###### Learning Outcomes:

On completion of Part A, it is expected that the students will have acquired an understanding of key concepts and principles and that they will have the ability to:

• Describe the rate of homogenous ET reactions in terms of elementary transition state theory and solution reaction kinetics expressions.

• Use harmonic oscillator potential energy curves to depict donor-acceptor-solvent, i.e., reactant and product, states.

• Illustrate how ET reaction rate depends on pre-exponential (transmission coefficient, attempt frequency) and Arrhenius factors (reaction activation energy, temperature).

• Describe the role of the reorganization energy (incl. inner & outer sphere contributions) in ET reactions.

• Distinguish between the Libby and Marcus models of self-exchange ET reactions.

• Distinguish between self- and cross-exchange homogenous ET reactions.

• Describe the Marcus equation and how the interplay between reaction free energy change, activation energy, and reorganization energy affects rates of homogenous adiabatic ET reactions (incl. Marcus inverted region).

• Describe the quantum mechanical tunneling of electrons through various potential barriers and the role and implications of electron tunneling in ET reactions.

• Use the Landau-Zener (L-Z) approach to identify factors that determine the probability that a system will undergo a transition from reactant to product potential energy curves (i.e., the electronic coupling matrix element, the nuclear velocity, and the slopes of the respective curves).

• Use the L-Z approach to derive an expression for the transmission coefficient (and assess the degree of adiabaticity of a homogenous ET reaction), and, from this, an expression for the rate of a homogenous non-adiabatic ET reaction.

• Describe the dependence of the ET reaction rate on the donor-acceptor separation distance in terms of the electronic coupling matrix element and the damping coefficient.

• Describe the factors affecting ET between and within proteins and the conditions under which the Marcus cross-relation may be used to estimate the rate of protein-protein ET.

• Describe the nature of singlet and triplet states in electronically excited molecules and their role in excited state relaxation by photo-physical and photochemical pathways.

• Develop a kinetic scheme for homogenous photochemical ET, i.e., ET by electronically-excited reactants in solution, that highlights the relevance of excited state lifetime, reaction free energy change, and reaction transmission coefficient.

• Describe exemplary/classic experiments to investigate the Marcus inverted region, the role of the reorganization energy, and the degree of reaction non-adiabaticity.

• Describe the importance of solar photocatalysis and how light-induced ET reactions may be used for water splitting.

• Write a kinetic scheme for light-induced ET reactions and identify and illustrate the key factors that affect the overall efficiency of solar energy conversion and storage.

On completion of Part B, it is expected that the students will have acquired an understanding of key concepts and principles and that they will have the ability to:

• Define the chemical potential for the particles of pure and mixed thermodynamic systems;

• Describe the concept of activity in thermodynamics and how it applies to liquid-liquid and liquid-solid mixtures.

• Explain the concept of an ideal-dilute solution and why electrolytes are non-ideal;

• Define the activity of an ion in an electrolyte and the mean ionic activity of an electrolyte solution;

• Use the Debye-Huckel equation to predict ion activity and understand the limitations of the model;

• Use the Bjerrum-Bronsted equation to explain the kinetics of reaction ions in presence of a non-participating electrolyte;

• Define the terms strong and weak as applied to electrolyte activity and assign solutions to these categories;

• Explain the principles of the Debye-Huckel-Onsager equation in terms of electrophoretic drag and ion-atmosphere relaxation;

• Calculate the activity of strong and weak electrolytes;

• Describe qualitatively the Born model for ion-solvent interactions and its limitations;

• Explain the meaning of dielectric and permittivity as applied to a continuum material;

• Describe the structure of water in the bulk and in proximity to an ion.

• Define the electrochemical potential of a systemin under the influence of an electric field and its relationship to the chemical potential;

• Starting from the electrochemical potential, derive expressions for the the membrane potential, electromotive force and liquid junction potential.

• Explain the origin of the liquid junction potential at a liquid-liquid interface and its implications for electrochemical measurement;

• Describe the modes of mass transport in bulk solution and in proximity to a charged interface;

• Explain how molecules diffuse by a random walk;

• Describe the structure of an electrolyte in proximity to a charged interface;

• Sketch various models for the electrical double layer and a solid-electrolyte interface;

• Define and calculate the Debye length for an electrolyte solution;

• Explain the kinetics of simple electron-transfer processes and an electrode-electrolyte interface using Butler-Volmer theory;

• Explain how electrocatalysis can be used to improve the kinetics of electron-transfer processes.

