Syllabus
1. Basic definitions, postulates (probability, ensemble). Link to thermodynamics, statistics and quantum mechanics. Canonical ensemble. 2. Micro-canonical and grand-canonical ensemble. Overview of characteristic functions and expressions for p, V, S, E in different ensembles. 3. Monoatomic ideal gas -- non-interacting particles. Fermi-Dirac, Bose-Einsetein and Maxwell-Boltzmann statistics. 4.-5. Diatomic and polyatomic molecules. Zero point energy. Translational, rotational, vibrational, electronic and nuclear contributions to thermodynamic functions. Equilibrium constant. Mixture of ideal gases. 6. Real gas -- interacting particles. Intermolecular potentials. Virial expansion. Virial coefficients from Mayer functions. Virial coefficients for pair potentials. 7. Statistico-mechanical theory of fluids. Quasi-classical approach -- pair correlation function. Van der Waals equation and Kirkwood equation. Perturbation methods. 8. Simulation methods: Molecular Dynamics and Monte Carlo. Distribution functions and thermodynamic functions and methods for their computation. 9. Ideal crystal. Frequency distribution. Enstein and Debye model of a crystal. Heat capacity and temperature limits. One-dimensional case, phonons. 10. Ising model. Phase transitions, fluctuations and long-range correlations. Mean field and renormalization group theories. 11. Thermodynamics at interfaces. Theory of adsorption. Intermolecular interactions at surfaces. Langmiur and BET isotherms. Distribution functions for selected geommetries. 12. Non-equilibrium thermodynamics. Liouville operator, time-dependent ensemble average. Boltzmann equation. Time-correlation functions. Absorption of radiation.
If desired, the advanced topics in the second part of the syllabus can be modified to meet individual needs of the participating students.
Annotation
This course is an optional supplement to the lecture Physical Chemistry IV - Statistical Thermodynamics (MC260P105). Within the course we will go through some more involved derivations which cannot be included in the lecture because of time constraints. We will also solve various problems in order to illustrate the applicability of the theoretical knowledge obtained within the lecture.
In the time of covid-19 restrictions the teaching will be done by means of a videoconference.