Description

This module will discuss important approaches for describing and understanding the behaviour and interactions in soft matter systems. In particular, topics explored in this module will include electrostatic and other interactions in solutions, random walks, conformation of (bio)polymers, diffusion processes, mechanics of soft membranes and hydrodynamic interactions in liquid films. In addition, it will introduce important experimental methods used to study soft matter systems and will discuss their theoretical bases.

Module Aims

The module will offer insights into the complex and fascinating physics of various systems generally known as soft matter. It aims to develop students' understanding of the physical principles, interactions and processes governing the behaviour of such systems and provide the necessary tools for quantitative description of their behaviour.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

• Module Specific Skills and Knowledge:
  1. describe the main forces controlling the behaviour of colloidal systems;
  2. use random walk models to describe Brownian motion, diffusion and conformation of polymer chains;
  3. solve a variety of diffusion problems using suitable mathematical techniques;
  4. describe the factors controlling the morphology of soft membranes and their thermal fluctuations;
  5. obtain the shape of liquid surfaces possessing surface tension;
  6. use the equations of Navier-Stokes to model the hydrodynamics of thin liquid films;
  7. describe the physical principles behind the experimental determination of important properties of soft matter systems;
• Discipline Specific Skills and Knowledge:
  8. apply a variety of mathematical techniques for quantitative description of complex systems;
  9. apply principles from classical mechanics, electromagnetism and thermal physics to soft matter systems;
• Personal and Key Transferable / Employment Skills and Knowledge:
  10. develop the ability to quantitatively model complex systems of practical importance such as suspensions, emulsions, membranes, polymers, foams etc.;
  11. use mathematical techniques to solve problems.

Syllabus Plan

1. Introduction to Soft Matter
2. Colloidal systems
   1. Introduction to colloids
   2. Electrostatic forces between surfaces in liquids.
      1. Electric double layer.
      2. Poisson-Boltzmann equation and the distribution of the electrostatic potential. Debye-Hückel approximation. Grahame equation.
      3. Pressure and interaction energy between two charged surfaces in aqueous solutions.
      4. Stern model of the double layer.
      5. Limitations of the Poisson-Boltzmann theory.
   3. Van der Waals interactions between surfaces.
      1. Van der Waals disjoining pressure and energy of interaction.
      2. Hamaker constant. Lifshitz theory.
   4. The DLVO theory of the stability of colloidal suspensions.
      1. The DLVO potential
      2. Effect of Hamaker constant, surface electrostatic potential and electrolyte concentration. Secondary minimum.
   5. Experimental measurement of surface forces.
   6. Beyond DLVO: hydration forces, hydrophobic interaction, steric and fluctuation forces.
3. Diffusion processes
   1. Introduction to Brownian motion.
   2. Random walk model. Diffusion equation.
   3. Langevin equation. Einstein-Smoluchowski relation.
   4. Diffusion equation: classical approach.
   5. Solution to the diffusion equation. Laplace transform.
   6. Experimental methods for determination of diffusion coefficients.
4. Polymers in solutions
   1. Introduction to macromolecules.
   2. Random walk model and polymer conformation. End-to-end distance and radius of gyration.
   3. Polymers in solution: frictional coefficient and diffusion.
   4. Entropic elasticity.
   5. Single molecule elasticity: experiments.
5. Soft membranes and free liquid surfaces
   1. Amphiphilic molecules. Supramolecular self-assembly.
   2. Mechanical properties of thin membranes.
   3. Curvature of surfaces. Curvature energy and bending rigidity. Shapes of lipid vesicles and biological membranes.
   4. Thermal fluctuation spectrum of soft membranes.
   5. Experimental determination of the bending elastic modulus and the area modulus of soft membranes.
   6. Surface tension. Laplace equation.
   7. Equilibrium shapes of free liquid surfaces. Exact and approximate solutions.
   8. Experimental determination of the surface tension.
6. Hydrodynamic interactions in thin liquid films
   1. The Navier-Stokes equations. The equation of continuity.
   2. An exact solution: Poiseuille flow.
   3. Lubrication approximation.
   4. Hydrodynamics of thin liquid films.

Learning and Teaching

Learning Activities and Teaching Methods

Assessment

Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

• Not applicable

Supplementary texts:

• Berg J.C. (2009), An Introduction to Interfaces and Colloids: The Bridge to Nanoscience, World Scientific, ISBN 978-9-814-29982-4
• Doi M. (2015), Soft Matter Physics, Oxford University Press, ISBN 978-0-199-65295-2
• Israelachvili J. (2011), Intermolecular and Surface Forces (3^rd edition), Academic Press, ISBN 978-0-123-91927-4
• Jones R.A.L (2002), Soft Condensed Matter, Oxford University Press, ISBN 978-0-198-50589-1

ELE:

• http://newton.ex.ac.uk/redirects/ELE/phy3071

Further Information

Prior Knowledge Requirements

Re-assessment

Re-assessment is not available except when required by referral or deferral.

Notes: See Physics Assessment Conventions.

KIS Data Summary

Miscellaneous