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We investigate the static correlations of a dipolar fluid in terms of the irreducible coefficients of the spherical harmonic expansion of the static structure factor. To this end, we develop a theoretical framework based on a soft-core version of Wertheim's solution of the mean spherical approximation (MSA), which renders the analytical determination of such coefficients possible. The accuracy of this approximation is tested by a comparison against the results obtained with the assistance of extensive molecular dynamics simulations at different regimes of concentration and temperature. Crucial aspects for the comparison of the results provided by the two methods are carefully discussed, concerning the different reference frames used in theory and simulations to describe rotations and orientations, and leading to important differences in the behavior of correlation functions with the same combination of spherical harmonic indices. We find a remarkable agreement between the two approaches in the fluid regime, thus providing a first stringent comparison of the irreducible coefficients of the spherical harmonic expansion of the dipolar fluid's static structure factor, provided by the MSA theory and molecular dynamics simulations.

A fundamental challenge of the theory of liquids is to understand the similarities and differences in the macroscopic dynamics of both colloidal and atomic liquids, which originate in the (Newtonian or Brownian) nature of the microscopic motion of their constituents. Starting from the recently-discovered long-time dynamic equivalence between a colloidal and an atomic liquid that share the same interparticle pair potential, in this work we develop a self-consistent generalized Langevin equation (SCGLE) theory for the dynamics of equilibrium multicomponent atomic liquids, applicable as an approximate but quantitative theory describing the long-time diffusive dynamical properties of simple equilibrium atomic liquids. When complemented with a Gaussian-like approximation, this theory is also able to provide a reasonable representation of the passage from ballistic to diffusive behavior. We illustrate the applicability of the resulting theory with three particular examples, namely, a monodisperse and a polydisperse monocomponent hard-sphere liquid, and a highly size-asymmetric binary hard-sphere mixture. To assess the quantitative accuracy of our results, we perform event-driven molecular dynamics simulations, which corroborate the general features of the theoretical predictions., Comment: 11 pages, 12 Figures

The mobility of a colloidal particle in a crowded and confined environment may be severely reduced by its interactions with other mobile colloidal particles and the fixed obstacles through which it diffuses. The latter may be modelled as an array of obstacles with random fixed positions. In this contribution, we report on the effects of the size-polydispersity of such fixed obstacles on the immobilization and dynamical arrest of the diffusing colloidal particles. This complex system is modelled as a monodisperse Brownian hard-sphere fluid diffusing through a polydisperse matrix of fixed hard spheres with a given size distribution. In the Lorentz gas limit (absence of interactions between the mobile particles), we first develop a simple excluded-volume theory to describe the localization transition of the tracer mobile particles. To take into account the interactions among the mobile particles, we adapt the multi-component self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics, which also allows us to calculate the dynamical arrest transition line, and in general, all the dynamical properties of the mobile particles (mean-squared displacement, self-diffusion coefficient, etc.). The scenarios described by both approaches in the Lorentz gas limit are qualitatively consistent, but the SCGLE formalism describes the dependence of the dynamics of the adsorbed fluid on the polydispersity of the porous matrix at arbitrary concentrations of the mobile spheres and arbitrary volume fractions of the obstacles. Two mechanisms for dynamical arrest (glass transition and localization) are analyzed and we also discuss the crossover between them using the SCGLEs.