PHY3071 
Soft Matter 
202324 

Dr P.G. Petrov 


Delivery Weeks: 
T2:0111 

Level: 
6 (NQF) 

Credits: 
15 NICATS / 7.5 ECTS 

Enrolment: 
33 students (approx) 

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:
 describe the main forces controlling the behaviour of colloidal systems;
 use random walk models to describe Brownian motion, diffusion and conformation of polymer chains;
 solve a variety of diffusion problems using suitable mathematical techniques;
 describe the factors controlling the morphology of soft membranes and their thermal fluctuations;
 obtain the shape of liquid surfaces possessing surface tension;
 use the equations of NavierStokes to model the hydrodynamics of thin liquid films;
 describe the physical principles behind the experimental determination of important properties of soft matter systems;

Discipline Specific Skills and Knowledge:
 apply a variety of mathematical techniques for quantitative description of complex systems;
 apply principles from classical mechanics, electromagnetism and thermal physics to soft matter systems;

Personal and Key Transferable / Employment Skills and Knowledge:
 develop the ability to quantitatively model complex systems of practical importance
such as suspensions, emulsions, membranes, polymers, foams etc.;
 use mathematical techniques to solve problems.
Syllabus Plan

Introduction to Soft Matter

Colloidal systems
 Introduction to colloids
 Electrostatic forces between surfaces in liquids.
 Electric double layer.
 PoissonBoltzmann equation and the distribution of the electrostatic potential. DebyeHÃ¼ckel approximation. Grahame equation.
 Pressure and interaction energy between two charged surfaces in aqueous solutions.
 Stern model of the double layer.
 Limitations of the PoissonBoltzmann theory.
 Van der Waals interactions between surfaces.
 Van der Waals disjoining pressure and energy of interaction.
 Hamaker constant. Lifshitz theory.
 The DLVO theory of the stability of colloidal suspensions.
 The DLVO potential
 Effect of Hamaker constant, surface electrostatic potential and electrolyte concentration. Secondary minimum.
 Experimental measurement of surface forces.
 Beyond DLVO: hydration forces, hydrophobic interaction, steric and fluctuation forces.

Diffusion processes
 Introduction to Brownian motion.
 Random walk model. Diffusion equation.
 Langevin equation. EinsteinSmoluchowski relation.
 Diffusion equation: classical approach.
 Solution to the diffusion equation. Laplace transform.
 Experimental methods for determination of diffusion coefficients.

Polymers in solutions
 Introduction to macromolecules.
 Random walk model and polymer conformation. Endtoend distance and radius of gyration.
 Polymers in solution: frictional coefficient and diffusion.
 Entropic elasticity.
 Single molecule elasticity: experiments.

Soft membranes and free liquid surfaces
 Amphiphilic molecules. Supramolecular selfassembly.
 Mechanical properties of thin membranes.
 Curvature of surfaces. Curvature energy and bending rigidity. Shapes of lipid vesicles and biological membranes.
 Thermal fluctuation spectrum of soft membranes.
 Experimental determination of the bending elastic modulus and the area modulus of soft membranes.
 Surface tension. Laplace equation.
 Equilibrium shapes of free liquid surfaces. Exact and approximate solutions.
 Experimental determination of the surface tension.

Hydrodynamic interactions in thin liquid films
 The NavierStokes equations. The equation of continuity.
 An exact solution: Poiseuille flow.
 Lubrication approximation.
 Hydrodynamics of thin liquid films.
Learning and Teaching
Learning Activities and Teaching Methods
Description 
Study time 
KIS type 
20×1hour lectures 
20 hours

SLT 
2×1hour problems/revision classes 
2 hours

SLT 
5×6hour selfstudy packages 
30 hours

GIS 
4×4hour problem sets 
16 hours

GIS 
Reading, private study and revision 
82 hours

GIS 
Assessment
Weight 
Form 
Size 
When 
ILOS assessed 
Feedback 
0% 
Guided selfstudy 
5×6hour packages 
Fortnightly 
111 
Discussion in class 
0% 
4 × Problems sets 
4 hours per set 
Fortnightly 
111 
Solutions discussed in problems classes. 
100% 
Final Examination 
2 hours 30 minutes 
January 
111 
Mark via MyExeter, collective feedback via ELE and solutions. 
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:
Supplementary texts:

Berg J.C. (2009), An Introduction to Interfaces and Colloids: The Bridge to Nanoscience, World Scientific, ISBN 9789814299824

Doi M. (2015), Soft Matter Physics, Oxford University Press, ISBN 9780199652952

Israelachvili J. (2011), Intermolecular and Surface Forces (3^{rd} edition), Academic Press, ISBN 9780123919274

Jones R.A.L (2002), Soft Condensed Matter, Oxford University Press, ISBN 9780198505891
ELE:
Further Information
Prior Knowledge Requirements
Prerequisite Modules 
Vector Mechanics (PHY1021), Properties of Matter (PHY1024), Electromagnetism I (PHY2021), Thermal Physics (PHY2023) and Mathematics with Physical Applications (PHY2025) 
Corequisite Modules 
none 
Reassessment
Reassessment is not available except when required by referral or deferral.
Original form of assessment 
Form of reassessment 
ILOs reassessed 
Time scale for reassessment 
Whole module 
Written examination (100%) 
111 
August/September assessment period 
Notes: See Physics Assessment Conventions.
KIS Data Summary
Learning activities and teaching methods 
SLT  scheduled learning & teaching activities 
22 hrs 
GIS  guided independent study 
128 hrs 
PLS  placement/study abroad 
0 hrs 
Total 
150 hrs 


Summative assessment 
Coursework 
0% 
Written exams 
100% 
Practical exams 
0% 
Total 
100% 

Miscellaneous
IoP Accreditation Checklist 
 N/A this is an optional module

Availability 
unrestricted 
Distance learning 
NO 
Keywords 
Physics; Colloids; Soft matter; Electrostics; Random walks; Diffusion; Polymers; Liquid Films; Transport. 
Created 
02Mar16 
Revised 
N/A 