Anisotropic pair correlations in binary and multicomponent hard-sphere mixtures in the vicinity of a hard wall: A combined density functional theory and simulation study

Abstract

The fundamental measure approach to classical density functional theory has been shown to be a powerful tool to predict various thermodynamic properties of hard-sphere systems. We employ this approach to determine not only one-particle densities but also two-particle correlations in binary and six-component mixtures of hard spheres in the vicinity of a hard wall. The broken isotropy enables us to carefully test a large variety of theoretically predicted two-particle features by quantitatively comparing them to the results of Brownian dynamics simulations. Specifically, we determine and compare the one-particle density, the total correlation functions, their contact values, and the force distributions acting on a particle. For this purpose, we follow the compressibility route and theoretically calculate the direct correlation functions by taking functional derivatives. We usually observe an excellent agreement between theory and simulations, except for small deviations in cases where local crystal-like order sets in. Our results set the course for further investigations on the consistency of functionals as well as for structural analysis on, e.g., the primitive model. In addition, we demonstrate that due to the suppression of local crystallization, the predictions of six-component mixtures are better than those in bidisperse or monodisperse systems. Finally, we are confident that our results of the structural modulations induced by the wall lead to a deeper understanding of ordering in anisotropic systems in general, the onset of heterogeneous crystallization, caging effects and glassy dynamics close to a wall, as well as structural properties in systems with confinement.

Dense ionic fluids confined in planar capacitors: in- and out-of-plane structure from classical density functional theory

“…(6). In principle, the total correlations can also be obtained from determining the pair distribution function g (2) νν ( r, r ) around a particle fixed at r, but this so-called test-particle route is problematic in situations where long-ranged particle interactions are present due to the finite boundaries of a numerically treated system (see also the discussion in [45]). We will therefore follow the compressibility route.…”

Anisotropy and memory during cage breaking events close to a wall

“…As we will show later, structural results will be important to understand the anisotropic cage breaking dynamics. For the system that we consider here, we have resolved the anisotropic structures in a previous work [13], where we studied a glass-forming binary hard-sphere mixture close to a wall by applying the White Bear mark II framework of fundamental measure theory [17], a quantitative benchmark DFT for hard spheres [18,19]. We found very good agreement between DFT and Brownian dynamics (BD) computer simulations and could observe cageforming structure.…”

“…We employ τ B = σ 2 1 /(3πD 1 ) as a suitable Brownian time throughout the article, where D 1 is the coefficient of free diffusion of the small spheres. More details about the simulations and an analysis of the hard sphere limit are given in a previous work [13], where we studied the structure of a binary hard-sphere system in the vicinity of a hard wall by simulations and DFT calculations.…”

“…The origin is located at the wall at the projected position of the trapped particle, i.e., the latter is located at the radial coordinate r = x 2 + y 2 = 0. (b) Two-particle pair correlation function as studied in previous work [13] by DFT and BD simulations. Here, we show data from DFT for a total packing fraction φ = 0.56, where a small particle is located at the wall and its neighbors form a cage.…”

Extension of the primitive model by hydration shells and its impact on the reversible heat production during the buildup of the electric double layer

“…This concept is naturally included in the restricted primitive model (RPM), where the electrolyte is modelled by charged hard spheres. The RPM and, in particular, its structural properties are well described in the theoretical framework of classical density functional theory (DFT) [22], because the framework remarkably well handles hard-sphere interactions within fundamental measure theory [23][24][25][26]. In consequence, DFT is able to describe the structure of the first layers of ions in the vicinity of an electrode [27][28][29], a property that recently has been discussed to be key for properties like the heat production during charging [10] and the differential capacitance in EDLs [30].…”