
Ulrich Schwarz
Sommer term lecture at the University of Leipzig, Institute of Theoretical Physics
Thu 13.30  15.00 (Linnestrasse room 224) and Fri 9.15  10.45 (Linnestrasse room 218)
Theory of soft and biomatter
This course provides an introduction to the theoretical concepts of soft matter physics. Soft matter is condensed matter which is characterized by an energy scale close to thermal energy and a length scale larger than the atomic length scale. Then a small elastic modulus results and thermal noise is sufficient to induce structural changes. Soft matter includes material systems like colloidal suspensions, fluidfluid interfaces, fluid membranes, polymers and liquid crystals. It also includes biomatter, like vesicles and protein filaments, which is a special focus of this course. We will start with a short review of statistical mechanics and the ideal gas. We then discuss important molecular and colloidal interactions and how they lead to different equations of state and to phase transitions. Next we deal with lowdimensional objects (strings and surfaces), which determine the properties of many soft matter systems, and with their interactions (either with each other or with walls). We introduce the basic concepts from elasticity theory and hydrodynamics, which often are important in soft matter physics, and finally discuss some dynamical issues and applications to biology.The first lecture will be on Thursday, April 10, 1.30 pm. The course is in English. Everybody is welcome, there are no special prerequisites except physics training on the level of Vordiplom, basic results from statistical mechanics, differential geometry, elasticity theory, hydrodynamics and stochastic dynamics will be explained in the course. If desired, there is a possibility for contributions by students.
Some examples of soft matter




Vesicle observed by video microscopy (Rumiana Dimova)  Nanocapsule undergoing mechanical instability in polymer solution (Edwin Donath)  Bicontinuous cubic crystal formed by lipidwater mixtures (Ulrich Schwarz)  Cell adhering to micropatterned substrate (Christopher Chen) 
Contents
 10.4.: Introduction and Overview: definition of soft matter, role of thermal fluctuations, structure of soft and biomatter, relevance to biological systems, examples from recent research
 11.4. + 17.4.: Noninteracting systems: ensembles, entropy and temperature, Einstein solid microcanonical, Boltzmann factor, partition sum, free energy, Einstein solid canonical, chemical potential, grandcanonical ensemble, Langmuir isotherm, ideal gas, equations of state
 24.4. + 25.4.: Interacting systems: real gas, dilute systems, virial expansion, second virial coefficient, hard spheres, Lennard Jones gas, van der Waals equation of state, fluidfluid phase transition, fluidsolid phase transition
 2.5. + 8.5. + 9.5.: Molecular and colloidal interactions: hardcore interactions, van der Waals interaction, Hamaker theory, Derjaguin approximation, electrostatic interactions, PoissonBoltzmann theory, strong coupling limit, DebyeHückel theory, Yukawa potential, ultrasoft potentials, dipolar fluids, hydrophilic/hydrophobic interactions, Gibbs phase rule, amphiphilic systems
 15.5. + 16.5. + 30.5.: Mean field and Landau theories: FeynmanBogoliubov inequality, Ising model, Ising chain, mean field theory, domain walls, Peierls argument, Landau theory, Phi^4theory, kink solution, surface tension
 5.6. + 6.6.: Fluidfluid interfaces: main results from differential geometry, surface tension, Laplace equation, wetting, Young equation, surfaces of constant mean curvature, minimal surfaces, capillary waves, RayleighPlateau instability, foams
 19.6. + 20.6.: Fluid membranes: deformation modes for thin shells, curvature energy for fluid membranes, Monge representation, thermal fluctuations, Helfrich interaction, membrane shapes, vesicles, ADEmodel, vesicle adhesion
 26.6. + 27.6.: Elasticity of soft material: strain and stress tensors, Hookean body, Young modulus and Poisson ratio, contact mechanics, Hertz model, JKR theory, viscoelasticity, plasticity, fracture
 3.7. + 4.7.: Hydrodynamics: Newtonian fluid, shear and bulk viscosities, NavierStokes equation, Reynolds number, Euler and Stokes flow, life at small Reynolds number, shear flow, plane and cylindrical Poiseuille flow, Stokes force, lubrication approximation, viscous adhesion
 10.7. + 11.7.: Dynamics in a fluctuating environment: diffusion versus directed transport, random walks and diffusion, reactiondiffusion systems, stochastic equations, reaction kinetics, dynamic force spectroscopy
 17.7. + 18.7.: Soft matter and cell biology: basic physical scales in cell biology, transport by diffusion and molecular motors, proteins as machines, cells as factories, cell shape, mechanical properties of cells, membrane rafts and fusion
Recommended literature
 PM Chaikin and TC Lubensky, Principles of condensed matter physics, Cambridge University Press, Cambridge 1995
 SA Safran, Statistical thermodynamics of surfaces, interfaces, and membranes, AddisonWesley, Reading 1994
 DF Evans and H Wennerström, The colloidal domain: where physics, chemistry, and biology meet, 2nd edition, Wiley 1998
 R. Lipowsky and E. Sackmann, Eds., Structure and Dynamics of Membranes, Elsevier, Amsterdam 1995
 M Doi and SF Edwards, The theory of polymer dynamics, Clarendon Press, Oxford 1986
 LD Landau and EM Lifschitz, Hydrodynamics (VI) and Elasticity Theory (VII), ButterworthHeinemann, Oxford
 HC Berg, Random walks in biology, expanded edition, Princeton University Press 1993
 J Howard, Mechanics of motor proteins and the cytoskeleton, Sinauer Associates, Sunderland, Massachusetts, 2001
 P Nelson, Biological Physics  Energy, Information, Life, to appear July 2003 with WH Freeman Co.