Physical Chemistry Iii
A.Y. 2023/2024
Learning objectives
Complete the Physico-Chemical background of the students, by providing a systematic and detailed microscopic interpretation of thermodynamics and of the matter at the solid state, as well as a brief account of the kinetic theory of gases and its application to transport phenomena and chemical kinetics.
Expected learning outcomes
Students will master basic thermodynamics and molecular computation of thermodynamic properties. They will have a basic knowledge of the matter at the solid state, its structure and its properties.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
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.
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.
Prerequisites for admission
Basic knowledge of maths and physics, in particular math analysis, linear algebra and mechanics.
Teaching methods
The course consists of theoretical lectures and exercises. Lectures will be given with the help of a presentation software and the slides will be made available to the students. Additional exercises will be provided upon request, aimed at the solution of typical exercises that are typically found at the exam.
Teaching Resources
Textbook: P. W. Atkins, Physical Chemistry, Oxford University Press
Presentation slides can be download from the web, as detailed in the Ariel web page dedicated to the course (http://ariel.unimi.it/).
Presentation slides can be download from the web, as detailed in the Ariel web page dedicated to the course (http://ariel.unimi.it/).
Assessment methods and Criteria
Learning assessment consists in a written axamination comprising 4 open questions on topics addressed during the classes, 8 multiple-choice questions and 2 numerical exercises on statistical thermodynamics problems. The available time (3 h) requires brief answers that are well-focused on the questions posed. Students will be given a complete formulary, that can be easily used only if the student knows the topics addressed by the course.
Educational website(s)
Professor(s)