Context of extraction and recycling of rare earths (lanthanides)

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Table of contents

Remerciements
1 Introduction générale
2 General introduction
3 From interactions of matter to numerical simulations
3.1 Motivation of this thesis
3.1.1 Context of radioactive waste storage
3.1.2 Context of extraction and recycling of rare earths (lanthanides)
3.2 Description of matter and equilibrium models
3.2.1 Description of the interactions of a system
3.2.2 Statistical thermodynamics
3.2.3 Distribution functions
3.3 Simulation methods
3.3.1 Molecular Dynamics
3.3.2 Periodic boundary conditions
3.3.3 Ewald
4 Calculation of free energy diérences
4.1 Reaction coordinate
4.2 Free energy
4.3 Potential of Mean Force
4.3.1 The Potential of Mean Force
4.3.2 The Potential of McMillan and Mayer
4.3.3 Practical calculation of McMillan and Mayer’s potential
4.4 The Problem of Barriers for the Calculation of the Potential of Mean Force
4.5 Umbrella Sampling Method
4.6 WHAM Method
4.7 Analysis of a spring problem, period and stiness constant
4.7.1 Analysis with Newton’s principles
4.7.2 Analysis with Hamiltonian formulation
4.7.3 Stiness constant, umbrella amplitude and period for our simulations
4.8 Calculation of coecients of interest
4.8.1 The association constant
4.8.2 The osmotic coecient of activity of the solvent
5 Study of the Potential of McMillan and Mayer at long distance
5.1 Mathematical problem
5.2 Numerical results
5.2.1 Size of a simulation box
5.2.2 Description of the AMOEBA model
5.2.3 Study of the potential of McMillan and Mayer for Na-Cl in aqueous phase
5.2.4 Macroscopic study for Na-Cl in aqueous phase
5.2.5 Comparison of our expansion with lanthanide salt potentials
5.3 Conclusion
6 Study of the difusion constant in confned conditions
6.1 Introduction
6.2 Method of calculating the difusion constant
6.3 Study in the non-periodic case
6.4 Study in the case with periodic boundary conditions
6.5 Conclusion
7 Conclusion and perspectives
Bibliographie