Enrollment into the program.

Homework assignment should be completed before taking the oral examination.

# Soft matter physics

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.

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.

Knowledge and understanding

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

Application

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.

Reflection

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.

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)

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. http://pre.aps.org/abstract/PRE/v88/i5/e052603. [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. http://iopscience.iop.org/0295-5075/100/6/66005. [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. http://pubs.acs.org/doi/abs/10.1021/ma3017508. [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].