Beyond the Butler-Volmer equation. Curved Tafel slopes from steady-state current voltage curves [keynote lecture]

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1 Loughborough University Institutional Repository Beyond the Butler-Volmer equation. Curved Tafel slopes from steady-state current voltage curves [keynote lecture] This item was submitted to Loughborough University's Institutional Repository by the/an author. Citation: FLETCHER, S. and VARLEY, T.S., 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 Additional Information: This is a conference lecture [ c Stephen Fletcher All rights reserved]. It was a keynote lecture delivered at Electrochem 2012: Electrochemical Horizons. Trinity College, Dublin, Tuesday. Metadata Record: Version: Not specified Publisher: RSC Faraday Division. c Stephen Fletcher 2012 Please cite the published version.

This item was submitted to Loughborough s Institutional Repository (https://dspace

2 This item was submitted to Loughborough s Institutional Repository ( by the author and is made available under the following Creative Commons Licence conditions. For the full text of this licence, please go to:

3 Beyond the Butler-Volmer equation. Curved Tafel slopes from steady-state current voltage curves. Stephen Fletcher & Thomas Stephen Varley Department of Chemistry Loughborough University Leicestershire LE11 3TU UK PHYS. CHEM. CHEM. PHYS., 13, (2011) Keynote Lecture Electrochem 2012: Electrochemical Horizons. Trinity College, Dublin, Tuesday.

4 The Electron is Coming Home! George Johnstone Stoney ( ) Graduated BA (Trinity College) 1848 Proposed the word electron 1894

Early Days Ludwig Boltzmann d.1906 Paul Drude d.

Drude modelled the flow of electrons through a metal,

5 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!

6 Where are we headed? Materials Molecules Orbitals 19 th C 20 th C 21 st C 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.

7 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.

8 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.

9 Tafel Analysis Traditional Tafel Slope Transfer coefficient n p = number of electrons prior to rate-determining step. n q = number of electrons actually in rate determining step (0 or 1) 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.

10 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.

11 Experimental Criteria 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). 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

12 An Ultra-Slow Electron Transfer Reaction Henry Taube PHOTO: U.S. DEPT. OF ENERGY Typical values 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".

13 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

Hund Mulliken Today, molecular orbitals are very well understood at the

14 Molecular Orbital Theory The concept of molecular orbital was introduced by Robert Mulliken in 1932, based on earlier work by Friedrich Hund. Hund Mulliken Today, molecular orbitals are very well understood at the level of molecular structure, but less well understood at the level of rates.

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

15 Ligand Field Theory A special case of molecular orbital theory is its application to transition metal complexes. This is called Ligand Field Theory. Ligand Field Theory describes the electrostatic interactions between ligands and the valence electrons of a metal. (John H. Van Vleck) Van Vleck For example, Ligand Field Theory for Co(NH 3 ) 6 3+ describes how the lone-pair of electrons on each ammonia ligand interacts with the 3d, 4s, and 4p orbitals of the cobalt.

16 3d Orbital Energies are Split by the Octahedral Field Complementary colours Cobalt (3+) has greater splitting than Cobalt(2+). This shows up in their colours. [Co(NH 3 ) 6 ] 3+ absorbs in the blue and therefore appears orange-brown. [Co(NH 3 ) 6 ] 2+ absorbs in the green and therefore appears red.

on the ammonia ligands (red spheres). So high energy.

17 Lone pairs cause the splitting Orbital end-capped by ammonia Orbital end-capped by ammonia (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.

18 The Co 2+ /Co 3+ Reaction Is Spin Forbidden For simplicity, the energy levels are shown equalized in the transition state. 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.

19 The electrode reaction is a little bit simpler......but interfacial Electron Transfer is still spin-forbidden.

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

21 The speciation of cobalt(iii) has been described by Compton et al molar ammonia guarantees pure hexamminecobalt(iii). High concentrations of ammonium ion also inhibit reactant and product adsorption.

22 Typical Current-Voltage Curve

23 Tafel Plot

24 Curvature

25 Tafel Slope Versus Potential The Tafel slope b varies linearly with potential.

26 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.

27 Time s up!

28 Any Questions?

8 Phenomenological treatment of electron-transfer reactions

8 Phenomenological treatment of electron-transfer reactions 8.1 Outer-sphere electron-transfer Electron-transfer reactions are the simplest class of electrochemical reactions. They play a special role