Physical Chemistry Iii

Statistical Thermodynamics: the concepts. The need of a statistical description. Derivation of the Boltzmann distribution and partition function. Canonical ensemble, configurations and weights, a second derivation of Boltzmann distribution. Basic properties. Molecular Partition Function. Mechanical variables, internal energy and generalized forces. Simple examples. Entropy, temperature, Helmholtz free energy. Thermodynamic potentials. Gibbs energy and Gibbs-Duhem equation.

Statistical Thermodynamics: Applications. Statistical mechanics of molecules: translational, rotational, vibrational and electronic contributions to the molecular partition function. Mean energies, heat capacities, entropy. Real gases: configurational integral, virial expansion, van der Waals equation. Chemical equilibrium.

Crystalline Solids. Lattices, basis vectors and unit cells. Bravais lattices. Reciprocal lattice, lattice planes, Miller indices. Scanning Tunneling Microscopy, Atomic Force Microscopy, Transmission Electron Microscopy. X-ray diffraction: interference, diffraction, von Laue condition, structure factor. Bonding and packing in solids: metallic, ionic, covalent and molecular solids. 2D and 1D materials. Electronic structure of solids: band theory, group velocity, electron transport. Metals, semiconductors and insulators. Doping in semiconductors, p-n junctions. Optical properties: Drude's and Lorentz models, dielectric permittivity, wave propagation. Excitons and polarons in condensed phases.

Molecules in Motion. Maxwell-Boltzmann distribution, cross-section, collisional frequency, mean free path. Elementary transport coefficients: diffusion coefficient, thermal and electric conductivity. Partial equilibrium. State-to-state rate constants, canonical rate constants. Reaction dynamics: potential energy surfaces, reaction dynamics, minimum energy paths, transition state, energy partitioning. Transition state theory.