
IMPRS lecture winter term 2002/03
Wednesday 10.30 am  12.00 am and Thursday 2.00  3.30 pm
Theory division seminar room
Jan Kierfeld and Ulrich Schwarz
Theory of soft and biomatter
This course provides an introduction to the theoretical concepts used in soft matter physics. Here soft matter means condensed matter which is characterized by an energy scale close to thermal energy and a length scale larger than atomic length scales. Then a small elastic modulus results and thermal noise is sufficient to induce structural changes. This is true for all kinds of noncovalent interactions and includes material systems like colloids, polymers, fluid membranes and liquid crystals. It also includes biomatter, like vesicles and networks of protein filaments, which is a special focus of this course. We will start with the basic principles from thermodynamics and statistical mechanics and first apply them to diluted systems. We then discuss important molecular interactions and how they lead to phase transitions, in particular for colloidal systems. Next we deal with lowdimensional objects (strings and surfaces), which determine the properties of many soft matter systems, and to their interaction with the physical environment (eg 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.Contents (dates refer to Wednesdaylecture, Thursdaylecture is one day later):
1) JK + US, 16.10.: Introduction and Overview
interdisciplinary research, definition of soft matter, role of thermal fluctuations and structure for soft and biomatter, examples from own research2) JK, 23.10.: Thermodynamics and statistical mechanics
equilibrium, state variables, energy and entropy, the laws of thermodynamics, ensembles, Boltzmann factor, partition sum, fluctuationdissipation theorem, thermodynamic limit, entropy as disorder3) US, 30.10.: Models for dilute systems
partition function for ideal gas, equations of state for ideal gas, application of ideal gas law to biology, virial expansion, second virial coefficient4) JK, 6.11.: Phase transitions I
van der Waals fluid, LennardJones systems, hard spheres, first and second order phase transitions5) JK, 13.11.: Phase transitions II
Ising model, mean field theory, critical phenomena, renormalization group, GinzburgLandau theory, liquid crystals, amphiphilic systems, Gibbs phase rule6) US, 20.11.: Molecular and colloidal interactions
Van der Waals interaction, electrostatic interaction, PoissonBoltzmann theory, strong coupling limit, DebyeHückel theory, DLVO theory, depletion interaction, hydrophilic and hydrophobic interactions, hydrophobic effect7) US, 27.11.: Interfaces
surface tension from GinzburgLandau model, introduction to differential geometry, surfaces of constant mean curvature, minimal surfaces, capillary waves, RayleighPlateau instability8) US, 4.12.: Membranes
three deformation modes for thin shells, curvature energy for membranes, role of topology, Monge representation, thermal fluctuations, Helfrich interaction, vesicles, membrane shapes9) JK, 11.12.: Polymers I
synthetic and biopolymers, ideal chain, freely jointed and freely rotating chains, self avoiding chain, FloryHuggins theory for interacting chains10) JK, 18.12.: Adsorption and wetting
physiosorption and chemisorption, Langmuir and BET isotherms, polymer adsorption, Young and Laplace equations, wetting transitions11) US, 8.1.: Elasticity of soft material
strain and stress tensors, Hooke's law, Young modulus and Poisson ratio, contact mechanics, Hertz model, JKRtheory, viscoelasticity and plasticity12) US, 15.1.: Hydrodynamics
viscosity, Newtonian fluids, NavierStokes equation, Euler and Stokes flow, shear and Poiseuille flow, Stokes drag, life at low Reynoldsnumber13) JK, 22.1.: Dynamics in a fluctuating environment
diffusion versus directed transport, random walks, Langevin equation, fluctuationdissipation theorem, FokkerPlanck and Smoluchowski equations14) JK, 29.1.: Polymers II
semiflexible polymers, polyelectrolytes, polymer gels15) US, 5.2.: Soft matter in cell biology
basic physical scales in cell biology, molecular transport (diffusion, directed transport by molecular motors, reaction kinetics), proteins as machines, membrane rafts and fusion, mechanical properties of cellsRecommended literature:
P. Atkins, Physical chemistry, 7th ed., Oxford University Press, 2002HE Callen, Thermodynamics and an introduction to thermostatistics, Wiley, NY
D Chandler, Introduction to modern statistical mechanics, Oxford University Press, NY
PM Chaikin and TC Lubensky, Principles of condensed matter physics, Cambridge University Press, Cambridge
SA Safran, Statistical thermodynamics of surfaces, interfaces, and membranes, AddisonWesley, Reading
DF Evans and H Wennerström, The colloidal domain: where physics, chemistry, and biology meet, 2nd edition, Wiley 1998
C. Holm et al., Eds., Electrostatic effects in soft matter and biophysics, Les Houches Summer School 2000, Kluwer 2001
R. Lipowsky and E. Sackmann, Eds., Structure and Dynamics of Membranes, Elsevier, Amsterdam
PG de Gennes, Scaling concepts in polymer physics, Cornell University Press, Cornell
M Doi and SF Edwards, The theory of polymer dynamics, Clarendon Press, Oxford
Last modified Wed Jan 8 15:28:56 CET 2003.