Soft matter physics

Physics, Second Cycle
2. year
Course director:
Hours per week – 1. semester:

Enrollment into the program.
Homework assignment should be completed before taking the oral examination.

Content (Syllabus outline)

Introduction. Phenomena and features of soft
condensed matter. Interparticle forces, viscoelastic response, microscopic interpretation of elasticity and viscosity. Generalized susceptibility.
Liquid state. Equilibrium themodynamics,
ideal and excess quantities, grand canonical
formalism. n-particle densities and n-particle
distribution functions. Radial distribution
function. YBG hierarchy. Energy, pressure, and
compressibility equations of state. Distribution function theories, Ornstein-Zernike equation; Yvon, Percus-Yevick, and hypernetted chain approximations. Virial expansion. Hard-sphere equation of state: Percus-Yevick and Carnahan-Starling equations of state. Perturbation theories: van der Waals equation of state. Liquid crystals. Onsager theory. Elastic theory
of nematics: Director, Frank elastic energy,
splay, twist and bend deformations. Surface anchoring: Extrapolation length; twisted cell. Nematic in magnetic field. Line defects: classification, strength, energy, stability.
Tensorial nematic order parameter. Landau-de Gennes theory of nematic-isotropic transition. Smectic elasticity: Order parameter, layer compression and bending.
Polymers. Single polymer chain: Freely jointed chain, radius of gyration, entropic elasticity. Persistence and Kuhn lengths. Worm-like chain. Expanded coil. Coil-globule transition. Polymer solutions: dilute, semidilute, and concentrated solutions, osmotic pressure. Dynamical models: Rouse modes, reptation. Gels: Flory-Stockmayer theory, rubber elasticity.
Colloids. Classification, characteristic
energies. Brownian motion: Einstein-Stokes
relation. van der Waals forces: nonretarded
and retarded interaction; Casimir interaction.
Electrostatic interaction: screening, Poisson-Boltzmann equation, Debye-Hückel approximation, force between like-charge
plates. Depletion interaction. Aggregation and stabilization of colloids: Derjaguin-Landau-
Verwey-Overbeek theory. Phase diagram of
hard spheres.
Amphiphiles. Types of micelles, critical
micelle concentration. Spherical micelles;
cylindrical micelles: distribution of micelle size;
bilayers. Theory of membrane elasticity:
bending and stretching moduli. Vesicles:
reduced volume, area-difference-elasticity theory, vesicle shapes.


R. A. L. Jones, Soft Condensed Matter, Oxford University Press, Oxford, 2002,
T. A. Witten, Structured Fluids, Oxford University Press, Oxford, 2004,
M. Daoud in C. E. Williams (eds.), Soft Matter Physics, Springer, Berlin, 1999,
I. W. Hamley, Introduction to Soft Matter, Wiley, Chichester, 2000,
P. M. Chaikin in T. C. Lubensky, Principles of Condensed Matter Physics, Cambridge University Press, Cambridge, 1995,
J.-P. Hansen in I. R. McDonald, Theory of Simple Liquids, Academic Press, San Diego, 1986,
G. Strobl, The Physics of Polymers, Springer, Berlin, 1997,
P.-G. de Gennes and J. Prost, The Physics of Liquid Crystals, Clarendon Press, Oxford, 1993.

Objectives and competences

To provide a broad overview of soft condensed matter, interpreting the phenomenology and the experimental results theoretically using classical thermodynamics, statistical physics, elasticity and hydrodynamics as well as electromagnetism.

Intended learning outcomes

Knowledge and understanding
Understanding of the physics of liquids, liquid crystals, polymers, colloids, and amphiphile aggregates as the building blocks of soft matter.

Students learn to use several physical theories (above all elasticity, electrostatics and statistical physics) to analyze the structures and phenomena in soft matter physics as well as for the understanding of the behavior and workings of selected materials and devices used in everyday life, such as rubber and liquid-crystal display.

