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Unit information: Soft and Active Matter in 2018/19

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Unit name Soft and Active Matter
Unit code PHYSM0037
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 2 (weeks 13 - 24)
Unit director Professor. Paddy Royall
Open unit status Not open




School/department School of Physics
Faculty Faculty of Science



1 To understand the relationship between microscopic interactions and the macroscopic behaviour of soft and active materials.

2 To be familiar with common soft materials such as colloids, polymers and proteins, and to understand the similarities and differences with respect to molecular systems.

3 To describe the dynamics of soft materials and synthetic active matter.

4 To understand examples of non-equilibrium behaviour such as nucleation and mechanical response.

The course provides a general introduction to soft and active matter. It emphasises a bottom-up approach, based on the interactions between the constituent particles. In the case of archetypal soft matter, the particles are polymers, colloids and nanoparticles: larger than atoms and yet small enough that thermal motion is important. We introduce the concept that the microscopic, particle-level interactions define the properties of the material. Here, colloidal solids and liquids have vastly different properties, and we see that this phase behaviour of the colloidal system is governed by the interactions between the particles. We explore steric, electrostatic and attractive interactions between colloidal particles. Because the interactions can be controlled, so can the material properties. Thus we can produce tuneable materials, for example a liquid which solidifies under predetermined conditions.

Building on this understanding of colloids, a link is made with atomic and molecular systems, which obey the same laws of statistical mechanics. This will involve a discussion of the relationship between intermolecular forces, and how these relate to soft materials such as hard spheres, hard discs, polymers, charged colloids (and proteins) and colloid-polymer mixtures. We introduce the extended law of corresponding states provides a means by which the phase behaviour soft materials may be designed a priori.

The dynamical behaviour of soft materials is covered. In particular, random walks and diffusion for colloids, and reptation for polymers. The discussion of dynamics leads naturally to active matter. We begin with active Brownian particles as a model example and focus on the phenomenology of these remarkable materials. In particular the surprising phase behaviour of demixing in the absence of attractions is explored.

Active matter is intrinsically non-equilibrium, and we conclude the course with non-equilibrium physics of Soft and Active Matter. Topics include nucleation, self-assembly and mechanical response to external perturbation (e.g. shear).

Intended learning outcomes

On completion of this course, students should be able to

  • construct the free energy of typical soft matter systems
  • map different classes of material onto each other. For example, to determine the effective hard sphere diameter which maps soft particles onto hard spheres
  • use the location of the critical point in the phase diagram to predict material properties through the extended law of corresponding states
  • describe classical nucleation theory
  • describe reptation and rationalise the scaling of the polymer motion that arises
  • compare the dynamics of active and passive Brownian particles.

Teaching details

18 x one hour lectures

3 x 2 hour examples classes.

Assessment Details

Examples classes provide formative assessment.

Summative assessment is by 2 hour written examination.

Reading and References

Hansen and Barrat “Basic Models for Complex Liquids”

Teraoka “Polymer Solutions”

Atkins “Quanta, Matter and Change”