Modeling for separation and containment

This modeling course aims to introduce modern methods of modeling matter that can be used to study separative chemistry and complex environments. The idea is to present the different scales of description used to describe chemistry, from molecular simulations to thermodynamic models such as those used in chemical engineering. Particular interest is shown in statistical thermodynamics, which allows these scales of description to be linked.

Hourly volumes:

CM: 12 H

Tutorial: 8 hours

The aim is to provide future master's graduates with a solid understanding of the molecular mechanics involved in separation chemistry and confinement. First, we will study how these theoretical methods can be used to optimize and predict processes and interpret experimental results. Second, to a lesser extent, we will learn how to implement a theoretical modeling approach in complex systems.

General chemistry – thermodynamics – solution chemistry

Final exam with a possible second session.

Review of thermodynamics and differential calculus

Derivation of functions of several variables – Thermodynamic variables – Fundamental principle of thermodynamics – Justification based on Boltzmann's formula – Evolution of non-isolated systems – Thermodynamic potentials F and G and their link to the entropy of the universe – Thermodynamic functions and equations of state

II The Micro-Canonical Set N V E

The magic trio of thermodynamics: T, P, ì - Link with entropy S - Reminders of combinatorics (factorial, arrangements and combinations, Stirling's relation) - Phase space - Hamiltonian - Application to the harmonic oscillator - Discretization and Heisenberg's uncertainty principle – Classical and quantum practical calculations – Application to ideal monoatomic gas – Sackür-Tétrode relation – Gibbs paradox – Quantum calculations – Applications: defects in crystals, hydrogen storage, regular solutions, calorimetry

III Other thermodynamic systems

Canonical set N V T – Probability distribution – Partition function – Practical calculations in the canonical set – Grand canonical set – Grand potential – Application to ideal gases – Energy equipartition theorem

Applications: heat capacities of solids and gases, equilibrium in the atmosphere, sedimentation, regular solutions, thermodynamic phase separations, liquid/vapor equilibrium, complexation in solution, adsorption on a surface (Langmuir isotherm, BET)

IV Introduction to molecular simulations

Theory – Model – Numerical Experiments – Purpose of atomic simulations – Monte Carlo simulations and equilibrium properties – Classical and ab initio molecular dynamics simulations – Setup (creation of simulation boxes, interaction potentials, periodic boundary conditions) – Trajectory generation (Verlet algorithm – thermostats and barostats) – Use of simulation results (molecular representations, structure, thermodynamic quantities (T, P, E, H), g(r), S(q), other quantities (S, transport properties)

Application: chemistry of f-elements in solution, organic phases, porous media for separative chemistry and confinement (glasses, oxides, geological media)

Administrative contact(s):

Master's Program in Chemistry Secretariat

https://master-chimie.edu.umontpellier.fr/