# 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

## Moodle Link

## In the programs

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Statistical thermodynamics**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**1 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Statistical thermodynamics**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**1 Hour(s) per week x 14 weeks

## Reference week

Mo | Tu | We | Th | Fr | |

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 |