Introductory description

N/A

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The module will be taught in two distinct sections. Here follows an illustrative syllabus for each section of the module.

Part 1: Statistical Mechanics

• The basic concepts of Statistical Mechanics
  o The connection between micro (quantum mechanics) and macro (thermodynamics) [L1]
  o The concept of ensemble and ensemble average [L1]
  o The concept of phase space [L2]
  o The concept of partition function [L2]
  o The NVE ensemble [L2]
  o [Key Skills 1] Liouville theorem and molecular dynamics – the ergodic principle [K1]
• The canonical ensemble
  o The canonical partition function [L3]
  o Thermodynamic quantities from the NVT partition function [L3]
  o Molecular partition functions [L4]
  o Fermi-Dirac, Bose-Einstein, and Boltzmann statistics [L4]
  o [Pen&paper Workshop 1] [PPW1]
• Toward chemical equilibrium: the diatomic ideal gas
  o The equilibrium constant of chemical reactions in terms of molecular partition functions [L5]
  o [Key Skills 2] The electronic partition function [K2]
  o The translational partition function - the thermal De Broglie wavelength [L6]
  o The vibrational partition function - choosing the zero of energy [L7]
  o The rotational partition function [L8]
  o Symmetry considerations and ortho-/para- hydrogen [L9]
  o [Pen&paper Workshop 2] Equilibrium constants of chemical reaction in gas phase: di-/a-ssociation of alkali metal vapours [PPW2]
• The statistical mechanics of liquids
  o The Statistical Mechanics of liquids: hard spheres and Lennard-Jones liquids [L10]
  o The radial distribution function [L11]
  o [Computational Workshop 1] Coordination numbers [CW1]
  o Ions in aqueous solutions [L12]
  o Debye-Hückel theory [L13]
  o [Computational Workshop 2] Molecular simulations [CW2]

Part 2: Electrochemistry

1. Electrolyte Solutions
   Structure of water. Electrolyte solutions. Hydration spheres. Structure making and breaking effects. Thermochemistry of ion solvation. Single ion hydration enthalpies and entropies. Partial molar quantities. Revision of ideal solutions. Activity coefficients and non-ideality. Molarity and ionic strength. Debye-Huckel theory and its application to solubilities and rates of reaction in solution.
2. Electrical Conductivity and Ion Transport in Solution.
   Conductivity and molar conductivity. Experimental measurement. Concentration effect for weak and strong electrolytes. Relaxation and electrophoretic effects. Determination of dissociation constants for a weak acid. Ion mobilites. Kohlrauschs law of independent migration. Influence of ion size on mobility. Stokes Law. Anomalous mobility (H+ and OH- in H2O, Cl- in SbCl3, HSO4- in H2SO4).
3. Electrode Surface and Electrified Interfaces
   Characterisation of electrode structure with the scanning tunnelling microscope (STM). Surface charge, surface potential and the electrical double layer. Practical applications.
4. Electrochemical Cells
   Thermodynamics of electrochemical cells. Relation between EO, G and K. Nernst equation. Sign convention. Experimental measurement of standard electrode potentials. Reference electrodes. Determination of S and H from EO. Worked examples. Fuel Cells, batteries, pH electrodes
5. Biological Electrochemistry
   Membrane transport. Diffusion, convection, migration, osmosis. Transdermal drug delivery. Membrane potentials. Electrical signals in biological systems. New microelectrochemical techniques from measuring membrane transport processes. Brain electrochemistry.
6. Dynamic Electrochemistry
   Experimental arrangement for dynamic electrochemical measurements. Role of mass transport versus electron transport in controlling the current signal. Diffusion-controlled current-voltage processes, Randles Sevcik equation. Dynamic electrochemistry in electroanalysis.

