Ruprecht Karls Universität Heidelberg

IMPRS lecture winter term 2001/02
Wednesday 10.15 am - 11.45 am
Reinhard Lipowsky 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, thus thermal noise is sufficient to induce
configurational 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 protein networks, which
are a special focus of this course. We will start with the basic principles from
thermodynamics and statistical mechanics. We then turn to lower-dimensional
objects (strings and interfaces), which determine the properties of many soft matter
systems, and to their interaction with a physical environment. We introduce the basic
concepts from elasticity theory and hydrodynamics, which often are important
in soft matter physics, and finally discuss stochastic systems. Here a special
focus will be molecular motors, which are responsible for directed transport in biological


1) 17.10.: Introduction and Overview

interdisciplinary research, role of thermal fluctuations and structure, thermodynamics and
statistical mechanics, examples from own research (shape and elasticity of droplets,
vesicles and cells, molecular motors, etc)

2) 24.10.: Classical thermodynamics and the 2nd law

equilibrium, state variables, entropy, heat flow, Sackur-Tetrode equation for ideal gas

31.10. no lecture (Reformationstag)

3) 7.11.: Principles of statistical thermodynamics

ensembles, entropy, Boltzmann factor, partition sum, fluctuation-dissipation theorem,
thermodynamic limit, entropy as disorder

14.11. no lecture (J�lich Soft Matter Days)

4) 21.11.: Models for dilute systems

partition function for ideal gas, equations of state for ideal gas, virial expansion, second
virial coefficient, important pair interaction potentials in colloidal sciences

5) 28.11.: Phase transitions

second virial coefficient for van der Waals fluid, instability of van der Waals equation of
state, Maxwell construction, first and second order phase transitions, critical point,
spinoidal, hysteresis, Gibbs phase rule, phase diagrams for hard spheres and Lennard-
Jones systems

6) 5.12.: Polymers as flexible strings

synthetic and biopolymers, Kuhn length, Gaussian chain, Gaussian propagator, path
integral representation, ring polymer, polymer in box

7) 12.12.: Membranes as flexible surfaces

three deformation modes for thin shells, curvature energy for membranes, role of
topology, Monge representation, thermal fluctuations, steric interaction, membrane shapes

8) 19.12.: Interfaces under tension

surface tension, Laplace equation, surfaces of constant mean curvature, minimal
surfaces, capillary waves, Rayleigh-Plateau instability, foams, wetting morphologies,
Young equation

9) 9.1.: Adsorption, adhesion and wetting phenomena

polymers, membranes and interfaces in contact with walls, entropic interactions,
adsorption and unbinding transitions

10) 16.1.: Elasticity of soft material

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

11) 23.1.: Hydrodynamics

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

12) 30.1.: Brownian motion

diffusion and random walks, Markov processes, Fokker-Planck equation, master
equations, Maxwell's demon

13) 6.2.: Molecular motors

cytoskeleton motors, two-state ratchet models, multiple-state ratchet models

Recommended literature:

HE Callen, Thermodynamics and an introduction to thermostatistics, Wiley, NY

F. Reif, Fundamentals of statistical and thermal physics, McGraw Hill, Boston

D Chandler, Introduction to modern statistical mechanics, Oxford University Press, NY

LE Reichl, A Modern course in statistical physics, Wiley, NY

H. Römer and T. Filk, Statistische Mechanik, VCH, Weinheim

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

H. Risken, The Fokker-Planck equation, Springer, Berlin

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

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