Soutenance de thèse : Lucas Varela Alvarez



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Systèmes coulombiens en une et deux dimensions : résultats exacts


Lucas Varela Alvarez


Soft matter often features charged units which interact through Coulomb forces, the treatment of which is difficult due to their long-range nature. This thesis gives results for three many-body systems where every long-range interaction is included, without approximations. First, we study exact results for a one-dimensional electroneutral salt-free suspension made of two fixed colloids and N neutralizing mobile counterions, with dielectric jumps at the colloids’ position. This includes the partition function, density profile and pressure. We find that for any N counterions system there may be like-charge attraction, unlike when the dielectric is homogeneous in which case N must be even. Secondly, we consider the previous system out of equilibrium within a homogeneous dielectric space, as a model for the dynamics of two electrical double- layers. Using a combination of exact calculations where possible and Brownian dynamics simulations, we compute the relaxation time towards equilibrium (τ). The parity of N leads to distinctly different dynamics: for N even, thermal effects are detrimental to relaxation, increasing τ, while they accelerate relaxation for N odd. In the two 1D systems we show that in the limit N→∞ at fixed colloid’s charge, the mean-field prediction is recovered. Finally, we analyse exactly the short-distance effective potential between two “guest” charges immersed in a two-dimensional two-component charge-asymmetric plasma composed of positively (q1 = +1) and negatively (q2 = −1/2) charged point particles. The result is valid in the collapse-free regime, where the Coulombic coupling (dimensionless inverse temperature) β < 4. At high Coulombic coupling β > 2, this model features like-charge attraction.


Jury :

Julien Barré, Institut Denis Poisson, rapporteur

Alonso Botero, Universidad de Los Andes, examinateur

Alexei Chepelianskii, LPS, examinateur

David Dean, LOMA, rapporteur

Bérengère Dubrulle, SPEC, examinatrice

Yan Levin, Universidade Federal do Rio Grande do Sul, examinateur

Gabriel Téllez, Universidad de Los Andes, directeur de thèse

Emmanuel Trizac, LPTMS, directeur de thèse

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