MPŠ MP&Scaron MP&Scaron MP&Scaron Avtorji

Jožef Stefan
Postgraduate School

Jamova 39
SI-1000 Ljubljana

Phone: +386 1 477 31 00
Fax: +386 1 477 31 10


Course Description

Liquid Crystals


Nanosciences and Nanotechnologies, third-level study programme


prof. dr. Samo Kralj


Student get basic knowledge on liquid crystals (LCs) and also get acquainted with several universal phenomena, that link LCs to other systems in nature (e.g. particle physics, cosmology…).


• Presentation of main liquid crystal (LC) phases.
• Modelling of LC phases: molecular (Maier-Saupe model) and continuum (Frank and Landau-de Gennes model) type approaches.
• Phase transitions: comparison with vapour-liquid-crystal, paramagnetic-ferromagnetic phase transition, and evolution of the Universe after the Big Bang.
• Defects in liquid crystals: i) comparison of forces among defects and forces among electric charges and quarks, ii) coarsening dynamics of defect pattern and the evolution of the Universe after the Big Bang, iii) structure of cores of defects, magnetic monopoles and cosmic strings, iv) comparison between dislocations in smectic phases and superconductors&superfluids.
• Confined liquid crystals: finite size effects, influence of surface interactions and disorder.
• Ferroelectric LCs and applications.
• LCs and life (biological cells, differentiation of cells, transport of information).

Course literature:

1. P.G. de Gennes and J. Prost, The Physics of Liquid Crystals, Clarendon press, Oxford, 1998.
2. M. Kleman, O.D. Lavrentovich, Soft Matter Physics, Springer-Verlag, New York, 2003.
3. P. M. Chaikin, T. C. Lubensky, Principles of Condensed Matter Physics, Cambridge University Press, Cambridge, England, 1995.
4. Articles available at:

Significant publications and references:

S. Kralj, E.G. Virga, Universal fine structure of nematic hedgehogs, J.Phys.A:Math.Gen.34, 829-838 (2001).

S. Kralj and V. Popa-Nita, Random anisotropy nematic model: connection with experimental systems, Eur. Phys. J E 14, 115-125 (2004).

S. Kralj, R. Rosso, and E.G. Virga., Periodic Saddle-Splay Freedericksz Transition in Nematic LiquidCrystals, Eur. Phys. J E 17, 37-44 (2005).

V. Popa-Nita and S. Kralj, Random anisotropy nematic model: nematic--non-nematic mixture, Phys. Rev. E 73, 041705 (2006).

G. Cordoyiannis, S. Kralj, G. Nounesis, Z. Kutnjak, and S. Žumer, Pretransitional effects near the smectic-A–smectic-C* phase transition of hydrophilic and hydrophobic aerosil networks dispersed in ferroelectric liquid crystals, Phys. Rev. E 75, 021702 (2007).


Seminar and oral exam.

Students obligations:

Seminar and oral exam.