Statistical thermodynamics
Summary
The course covers two topics: an introduction to interfacial chemistry, and statistical thermodynamics. The second part includes concepts like the Boltzmann distribution law, partition functions, ensembles, calculations of thermodynamic properties, quantum statistics, metals, and applications.
Content
A.Interfacial Chemistry
A. 1. Surfaces and interfaces, thermodynamics of interfaces
Surface tension and thermodynamic surface functions, Young and Laplace equations, vapor pressure at curved interfaces, capillary forces, contact angle, measurement of contact angles
A.2. Thermodynamics of adsorption at interfaces, Colloids/Micelles
Gibbs adsorption equation, surfactants, hydrophobic effect, formation of micelles, monomolecular films (Langmuir-Blodgett)
A.3. Adsorption at solid/gas and solid/liquid interfaces
Langmuir isotherm, Fowler-Guggenheim, BET, adsorption in porous solids, capillary condensation in mesoporous systems
B. Statistical Thermodynamcics
B.1. The Boltzmann distribution law
Derivation, Approximation
B.2. Partition function
The translational, rotational, vibrational and electronic partition functions
B.3. Thermodynamic functions from statistical thermodynamics
U, CV, heat and work, Entropy, Helmholtz¿ and Gibbs¿ free energies, Chemical potential
B.4. Ensembles
The canonical ensemble, the canonical partition function, the equilibrium constant
B.5. Quantum statistics
Bose-Einstein statistics, Fermi-Dirac statistics, the grand canonical partition function
B.6. Applying partition functions and ensembles
Heat capacity of solids, Computational chemical methods
B.7. Applications of statistical thermodynamics
Keywords
Boltzmann distribution
Partition function
Ensembles
Quantum statistics
Learning Prerequisites
Required courses
Quantum Chemistry
Physics II; Thermodynamics
Important concepts to start the course
Laws of thermodynamics
Equations for quantum energy levels of particle-in-a-box, rotation and vibtration.
Learning Outcomes
By the end of the course, the student must be able to:
- Contextualise the connection between quantum mechanics and thermodynamics
- Apply the molecular partition functions
- Derive the vibrational and translational partition function
- Derive and compute thermodynamic functions from partition functions
- Describe the different ensembles
- Apply Fermi-Dirac and Bose-Einstein statistics to solids
Teaching methods
Lectures with hand outs. Exercises.
Assessment methods
Written exam
Supervision
| Office hours | Yes |
| Assistants | Yes |
| Forum | No |
Resources
Virtual desktop infrastructure (VDI)
No
Bibliography
Handouts of Lecture Notes and exercises, Moodle
Reference books:
Interfacial Chemistry:
Textbooks: Interfacial Science: An Introduction; G.T Barnes and I. Gentle, Oxford University Press available at Amazon.de
and/or
H. J. Butt, K. Graf, M. Kappl, Physics and chemistry of interfaces, Weinheim Wiley- VCH, 2013.
Statistical Thermodynamics:
Benjamin Widom, Statistical Mechanics: A Concise Introduction for Chemists, Cambridge University Press - 2002, ISBN-13: 978-0521009669
Donald A. McQuarrie, Statistical Mechanics, University Science Books - 2000, ISBN - 1-891389-15-7.
For introduction and as a reference for classical thermodynamics
Pierre Infelta & Michael Grätzel, Thermodynamique: Principles et Applications. BrownWalker Press - 2006. ISBN - 1-58112-995-5.
Ressources en bibliothèque
- Thermodynamique / Infelta
- Statistical mechanics / Widom
- Physics and chemistry of interfaces / Hans-Jürgen Butt, Karlheinz Graf, Michael Kappl, 4th ed., 2023
- Interfacial Science: An Introduction / G.T Barnes and I. Gentle
- Statistical mechanics / McQuarrie
Moodle Link
Dans les plans d'études
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Statistical thermodynamics
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 1 Heure(s) hebdo x 14 semaines
- Type: obligatoire
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Statistical thermodynamics
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 1 Heure(s) hebdo x 14 semaines
- Type: obligatoire
Semaine de référence
| Lu | Ma | Me | Je | Ve | |
| 8-9 | |||||
| 9-10 | |||||
| 10-11 | |||||
| 11-12 | |||||
| 12-13 | |||||
| 13-14 | |||||
| 14-15 | |||||
| 15-16 | |||||
| 16-17 | |||||
| 17-18 | |||||
| 18-19 | |||||
| 19-20 | |||||
| 20-21 | |||||
| 21-22 |
Légendes:
Cours
Exercice, TP
Projet, autre