Ó Andrzej BUDKOWSKI (IF UJ)

http://www.if.uj.edu.pl/pl/ZINM/polyfilms/

22 h long coure on ‘Introduction to condensed matter physics I (crystals and soft matter)’.

Contents:

1. CHEMICAL BONDS IN CONDENSED MATTER. Classification. Weak (van der Waals, hydrogen) and strong (covalent, ionic, metallic; role of electronegativity) chemical bonds. Detailed description of ionic, covalent and van der Waals bonds (cohesive energy). One-electron (molecular oribital) and two-electron (origin of magnetic exchange interaction) description of covalent bond. Hybridization of atomic orbitals, directional bonds and 1-, 2-, 3-dimensional atomic structures. Fullerenes and nanotubes.

2. CRYSTAL STRUCTURE. Direct lattice (unit cell, Miller indices, symmetry operators) and reciprocal lattice (interplanar distance). Lattice symmetry (allowed rotations, 7 crystal systems, 32 point groups, 14 Bravais lattices, impact on crystal morphology). Crystal structures (hcp, fcc, bcc, binary) and their direct imaging (scanning probe microscopy STM and AFM, electron microscopy). International tables for crystallography. Aperiodic crystals and new definition of crystal.

3. DIFFRACTION FROM CRYSTAL (kinematic theory). Diffraction conditions (by Laue, Ewald, Bragg, Brillouin zone boundaries). Scattering amplitude and atomic distribution in unit cell. Diffraction methods for monocrystals (Laue, rotating crystal, 4-circle diffractometer) and for polycrystalline solids (Debye-Scherrer camera, powder diffractomer, angle and energy dispersion). Electron diffraction (shape effect). Neutron diffraction [(in)coherent (in)elastic scattering, nuclear and magnetic structure factors].

4. ATOM DYNAMICS IN (1-dimensional monatomic and diatomic) CRYSTAL LATTICE [approximations: adiabatic, harmonic and classical-mechanics; degrees of freedom, normal modes of vibration]. Acoustic and optic branches of dispersion relation. Density-of-states in momentum space and in energy. Energy of lattice vibrations (classical vs. quantum description). Phonons as quantized energy of lattice vibrations (Bose-Einstein statistics). Inelastic neutron scattering of phonons.

5. THERMAL PROPERTIES OF CRYSTAL LATTICE. Classical (Dulong-Petit law) and quantum models of specific heat: (lattice dynamics,) Einstein (optical lattice vibrations), Debye (acoustic lattice vibration) models. Adiabatic and differential scanning (DSC) calorimetry.

6. CRYSTALS VS. SOFT MATTER. PHASE DIAGRAMS AND PHASE TRANSITIONS. Ordering and phase diagram (examples) of (a)periodic crystals and crystals with electrons (magnetism, electric polarization, superconductivity). Ordering and phase diagram (examples) of soft matter: thermotropic and lyotropic liquid crystals, colloidal and polymer systems. Characteristic features of soft matter (meso-scopic scales, thermal fluctuations/ Brown motion, self-organization). Ehrenfest classification of phase transitions. Order parameter. Landau theory. Critical exponents (scaling hypothesis, scaling laws).

7. LIQUID CRYSTALS (LC). Calamitic and discotic mesogens. Orientational and limited-positional order. LC phases (nematic, chiral, smectic). (Nematic and smectic) Order parameters. LC order theories (Maier-Saupe, Landau-de Gennes). Phase transitions (I-N, I-N-A). LC phase identification (texture, diffraction patterns). Freédericksz transition and LC displays.

8. SUPRAMOLECULAR SELF-ORGANISATION. Role of non-covalent interactions and Brown motion. Self-organisation of amphiphilic molecules in solvents (surfactant layers, meso-structures, lyotropic LC). Self-organisation of colloid systems (micro-emulsion and 3-component ordered structures, zols and colloid crystals). Macro-phase (homopolymer blends) and micro-phase (copolymers) self-organisation of polymer systems.