Learning outcomes

By the end of the module, students should be able to:

• Describe how Statistical Mechanics enables to make a connection between Quantum Mechanics (microscopic world) and Thermodynamics (macroscopic world)
• Remember the concepts of ensemble, phase space and partition function.
• Understand the significance of the ergodic principle
• Explain why Statistical Mechanics can be considered as the cornerstone of molecular simulations.
• Elaborate on the conceptual and formal differences between the microcanonical and the canonical ensemble
• Compute the translational, vibrational, rotational and electronic contribution to molecular partition functions.
• Take into account symmetry considerations (due to the bosonic/fermionic nature of subatomic particles) when computing rotational partition functions
• Extract thermodynamic quantities such as entropy and free energy from molecular partition functions
• Calculate equilibrium constants for simple chemical reactions
• Discuss the structural properties of liquids and ionic solutions
• Compute the pair correlation function of a simple liquid from molecular dynamics trajectories
• Understand the molecular origins of the properties of ionic solutions and of Debye-Hückel theory
• Analyse the structure of water around selected cations - as obtained via molecular simulations
• Make a connection between the statistical mechanics of liquids and the foundations of Electrochemistry
• Write computer scripts in Python to e.g. analyse the results of molecular simulations.

Indicative reading list

Part 1: Statistical Mechanics
None of these books is essential, in that the whole of the course content will be covered within the lectures. However, these books will definitely make the students’ life easier, as they all contain a number of solved problems. They also present many of the topics of this module in great detail. Whoever is curious/keen on the topic of molecular simulations should definitely indulge in the Tuckerman (Statistical Mechanics: Theory and Molecular Simulation), while an excellent addition to anyone's library would be the Chandler (Introduction to Modern Statistical Mechanics).

• Statistical Mechanics: Theory and Molecular Simulation - Mark Tuckerman 2010
• Highly Recommended - This excellent book offers a very clear overview of Statistical Mechanics. The key concepts of ensemble, phase space, and partition function are especially well covered. The following chapters will thus be of particular interest: 2. Theoretical Foundations of Classical Statistical Mechanics 3. The Microcanonical Ensemble and Introduction to Molecular Dynamics 4. The Canonical Ensemble. Incidentally, it is arguably one of the best, most useful textbooks ever written for those who are interested in molecular simulations.
• Statistical Mechanics - Donald A. McQuarrie 2000
• Highly Recommended - This classic textbook provides a comprehensive, rigorous introduction to Statistical Mechanics. It is very concise and goes well beyond the course. The following chapters will be of particular relevance: 4. Boltzmann statistics, Fermi-Dirac statistics, and Bose-Einstein statistics 5. Ideal monoatomic gas 6. Ideal diatomic gas 9. Chemical equilibrium 13. Distribution functions in classical monoatomic liquids.
• Introduction to Modern Statistical Mechanics - David Chandler 1987
• Recommended - This is a rather old, amazingly concise book which nonetheless manages to cover most of the essential principles and applications of Statistical Mechanics. It also contains a good number of problems, and on top of everything is quite cheap. A very good addition to anyone's library.
• Statistical Mechanics: A Concise Introduction for Chemists - B Widom 2002
• Recommended - This book contains a number of useful, chemistry-oriented examples. It also covers a good portion of the course (particularly with reference to Chapter 5), but fails to provide a rigorous presentation of the basic principles of Statistical Mechanics. Highly recommended in terms of applications and case studies.
• Statistical Mechanics: An Advanced Course with Problems and Solutions - Ryogo Kubo, H. Ichimura, T. Usui, N. Hashitsume 1988
• Further Reading - Here be dragons!
  Part 2: Electrochemistry
  The Chemistry primer 'Electrode Potentials' by R. G. Compton and G. H. W. Saunders, Oxford University Press 1996, covers most of the material in this course. Atkins ' Physical Chemistry' also provides a good introduction to ions in solution and electrochemical cells.

Research element

e.g. essay, dissertation, individual or group research, research skills activity, etc.

Subject specific skills

Numeracy
Problem solving
Critical thinking
Written communication
Oral communication
Organisation and time management
Independence and initiative
Information literacy and research skills
Digital skills and literacy

Transferable skills

Numeracy
Problem solving
Critical thinking
Written communication
Oral communication
Organisation and time management
Independence and initiative
Information literacy and research skills
Digital skills and literacy