MSc by Research Soft Matter and Liquid Crystals Physics

The unit covers three core topics in physical chemistry: (1) statistical thermodynamics; (2) vibrations in molecules and solids; and (3) physical organic chemistry. Each topic is taught in a blended format with three independent-study and four in-person sessions. The majority of the teaching follows the “flipped classroom” approach, with students asked to watch short videos during the independent-study sessions which are then supported with summaries and worked examples in the in-person sessions. 

Pre-requisite units: CHEM10212, CHEM20212 

The unit aims to provide students with a working knowledge of three core topics in physical chemistry: (1) statistical thermodynamics; (2) vibrations in molecules and solids; and (3) physical organic chemistry. 

On successful completion of the course students should be able to:  

Explain the key steps in the derivation of the Boltzmann distribution;

Select and apply the tools of statistical thermodynamics to predict gaseous properties;

Explain the theoretical basis for modelling vibrations in polyatomic molecules and phonons in solids;

Describe the connection between imaginary harmonic modes and the potential-energy surface (PES) of molecules and solids;

Interpret data from statistical thermodynamics and phonon spectra to characterise phase transitions in solids;

Select and apply concepts in transition-state theory and the Eyring equation to predict and explain dynamical and kinetic behaviour in small molecules;

Explain the detailed nature of the relationship between the free energy, equilibrium constant and reactivity in the context of organic chemistry;

Design experiments to measure and rationalise chemical reaction mechanisms;

Apply the principles of physical and physical-organic chemistry explain and rationalise the structure and properties of topical supramolecular materials. 

Statistical thermodynamics (Dr C. Trujillo, 7 sessions) 

• Classical thermodynamics.
• Statistical definition of entropy: microstates.  
• Microscopic and macroscopic properties: ensembles, Boltzmann distribution.  
• Partition function: internal energy, entropy, Helmholtz free energy.
• Ideal gases of atoms: translational partition function.  
• Ideal gases of diatomic molecules: rotational partition function, rotational temperature, symmetry number.
• Vibrational partition function: diatomic and polyatomic molecules, total vibrational partition function, vibrational temperature.  
• Electronic partition function.  
• Statistical mechanics and equilibrium: Gibbs free energy, equilibrium constants. 

Vibrations in molecules and solids (Dr. J. M. Skelton, 7 sessions) 

• Vibrations in polyatomic molecules: Hessian and dynamical matrices, frequencies and eigenvectors.
• Phonons in solids: the Bloch theorem, wavevectors, the phonon dispersion and density of states.
• Energetic and dynamical stability: Helmholtz free energy of solids, imaginary harmonic modes, potential energy surfaces (PES) and stationary points, phase transitions.
• Reaction dynamics: transition state theory and the Eyring equation.

Physical organic chemistry: (Prof. S. J. Webb, 7 sessions) 

• Relationships between free energy changes, equilibrium constants and reactivity.
• Physical concepts in the design of experiments to test or establish reaction mechanisms and the application of physical methods to mechanistic problems.
• Effects of structural variation and change of reaction conditions on organic reactivity.
• Types of supramolecular interactions and their relative strengths.
• Applications of supramolecular chemistry. 

Analytical, problem-solving, numeracy and mathematical skills. 

Students will have access to a significant quantity of problems and worked solutions, provided as part of the workshops, that they can use to check their progress. A summative revision session held at the end of the course provides an opportunity for cohort-level feedback on more challenging topics. Students also have the opportunity for direct feedback from course staff during the in-person sessions and/or office hours. 

P. Atkins and J. de Paula, Atkins’ Physical Chemistry (10th Ed.), OUP, 2014

A. Maczek, Oxford Chemistry Primers 58: Statistical Thermodynamics, OUP, 1998

M. T. Dove, Introduction to Lattice Dynamics, CUP, 1993

J. I. Steinfeld, J. S. Francisco & W. L. Hase, Chemical Kinetics and Dynamics, Pearson, 1998

H. Maskill, The Physical Basis of Organic Chemistry, OUP, 1985 (ISBN: 9780198551997)

E. V. Anslyn and D. A. Dougherty, Modern Physical Organic Chemistry, University Science Books, 2006 (ISBN: 9781891389319)

J. W. Steed and J. L. Atwood, Supramolecular Chemistry, Wiley, 2000 (ISBN: 0471987918)

P. Beer, P. Gale and D. K. Smith, Supramolecular Chemistry, OUP, 1999 (ISBN: 9780198504474)

J. M. Seddon and J. D. Gale, Thermodynamics and Statistical Mechanics, RSC, 2001