On completion of Part C, it is expected that the students will have acquired an understanding of key concepts and principles and that they will have the ability to:

• Explain the principles of steady-state voltammetry at a macro-disk and a micro-disk electrode;

• Understand the relationship between current and diffusion coefficient in simple examples of steady-state electro-analysis;

• Describe the relationship between measured current, analyte concentration profile and analyte diffusion for simple chronoamperometric experiments;

• Utilize the Cottrell equation to analyze simple chronoamperometric data;

• Explain the basic concepts of cyclic voltammetry and the relationship between measured current, analyte concentration profile, diffusion coefficient and sweep rate;

• Sketch the expected results for simple mass-transfer controlled cyclic voltammetry experiments, and the relationship between the wave shape and Nernst equation;

• Explain how electron transfer can be coupled to proton transfer and how this manifests in voltammetry data;

• Explain how the EC and EC' mechanisms manifest in cyclic voltammetry for coupled chemical reactions;

• Utilize the Butler-Volmer model to describe electron transfer to and from an electrode and how the model collapses to the Nernst equation at equilibrium and for facile electron transfer rates;

• Describe how cyclic voltammetry data changes for sluggish electron transfer rates and under mixed electron transfer/mass transfer control;

• Describe mechanism of various important inner-sphere electrochemical processes sung as the oxygen reduction reaction (ORR) and hydrogen evolution reaction (HER).

• Explain the principles of electrodeposition and how additives and brighteners are used to improve electrodeposition in practice;

• Explain how electrodes can be modified for sensing applications;

• Describe historical and recent models of the electrochemical double layer (EDL) and the influence of the electrical double layer on mass transport and cyclic voltammetry data;

• Describe the implications of nano-confinement on mass transport as a consequence of overlapping electrical double layers;

• Describe the fundamentals and principle applications of scanning electrochemical microscopy (SECM);

• Explain ion-current rectification and electro-osmosis phenomena in nanopore ion transport.

###### Indicative Module Content:

Section A (Electron Transfer) [3 lectures/week]

Week 1 - Electron Transfer Theory – Introduction

Classification of electron transfer reactions; rate of a homogenous electron transfer reaction; self-exchange ET reactions; Inner-sphere re-organization energy; cross-exchange ET reactions, the Marcus equation and inverted region.

Week 2 – Electron Tunnelling

Quantum mechanical tunnelling; distance-dependence of electron tunnelling (STM); electron tunnelling in ET reactions.

Week 3 - Adiabatic vs Non-adiabatic ET

Degree of adiabaticity – Landau-Zener approach, homogenous non-adiabatic ET reactions, ET between and within proteins, Marcus cross-relation; dependence of electron transfer rate constant on D-A separation distance.

Week 4 - ET by Electronically Excited Reaction

Electronic Transitions & Franck-Condon Principle, excited states, kinetic scheme for an electronically excited ET reaction, excited state lifetime.

Section B (Physical Electrochemistry) [2 lectures, 1 workshop /week]

Week 5 – Ion-Ion Interactions

Open thermodynamic systems, chemical activity, liquid-solid solutions and electrolytes as non-ideal solutions.

Week 6 – Ion-Solvent Interactions

Electrochemical potential and particle flow in an electric field, derivation of equations for electromotive force and the liquid junctions, the continuum model of a solvent and the hydration of ions. Ion-selective electrodes.

Week 7 – Bulk Transport in Electrolytes

Conductivity and mobility, current as the flow of charge, Fick's laws of diffusion, migration and random walk.

Week 8 – The Electrode-Electrolyte Interface

Models for the electrical double layer (EDL), the Debye length, derivation of the Butler-Volmer equation and its relationship to the Nernst equation, Tafel analysis.

Section C (Analytical Electrochemistry) [2 lectures. 1 workshop /week]

Week 9 – Diffusion-Limited Current

Current under mass-transfer control; steady state voltammetry at a micro-disk and a macro-disk electrode, chronoamperometry and derivation of the Cottrell equation.

Week 10 – Voltammetry

Time-dependent (cyclic) voltammetry at a macro-disk and expected results for simple outer-sphere transfer processes. the influence of electron transfer on voltammetry data, proton-coupled electron transfer and the EC and EC' mechanisms.

Week 12 – Electrochemistry for Adsorbed and Immobilized Species

Inner sphere electron transfer, the hydrogen evolution reaction (HER) and oxygen reduction reaction (ORR), electrocatalysis, electrodeposition, modification of electrodes.

Week 12 – Electrochemistry at the Nanoscale

Developments in nano-electrochemistry and electrochemical imaging, scanning electrochemical microscopy, ion transport under nanoconfinement and applications for bio-sensing, nanopores.