COMPLEX SYSTEMS ANALYSIS

The aim of the course is to provide the student with a general overview of Soft Matter systems, within the unifying approach of Statistical Thermodynamics. The students will then be exposed to these topics at a PhD level, with a special emphasis on current on-going work.

This course is divided into two parts. The first part (15 h) dealing with the general topic and the techniques, the second part (15 h) discussing a set of case studies with practical sessions. At the end of the course, students are expected to be able to read the current literature in this area, identify the optimal technique (experimental, theoretical or computational), and tackle a specific problem, knowing the pros and cons of each of them.

Any student with a scientific general background (e.g. Chemistry, Physics, Material Science etc) at the Master level is expected to be able to find this course useful. Some previous knowledge of computer programming could be useful but not necessary.

Part I Statistical Thermodynamics (3 hours)
Review of Thermodynamic potentials and Legendre transformation, Gibbs ensembles (NVE, NVT, NPT, μVT) ; Universality and Scaling,

Part II: Liquid Theory (3 hours)
Virial expansion, Perturbation theory, Mean Field theory; Exact solutions, Phase transitions; Maxwell construction and van der Waals gas; Integral equation theory; Electrostatic theory, Debye Huckel theory; Polar and non-polar solvents.

Part III Colloidal systems (2 hours)
Energy and length scales; Packing problems; Entropically driven transitions, Glasses and gels; Depletion interactions; Patchy particles; Janus fluids;

Part IV Liquid Crystals (2 hours)
Historical perspectives; Liquid crystals phases; Technological applications; Theoretical approaches (Onsager theory, Density Functional Theory)

Part V Non-equilibrium systems (2 hours)
Euler equation for fluids, Viscosity, Navier-Stokes equation, Stokes Law, Brownian motion, Langevin equation, White noise, Diffusion equation, Stokes-Einstein relation, Fokker-Planck equation, Arrhenius law,

Part VI Polymers: Equilibrium properties (2 hours)
Linear polymers; Connection with Diffusion Equation; Phase diagram; Flory Theory; Solvent effects; Polymer solutions; Flory-Huggins for solutions; Experimental probes

Part VII Polymers: Dynamical properties (1 hour)
The Rouse model, Comparison with experiments, The Oseen tensor, The Zimm model

Practical Cases Studies (15 hours)

General part, fluids, colloidal systems
• 530.13KARDM M. Kardar Statistical Physics of Particles (Cambridge Univ. Press 2007)
• 547.7HAMLI Hampley Introduction of Soft Matter (Wiley 2002)
• 541.3FUNIC1 Lyklema, Fundamental of interfaces and colloidal science Vol 1-5 (Academic 1991)
• 530.413.FOFTM Gompper, Schick, Soft Matter Vol 1-3 (Wiley 2006)
• 530.4 HANSJP Hansen, MCDonald Theory of Simple Liquids (Academic 2006)
• 530.42.BARRJ Barrat, Hansen, Basic Concepts for Simple and Complex Liquids (Cambridge 2003)

Numerical and Computational techniques
• 532.01ALLENMP Allen, Tildesley Computer Simulations of Liquids (Clarendon 1987)
• 539.6FREND Frenkel, Smit Molecular Simulations (Academic 2002)

Polymers
• LT547.7.DOIM Doi, Edwards, Theory of Polymer Dynamics (Oxford, 1986)
• 530.41RUBIC Rubinstein, Colby Polymer Physics (Oxford 2003)

Liquid Crystals
• 530.429 GENNPF de Gennes, Prost The Physics of Liquid Crystals (Oxford 1993
• 530.41 CHAIPM Chaikin, Lubensky Principles of Condensed Matter Physics (Cambridge 1995)

Proteins and DNA
• 574.19FINKAV Finkelstein, Ptitsyn Protein Physics (Academic Press 2002)
• 574.1.CANTC Cantor, Schimmel, Biophysical Chemistry (Vol 1,2,3) (Freeman 1980)
• LT574.19.LEHNA.4 Nelson, Cox, I Principi di Biochemica di Lehninger (Zanichelli 2004)

The final exam will be based on a report and a presentation by the students on a specific topic/case study agreed with the instructor

scritto e orale

Traditional interacting methods, on-line teaching, or a combination of the two will be used, depending on students logistic and situations