The students become aware of the omnipresence of soft materials and of their role in modern technology. In addition, they become acquainted with several minimal models of rather complex physical structures which help to understand that the origin of complex behavior may well be simple.

Transferable skills
The students better understand the importance of a proper choice of the theoretical framework as well as a suitable time and lengthscale for the description of a given physical phenomenon.

Learning and teaching methods

lectures, tutorials, seminars, homework assignments, consultations


Completed homework assignment (written report, presentation) counts as problem-solving examination
Oral examination
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

red. prof. dr. R. Podgornik:
SVENŠEK, Daniel, GRASON, G. M., PODGORNIK, Rudolf. Tensorial conservation law for nematic polymers. Physical review. E, Statistical, nonlinear, and soft matter physics, ISSN 1539-3755, 2013, vol. 88, iss. 5, str. 052603-1-052603-7, ilustr. [COBISS-SI-ID 2615908],
SVENŠEK, Daniel, PODGORNIK, Rudolf. Confined chiral polymer nematics : ordering and spontaneous condensation. Europhysics letters, ISSN 0295-5075, 2012, vol. 100, no. 6, str. 66005-p1-66005-p6. [COBISS-SI-ID 2523492].
PODGORNIK, Rudolf, HOPKINS, J., PARSEGIAN, Vozken Adrian, MUTHUKUMAR, M. Polymers pushing polymers : polymer mixtures in thermodynamic equilibrium with a pore. Macromolecules, ISSN 0024-9297, 2012, vol. 45, iss. 21, str. 8921-8928. [COBISS-SI-ID 2496868].
SVENŠEK, Daniel, VEBLE, Gregor, PODGORNIK, Rudolf. Confined nematic polymers : order and packing in a nematic drop. Physical review. E, Statistical, nonlinear, and soft matter physics, ISSN 1539-3755, 2010, vol. 82, str. 011708-1-011708-14, doi: 10.1103/PhysRevE.82.011708. [COBISS-SI-ID 2254948].
LIČER, Matjaž, PODGORNIK, Rudolf. Polyelectrolyte-mediated bridging interactions : columar macromolecular phases. Journal of physics, Condensed matter, ISSN 0953-8984, 2010, vol. 22, št. 41, str. 414102-1-414102-9, doi: 10.1088/0953-8984/22/41/414102. [COBISS-SI-ID 2266724].
izr. prof. dr. P. Ziherl:
1. GEORGIOU, Ioannis, ZIHERL, Primož, KAHL, Gerhard. Antinematic local order in dendrimer liquids. Europhysics letters, ISSN 0295-5075, 2014, vol. 106, no. 4, str. 44004-1-44004-6, doi: 10.1209/0295-5075/106/44004. [COBISS-SI-ID 27870247].
2. DOTERA, T., OSHIRO, T, ZIHERL, Primož. Mosaic two-lengthscale quasicrystals. Nature, ISSN 0028-0836, 2014, vol. 506, no. 7487, str. 208-211, doi: 10.1038/nature12938. [COBISS-SI-ID 27499815].
3. ZIHERL, Primož, SVETINA, Saša. Nonaxisymmetric phospholipid vesicles : rackets, boomerangs, and starfish. Europhysics letters, ISSN 0295-5075, 2005, letn. 70, str. 690-696. [COBISS-SI-ID 19493159].
4. ZIHERL, Primož, KAMIEN, Randall D. Maximizing entropy by minimizing area : towards a new principle of self-organization. The journal of physical chemistry. B, Materials, surfaces, interfaces & biophysical, ISSN 1089-5647, 2001, vol. 105, str. 10147-10158. [COBISS-SI-ID 16451111].
5. ZIHERL, Primož, PODGORNIK, Rudolf, ŽUMER, Slobodan. Wetting-driven Casimir force in nematic liquid crystals. Physical review letters, ISSN 0031-9007. [Print ed.], 1999, 82, str. 1189-1192. [COBISS-SI-ID 860516].