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Soft Matter

This course offers an introduction to soft condensed matter, or “complex fluids” with emphasis on physical principles that govern their behavior. Soft matter is a subfield of condensed matter comprising a variety of physical states that are easily deformed by thermal stresses or thermal fluctuations. They include liquids, colloids, polymers, foams, gels, granular materials, and a number of biological materials. These materials share an important common feature in that predominant physical behaviors occur at an energy scale comparable with room temperature thermal energy. Concepts, experimental techniques, and open questions will be presented and discussed with students.

Syllabus : " Soft Matter "

- Lectures 30 hours, Tutorials 20 hours (1st Semester) -

(Giuseppe Foffi, Anniina Salonen)

Chapter 1:
Introduction
What is soft matter ?
Forces, energies and timescales

Chapter 2:
Surface energy and interactions
Surface energy and tension
Wetting: Young’s equation and contact angles
Hydrophobicity and hydrophilicity
Capillarity

Chapter 3:
Interactions
Van der Waals interactions: from molecules to colloidal objects
Electrostatic interaction: linear approximation (Debye theory)
Interactions between colloidal particles, DLVO potential
Stability and Aggregation
Other interactions: Entropy-driven interactions, Hydrogen bounding Hydrophobic interactions

Chapter 4:
Statistical Mechanics for Simple and Complex Liquids (Statics)
Review of relevant results in Thermodynamics and Statistical Mechanics
Static structure of a liquid: radial distribution functions and structure factors
Theory of Static Scattering
The hard-sphere model: thermodynamics, structure and melting
Thermodynamic perturbation theory
The role of short range attractions on the phase diagram
An analytical solution: the Baxter Model

Chapter 5:
Elements of complex-fluid dynamics: random walk and the diffusion equation
Brownian Motion of colloidal particles
Langevin Equation
Theory of Dynamic Light Scattering (DLS)
Fokker-Planck and Smoluchowski equations
Hydrodynamics
Navier-Stokes equation and Reynolds number
Linearized Hydrodynamics: Stokes Equation and consequences
Stokes Law and drag, Hydrodynamic interaction between colloidal particles, Viscosity of a hard sphere suspension
Examples: Implications for living systems (Purcel’s “Life at low Reynold Nuber”)
The glass transition in soft matter
The ideal glass transition: Mode Coupling Theory (MCT)
Linear viscoelasticity; Simple phenomenological models; Examples
Implications for living systems

Chapter 6:
Self assembly
Aggregation of amphiphilic molecules; Critical micelle concentration; Shape of micelles
Lipid bilayers, Nature of the cell membrane
Curvature elasticity, Fluctuations of membranes
Self assembly of colloidal systems
Liquid crystals
Examples of self assembly: viruses
Applications in nanotechnology

Chapter 7:
Polymers and biological macromolecules
Examples of polymers
Single-chain statistics, self-avoiding walks
Entropic forces and excluded volume
Wormlike chain and persistence length, DNA
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 in the Rouse model; Rubber elasticity

Chapter 8:
Experimental and computational tools
Optics
Rheology, Microfluidics
Scattering (Static and Dynamics)
Computational tools (MC, MD and Multiscale)

Recommended textbooks:

  • Fluid Dynamics for Physicists, Faber T.E (CUP 1995)
  • Soft Condensed Matter, R. A. L. Jones, (2002) Oxford University Press, Oxford
  • Biological Physics: Energy, Information, Life , P. Nelson (2003) W. H. Freeman
  • Molecular Driving Forces, K.A. Dill ,S. Bromberg , D. Stigter ( 2003) Garland Science
  • Structured Fluids: Polymers, Colloids, Surfactants, T. A. Witten (2004) Oxford
  • Colloid Science: Principles, Methods and Applications, 2nd Edition, Terence Cosgrove Editor (2010) Wiley-Blackwell ISBN: 978-1-4443-2020-6
  • Introduction to Soft Matter (2nd edition), I. Hamley, (2000) J. Wiley, Chichester

Advanced texts:

  • Colloidal Dispersions, W. B. Russel, D. A. Saville, W. R. Schowalter (Cambridge University Press 1992)
  • An introduction to the dynamics of colloids, J. Dhont (Elsevier, 1996)
  • Stochastic Processes in Physics, N. G. Van Kampen (Elsevier, 2011)
  • Thermodynamics of Surfaces, Interfaces and Membranes, S. A. Safran (AddisonWesley 1994)
  • Applied Biophysics, T. A. Waigh (Wiley 2007)
  • Physical Biology of the Cell, R. Phillips et al. (Garland 2009)
  • Molecular Biophysics, M. Daune (OUP 1999)

Course prerequisites and corequisites

Knowledge of thermodynamics and basic statistical mechanics and some familiarity with differential equations, hydrodynamics and phase diagrams.

Course concrete goals

On completion of the course students should be able to:

— define and discuss the basic concepts and physics of soft matter
— apply elementary models to explain phase behavior of soft matter and use universalities between different systems
— analyze the behavior and phenomena in soft matter systems based on energy and entropy arguments
— suggest suitable experimental tools to study a particular problem in soft matter
— pursue graduate studies on materials science , soft matter or physical biology.