnitude of the reorganization energy.

Traditional Tafel Slope

np = number of electrons prior to rate-determining step. nq = number of electrons actually in rate determining step (0 or 1)

04 Sept 2012


Predicted Tafel slopes for some elementary reaction schemes. If a chemical reaction controls the rate-determining step (indicated here by a circumflex accent) then no curvature should appear in the Tafel slope. But if Electron Transfer controls the rate-determining step then some curvature should always appear in the Tafel slope.

04 Sept 2012


i. A “slow” electron transfer step (no chemical rate-determining step, no back reaction) ii. No ligand substitution in the inner sphere of the reactant species iii. A single reactant species (no significant speciation) iv. A high concentration of reactant species (no diffusion control) v. A low faradaic background current (no parallel reactions) vi. Minimal mains interference (or suitable digital filtering thereof) vii. Minimal IR drop (minimal ohmic distortions) viii. A high concentration of supporting electrolyte, and a low electrode potential (<1V) (no significant reactant or product adsorption) ix. Minimal capacitive charging currents. x. Enough data to provide 95% confidence in derived parameters. xi. “Innocent” ligands (not redox active).

Experimental Criteria

It is VERY DIFFICULT to meet all these criteria simultaneously. However, it is just feasible if a substitution-inert, ultra-slow, electron transfer species can be found…

04 Sept 2012


An Ultra-Slow Electron Transfer Reaction

The 1983 Nobel Prize in Chemistry was awarded to Henry Taube "for his work on the mechanisms of electron transfer reactions, especially in metal complexes".

Henry Taube

“Typical” values

PHOTO: U.S. DEPT. OF ENERGY

04 Sept 2012


Why Does Cobalt Hexammine React So Slowly?

Note: Ruthenium hexammine reacts a billion times faster!

Obviously there is something “special” about cobalt hexammine. But what is it? To answer this question, we need to know something about molecular orbital theory…

04 Sept 2012


Molecular Orbital Theory

Today, molecular orbitals are very well understood at the level of molecular structure, but less well understood at the level of rates.

Hund Mulliken

The concept of “molecular orbital” was introduced by Robert Mulliken in 1932, based on earlier work by Friedrich Hund.

04 Sept 2012


A special case of molecular orbital theory is its application to transition metal complexes. This is called Ligand Field Theory.

Ligand Field Theory

Van Vleck

Ligand Field Theory describes the electrostatic interactions between ligands and the valence electrons of a metal. (John H. Van Vleck)

For example, Ligand Field Theory for Co(NH3)6

3+ describes how the “lone-pair” of electrons on each ammonia ligand interacts with the 3d, 4s, and 4p orbitals of the cobalt.

04 Sept 2012


3d Orbital Energies are Split by the Octahedral Field

Cobalt (3+) has greater splitting than Cobalt(2+). This shows up in their colours.

[Co(NH3)6]3+ absorbs in the blue and therefore appears orange-brown. [Co(NH3)6]2+ absorbs in the green and therefore appears red.

Complementary colours

04 Sept 2012


Lone pairs cause the splitting…

(Top) These d-orbitals cannot avoid repulsive interactions with the lone pairs on the ammonia ligands (red spheres). So high energy. (Bottom) These d-orbitals can avoid repulsive interactions with the lone pairs on the ammonia ligands (blue spheres). So low energy.

Orbital “end-capped” by ammonia

Orbital “end-capped” by ammonia

04 Sept 2012


The Co2+/Co3+ Reaction Is “Spin Forbidden”

The electrons distribute themselves differently in the two different oxidation states of cobalt. The 2+ state is high-spin (three unpaired electrons) whereas the 3+ state is low-spin (no unpaired electrons). Thus, electron transfer is accompanied by a change of spin state, making the whole reaction very slow indeed.

For simplicity, the energy levels are shown equalized in the transition state.

04 Sept 2012


...but interfacial Electron Transfer is still “spin-forbidden”.

The electrode reaction is a little bit simpler...

04 Sept 2012


RAM Electrodes

Assemblies of carbon microelectrodes are almost ideal for the measurement of steady-state Tafel slopes.

04 Sept 2012


The speciation of cobalt(III) has been described by Compton et al.

10-2 molar ammonia guarantees pure hexamminecobalt(III). High concentrations of ammonium ion also inhibit reactant and product adsorption.

04 Sept 2012


Typical Current-Voltage

Curve

04 Sept 2012


Tafel Plot

04 Sept 2012


Curvature

04 Sept 2012


Tafel Slope Versus

Potential

The Tafel slope b varies linearly with potential.

04 Sept 2012


The Reorganization Energy

For a symmetry factor of one-half, this implies an activation energy of ~15 kJ mol-1 This is comparable to the strength of a hydrogen bond.

04 Sept 2012


Time’s up!

04 Sept 2012


Any Questions?