Modeling for Separation and Containment

The purpose of this modeling course is to introduce modern methods of modeling matter that can be used to study separative chemistry and complex systems. The goal is to present the various scales of description used to describe chemistry, ranging from molecular simulations to thermodynamic models such as those used in chemical engineering. Particular emphasis is placed on statistical thermodynamics, which serves as a bridge between these scales of description.

Hourly volumes*:

CM: 12:00 p.m.

TD: 8 H

The goal is to provide future master’s degree graduates with a solid foundation of knowledge to understand the molecular mechanics involved in separative chemistry and confinement. The primary focus is on studying how these theoretical methods can be applied to optimize and predict processes, as well as to interpret experimental results. To a lesser extent, the goal is also to be able to implement a theoretical modeling approach in these complex systems.

General Chemistry – Thermodynamics – Chemistry of Solutions

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 Equation – Evolution of Non-Isolated Systems – Thermodynamic Potentials F and G and Their Relationship 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 – Connection to entropy S – Review of combinatorics (factorials, arrangements and combinations, Stirling’s formula) – Phase space – Hamiltonian – Application to the harmonic oscillator – Discretization and Heisenberg’s principle – Practical classical and quantum calculations – Application to the monoatomic ideal gas – Sackür–Tétrode relation – Gibbs’ paradox – Quantum calculations – Applications: defects in crystals, hydrogen storage, regular solutions, calorimetry

III Other Thermodynamic Sets

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, atmospheric equilibria, sedimentation, regular solutions, thermodynamic phase separations, liquid-vapor equilibria, 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) – Analysis of simulation results (molecular representations, structure, thermodynamic quantities (T, P, E, H), g(r), S(q), other quantities (S, transport properties))

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

Administrative contact(s):

Master's in Chemistry Office

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