Propriedades difusivas de sistemas clássicos confinados

Abstract

In this thesis, we studied diffusive properties of a classical system of charged particles in narrow quasi-one-dimensional (Q1D) channels. In Chapter 2, we present a revision of diffusion equation and Brownian motion. We showed that Einstein’s and Langevin’s approaches to the Brownian motion problem are equivalent in the limit of very long time scales. We calculated analitically the mean-square displacement (MSD) of a purely 1D system of N non–interacting particles by solving the diffusion equation. In Chapter 3, we introduced the method of Molecular Dynamics (MD) simulations, which has been widely used in computational simulations for N-particles interacting systems. We present two numerical integration schemes for the integration of the equations of motion: the Verlet and the leapfrog algorithms. We briefly show the method of Langevin Molecular Dynamics (LMD) simulations, which includes a term of stochastic fluctuations (stochastic forces) due to the collisions of the molecules of the medium with the Brownian particles. We also present the Brownian Dynamics (BD) approximation. In Chapter 4, we studied diffusive properties of a monodisperse system of interacting particles confined to a Q1D channel using MD simulations. We calculate numerically the MSD and investigate the influence of the width of the channel (or the strength of the confinement potential) on diffusion in finite-size channels of different shape (i.e., straight and circular). The transition from single-file diffusion (SFD) to the two-dimensional diffusion regime is investigated. We discussed the validity of our numerical results compared to analytical results found in literature. Finally, in Chapter 5, we presented a compilation of the obtained results, and we discussed perspectives and suggestions for future works