##### Prerequisites

This course naturally follows from the Part II Statistical Mechanics, and uses lots of concepts from IB Electromagnetism and IB Dynamics. Everyone attending this course would have done these courses, so should have no trouble following the new material.

##### Learning Outcomes and Assessment

This course is somewhat unusual (although there will be many more in this style later on). Its material is quite multidisciplinary and gathers many qualitative ideas from a large variety of classical physics subjects; to use a fashion word: a lot of "fusion" is taking place. At the same time (the other side of the same coin), it is often impossible to be mathematically rigorous in describing such a multi-parameter physical system, and large parts of this subject rely on qualitative estimates and what some may feel like "leaps of logic". In reality, Soft Matter is a mature subject and all such "leaps" can be (and most have been) well-justified - but that requires perhaps a higher level of theory than we shall reach this time.

As a result, the main outcome (or the measure of success in this course) is the ability to bring together several ideas (from dynamics, electromagnetism, statistical physics) to qualitatively capture the physical behaviour of a complex system driven simultaneously by mechanical, electromagnetic and entropic forces. Make an order of magnitude estimates predicting such a behaviour. Isolate the main factors and discard the less relevant influences that affect such a system.

##### Synopsis

**Introduction: **What is soft matter? Forces, energies and timescales.

**Elements of fluid dynamics:** Navier-Stokes equation; Reynolds number; Laminar and boundary layer flows; Stokes Law and drag; Viscosity of a hard sphere suspension; Hydrodynamic interaction between colloidal particles; Implications for living systems; How bacteria swim.

**Viscoelasticity and Brownian motion: **Non-Newtonian behaviour; Idea of complex viscosity; Linear viscoelasticity; Simple phenomenological models pf viscoelastic response. Stochastic force and Langevin equation; Free Brownian motion; Brownian motion in external potentials; Diffusion equation; Fokker-Planck and Smoluchowski equations; Kramers problem - escape over a potential barrier.

**Surface energy and interactions**: Surface energy and tension; Cahn-Hilliard model of a liquid interface; Wetting: Young’s equation and contact angles; Hydrophobicity and hydrophilicity; Electrolyte solutions: Debye-Huckel theory; Interactions between colloidal particles, DLVO potential.

**Self assembly:** Chemical potential of systems that aggregate; Aggregation equilibria; Aggregation of amphiphilic molecules; Critical micelle concentration; Shape of micelles; Lipid bilayers; Nature of the cell membrane; Curvature elasticity; Fluctuations of membranes; Examples of self assembly: viruses and nanotechnology.

**Polymers and biological macromolecules**: Examples of polymers; Single-chain statistics, self-avoiding walks; Gaussian correlations in the chain; Entropic forces and excluded volume; Wormlike (semiflexible) chain and persistence length, DNA; Single chain in good and poor solvents: coil-globule transition and protein folding; Phase transitions: Flory Huggins free energy for solutions; Good, {theta} and poor solvent conditions; Osmotic pressure in dilute conditions; Scaling in semi-dilute solutions; Chain dynamics: Rouse model; Rubber elasticity.

**KEY BOOKS (this is what students feel helps them the most in this course)**

*Soft Matter Physics*, Doi M. (OUP 2013)

*Soft Condensed Matter*, Jones R.A.L. (OUP 2002)

**USEFUL BOOKS (for several specific sections of this course)**

*Fluid Dynamics for Physicists*, Faber T.E (CUP 1995)

*Biological Physics*, Nelson P. (Freeman 2003)

*Molecular Driving Forces*, Dill K.A. and Bromberg S., (Garland 2003)

**MORE TEXTS THAT SOME PEOPLE FIND SOMETIMES USEFUL**

*Statistical Thermodynamics of Surfaces, Interfaces and Membranes*, Safran S.A. (Addison Wesley 1994)

*Applied Biophysics*, Waigh, T.A. (Wiley 2007)

*Physical Biology of the Cell*, Phillips, R. Et al, (Garland 2009)

*Molecular Biophysics*, Daune M. (OUP 1999)