Soft matter physics

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

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. Chiral nematics and blue phases. Topology of liquid crystals, 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. Defects in smectic liquid crystals. Dynamics of liquid crystals: Ericksen-Leslie theory. Active liquid crystals. Liquid-crystal colloids.
Polymers. Single chain conformations: Freely jointed chain, radius of gyration, entropic elasticity. Real chains: Excluded-volume and self-avoiding walks. Persistence and Kuhn lengths. Worm-like chain. Deforming ideal and real chains. Expanded coil. Coil-globule transition. Polymer solutions: Thermodynamics of mixing, dilute, semidilute, and concentrated solutions, osmotic pressure. Dynamics: Rouse modes, Zimm model, entangled polymer dynamics. Gels: Branching without gelation, Flory-Stockmayer theory, rubber elasticity, phantom-network elasticity, linear viscoelasticity.
Colloids. Classification, characteristic energies. Brownian motion: Einstein-Stokes relation. Hydrodynamics: Motion of single sphere, Oseen tensor, Stokeslet. Dispersion forces: intermolecular forces and microscopic theory, continuum theory, dielectric response of materials. Electrostatic interaction: Gouy-Chapman model of diffuse layer, screening, Debye-Hückel approximation, force between like-charge plates. Depletion interaction. Aggregation and stabilization of colloids: Derjaguin-Landau-Verwey-Overbeek theory. Equilibrium phase behavior: Phase diagram of hard spheres, disorder-order transition in charged spheres. Rheology.
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 in J. Prost, The Physics of Liquid Crystals, Clarendon Press, Oxford, 1993.

M. Rubinstein in R. H. Colby, Polymer Physics, Oxford University Press, Oxford, 2003.

W. B. Russel, D. A. Saville in W. R. Schowalter, Colloidal Dispersions, Cambridge University Press, Cambridge, 1989.

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
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
Oral examination

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].