Modélisation des fluctuations électriques au voisinage d'une électrode pour sonder les propriétés des électrolytes aux interfaces

Electric fluctuations measured at electrodes in nanoelectrochemical devices are directly linked to the microscopic dynamics of the surrounding electrolyte. These fluctuations fundamentally arise from the polarization of electrode surfaces in response to external charges, resulting in induced charge densities at the electrode-electrolyte interface. The relationship between the electrode's response and the external charge distribution suggests that the induced charge encodes valuable information about both the static and dynamic properties of the electrolyte. The behavior of the electrode-electrolyte interface emerges from the interplay between the metal's electronic response to ions and solvent molecules and the subsequent reorganization of these species driven by the induced charge distribution at the metal surface. Classical molecular dynamics (MD) simulations have provided important insights into these interfaces and the role of electrolyte-induced charge within the metal, especially through constant potential simulation methods. However they do not fully capture the metallic character of the electrode, which can be incorporated using the Thomas-Fermi model by introducing a characteristic length l_TF. The influence of metallic character on induced charge properties remains underexplored. In this thesis, we investigate how the electronic screening within a solid, characterized by the Thomas-Fermi screening length (l_TF), affects the charge induced in a metal by an ion. We first study the charge induced in a Thomas-Fermi metal by an ion in vacuum using constant-potential molecular simulations and compare these results with continuum electrostatics predictions, incorporating new analytical expressions that account for periodic boundary conditions. By varying the Thomas-Fermi screening length and the ion distance (d) from the metal surface, we find that continuum models capture most of the features observed in the atomic description, except for oscillations due to the atomic lattice structure when both d and l_TF exceed interatomic distances. We then examine the effect of metallicity on the induced charge by ions in polar solvents, using both explicit MD simulations and implicit Molecular Density Functional Theory (MDFT). MDFT accurately reproduces fine details of the interfacial solvent structure around the ion while significantly reducing computational cost. By tuning the Thomas-Fermi screening length, ion nature, and solvent properties, we explore the interplay between electronic screening inside the metal and solvent response, analyzing their combined effects on induced charge, solvent structure, and interfacial thermodynamics. Finally, we compute the potential of mean force as a function of ion distance from the electrode using MDFT, showing promising agreement with existing MD results. These findings demonstrate MDFT's promise for efficiently modeling electrochemical interfaces at the molecular level and provide a foundation for predicting Marcus free energy curves relevant to electron transfer reactions at the interface.