260129 VO Soft matter physics (2015S)

Introduction. Phenomena and features of soft matter. Interparticle forces, Viscoelastic response, microscopic interpretation of elasticity and viscosity. Generalized susceptibility. (lecture)

Liquid state I. 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. (lecture)

Thermodynamic inconsistency. Third virial coefficient for hard spheres. (tutorial)

Liquid state II. Distribution function theories, Ornstein-Zernike equation; Yvon, Percus- Yevick, and hyernetted chain approximations. Virial expansion. Hard-sphere equation of state: Percus-Yevick and Carnahan-Starling equations of state. Petrurbation theories: van der Waals equation of state. (lecture)

Phase diagram of binary liquid mixtures. Tonks gas. (tutorial)

Liquid crystals I. Onsager theory. Elastic theory of nematics: Director, Frank elastic energy, splay, twist and bend deformations. (lecture)

Frank free energy. Hybrid nematic cell. (tutorial)

Liquid crystals II. Surface anchoring: Extrapolation length; twisted cell. Nematic in magnetic field. Line defects: classification, strength, energy, stability. (lecture)

Frederiks transition. Maier-Saupe theory. (tutorial)

Liquid crystals III. Tensorial nematic order parameter. Landau-de Gennes theory of nematic-isotropic transition. Smectic elasticity: Order parameter, layer compression and bending. (lecture)

Landau-de Gennes theory. Undulation instability in smectics. Analogy between smectics and superconductors. (tutorial)

Polymers I. Single polymer chain: Freely jointed chain, radius of gryation, entropic elasticity. Persistence and Kuhn lengths. Expanded coil. Coil-globule transition.

Worm-like chain. Confined polymer chain. (tutorial)

Polymers II. Polymer solutions: dilute and semidilute solutions, osmotic pressure. Dynamical models: Rouse modes, reptation. (lecture)

Self-consistent field theory for polymers. Polyelectrolytes. Rotational isomeric state model. (tutorial)

Polymers III. Gels: Flory-Stockmayer theory. Rubber elasticity. (lecture)

Mean-field self-consistent-field-theory treatment of a polymer brush. Renormalization- group analysis of percolation. Complex amphiphile/diblock copolymer morphologies. (tutorial)

Colloids I. Classification, characteristic energies. Brownian motion: Einstein-Stokes relation. van der Waals forces: nonretarded and retarded interaction; Casimir interaction. (lecture)

Depletion interaction between spheres. Derjaguin approximation. (tutorial)

Colloids II. Electrostatic interaction: screening, Poisson-Boltzmann equation, Debye-Hueckel approximation, force between like-charge plates. Depletion interaction. Derjaguin-Landau-Verwey-Overbeek theory. Aggregation and stabilization of colloids. (lecture)

Van der Waals forces. (tutorial)

Colloids III. Phase diagram of hard spheres. (lecture)

Amphiphiles I. Types of micelles, critical micelle concentration. Spherical micelles; cylindrical micelles: distribution of micelle size; bilayers. (lecture)

Relative stability of disk- and sphere-like membranes. Energy of model neck in a lipid membrane. (tutorial)

Amphiphiles II. Theory of membrane elasticity: bending and stretching moduli. (lecture)

Minimal surfaces in soft matter. Persistence length of membranes. (tutorial)

Amphiphiles III. Vesicles: reduced volume, ADE theory, vesicle shapes. (lecture)

Limiting shapes of lipid vesicles. (tutorial)

Granular matter. (lecture)