Ruprecht Karls Universität Heidelberg

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 non-covalent 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 low-dimensional 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 Wednesday-lecture, Thursday-lecture 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 research

2) JK, 23.10.: Thermodynamics and statistical mechanics

equilibrium, state variables, energy and entropy, the laws of thermodynamics, ensembles, Boltzmann factor, partition sum, fluctuation-dissipation theorem, thermodynamic limit, entropy as disorder

3) 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 coefficient

4) JK, 6.11.: Phase transitions I

van der Waals fluid, Lennard-Jones systems, hard spheres, first and second order phase transitions

5) JK, 13.11.: Phase transitions II

Ising model, mean field theory, critical phenomena, renormalization group, Ginzburg-Landau theory, liquid crystals, amphiphilic systems, Gibbs phase rule

6) US, 20.11.: Molecular and colloidal interactions

Van der Waals interaction, electrostatic interaction, Poisson-Boltzmann theory, strong coupling limit, Debye-Hückel theory, DLVO theory, depletion interaction, hydrophilic and hydrophobic interactions, hydrophobic effect

7) US, 27.11.: Interfaces

surface tension from Ginzburg-Landau model, introduction to differential geometry, surfaces of constant mean curvature, minimal surfaces, capillary waves, Rayleigh-Plateau instability

8) 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 shapes

9) JK, 11.12.: Polymers I

synthetic and biopolymers, ideal chain, freely jointed and freely rotating chains, self- avoiding chain, Flory-Huggins theory for interacting chains

10) JK, 18.12.: Adsorption and wetting

physiosorption and chemisorption, Langmuir and BET isotherms, polymer adsorption, Young and Laplace equations, wetting transitions

11) US, 8.1.: Elasticity of soft material

strain and stress tensors, Hooke's law, Young modulus and Poisson ratio, contact mechanics, Hertz model, JKR-theory, viscoelasticity and plasticity

12) US, 15.1.: Hydrodynamics

viscosity, Newtonian fluids, Navier-Stokes equation, Euler and Stokes flow, shear and Poiseuille flow, Stokes drag, life at low Reynolds-number

13) JK, 22.1.: Dynamics in a fluctuating environment

diffusion versus directed transport, random walks, Langevin equation, fluctuation-dissipation theorem, Fokker-Planck and Smoluchowski equations

14) JK, 29.1.: Polymers II

semiflexible polymers, polyelectrolytes, polymer gels

15) 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 cells

Recommended literature:

P. Atkins, Physical chemistry, 7th ed., Oxford University Press, 2002

HE 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, Addison-Wesley, 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.

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