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Motivation:
Have you ever wondered why it is so hard to get ketchup out of its bottle or why you need to whip egg whites to make meringue? Why Cheerios floating on milk seem to attract each other? Why a gel can swell to many times its own size, while a crystal already breaks at a deformation of few percents? How large scale complex structures can assemble out from simple nano-scale units? Or how your LCD display works? Soft matter is the physics of everyday life!
Soft matter systems are characterized by a characteristic energy that is on the order of thermal energy at room temperature. They display unique physics, including fractality, phase transitions, and self-organization, as well as peculiar material properties and dynamics. We will discuss the main theoretical concepts needed to describe soft condensed matter systems like polymers, liquid crystals, membranes, complex fluids and colloids.
Lehrziel
Possible topics: Polymers 1. Basics of single chains: random walk, Gaussian chain, entropic elasticity, solvent effects 2. Many chains: mixtures, semi-dilute systems, polymer melts 3. Dynamics: Rouse model, Zimm model, reptation 4. Polymer networks: rubbers, elastomers, gels Liquid crystals 5. isotropic-nematic phase transition, Frank elastic energy, LCD displays 6. Defects, dynamics Membranes/Surfactants 7. Helfrich energy, shape diagram, membrane fluctuations 8. surfactants, self-assembly Theory of soft systems dynamics 9. basics of non-equilibrium: force-flux relations, examples: hydrodynamics, diffusion 10. Langevin equation, Mori-Zwanzig formalism, Fokker-Planck equation 11. Correlation and response, Fluctuation Dissipation theorem, scattering 12. Liquid-state theory: g(r), Ornstein-Zernike equation, Density functional theory (DFT), Complex fluids 13. continuum mechanics, viscoelasticity 14. suspensions, emulsions Electrostatic effects in Soft Matter 15. Debye Hückel/Poisson-Boltzmann equation; Manning condensation 16. Colloids: effective interactions, stabilization, colloidal effects Computational methods 17. Particle-based: molecular dynamics (MD) vs. Monte Carlo (MC) 18. (Navier-)Stokes: Lattice Boltzmann method, Oseen tensor, boundary integral method
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