Structural properties of additive binary hard-sphere mixtures

S. Pieprzyk, A. C. Brańka, S. B. Yuste, A. Santos, and M. López de Haro

Phys. Rev. E 101, 012117 – Published 13 January 2020

Abstract

An approach to obtain the structural properties of additive binary hard-sphere mixtures is presented. Such an approach, which is a nontrivial generalization of the one recently used for monocomponent hard-sphere fluids [S. Pieprzyk, A. C. Brańka, and D. M. Heyes, Phys. Rev. E 95, 062104 (2017)], combines accurate molecular-dynamics simulation data, the pole structure representation of the total correlation functions, and the Ornstein-Zernike equation. A comparison of the direct correlation functions obtained with the present scheme with those derived from theoretical results stemming from the Percus-Yevick (PY) closure and the so-called rational-function approximation (RFA) is performed. The density dependence of the leading poles of the Fourier transforms of the total correlation functions and the decay of the pair correlation functions of the mixtures are also addressed and compared to the predictions of the two theoretical approximations. A very good overall agreement between the results of the present scheme and those of the RFA is found, thus suggesting that the latter (which is an improvement over the PY approximation) can safely be used to predict reasonably well the long-range behavior, including the structural crossover, of the correlation functions of additive binary hard-sphere mixtures.

Received 4 November 2019

DOI:https://doi.org/10.1103/PhysRevE.101.012117

Physics Subject Headings (PhySH)

Liquids

Molecular dynamics

Statistical Physics & Thermodynamics

Authors & Affiliations

S. Pieprzyk ^* and A. C. Brańka ^†

Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland

S. B. Yuste ^‡ and A. Santos ^§

Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, Badajoz E-06006, Spain

M. López de Haro ^∥

Instituto de Energías Renovables, Universidad Nacional Autónoma de México (U.N.A.M.), Temixco, Morelos 62580, Mexico

^*pieprzyk@ifmpan.poznan.pl
^†branka@ifmpan.poznan.pl
^‡santos@unex.es
^§andres@unex.es
^∥malopez@unam.mx

Structural properties of additive binary hard-sphere mixtures. II. Asymptotic behavior and structural crossovers

Sławomir Pieprzyk, Santos B. Yuste, Andrés Santos, Mariano López de Haro, and Arkadiusz C. Brańka

Phys. Rev. E 104, 024128 (2021)

Structural properties of additive binary hard-sphere mixtures. III. Direct correlation functions

Sławomir Pieprzyk, Santos B. Yuste, Andrés Santos, Mariano López de Haro, and Arkadiusz C. Brańka

Phys. Rev. E 104, 054142 (2021)

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Vol. 101, Iss. 1 — January 2020

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Images

Figure 1
DCF for the monocomponent HS fluid in the regions (a) $0 < r / σ < 1$ and (b) $1 < r / σ < 2$ . The densities are, from top to bottom in (a) and from bottom to top in (b), $ρ σ^{3} = 0.2, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9$ . In panel (b), the curves have been shifted vertically for better clarity. The open circles represent the results obtained from the WM-scheme (which combines MD data with the pole representation as described in Sec. 3), the dashed lines are from the PY approximation, and the solid lines are from the RFA. Note that $c^{PY} (r) = 0$ for $r / σ > 1$ .
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Figure 2
(a) First ( $Π_{1}$ ) and (b) second ( $Π_{2}$ ) poles of the monocomponent HS system for a number of different densities representative of the entire fluid region, from $ρ σ^{3} = 0.05$ (top point in each panel) to $ρ σ^{3} = 0.94$ (bottom point in each panel). Here, $α_{n}$ and $ω_{n}$ denote the damping coefficients and the oscillation frequencies, respectively [see Eq. (3)]. The open circles are the results obtained from the WM-scheme in Ref. [28] (i.e., the solution of Eqs. (21) for the monocomponent HS fluid). The dashed lines are from the PY approximation, and the solid lines are from the RFA.
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Figure 3
Plots of (a) small-small, (b) small-big, and (c) big-big DCFs in the region $0 < r < σ_{i j}$ for additive BHS mixtures with a size ratio $σ_{s} / σ_{b} = 0.648$ and a total packing fraction $η = 0.5$ . The partial packing fractions are, from top to bottom, $η_{s} = 0.05, 0.10, 0.20, 0.30, 0.35$ . The open circles represent the results obtained from the WM-scheme, the dashed lines are from the PY approximation, and the solid lines are from the RFA. In the insets, the differences $Δ_{PY} = c_{i j}^{WM} (r) - c_{i j}^{PY} (r)$ and $Δ_{RFA} = c_{i j}^{WM} (r) - c_{i j}^{RFA} (r)$ are shown, those differences increasing with increasing $η_{s}$ .
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Figure 4
Plots of (a) small-small, (b) small-big, and (c) big-big DCFs in the region $r > σ_{i j}$ for additive BHS mixtures with a size ratio $σ_{s} / σ_{b} = 0.648$ and a total packing fraction $η = 0.5$ . The partial packing fractions are, from bottom to top, $η_{s} = 0.05, 0.10, 0.20, 0.30, 0.35$ . The curves have been shifted vertically for better clarity. The open circles represent the results obtained from the WM-scheme and the solid lines are from the RFA. Note that $c_{i j}^{PY} (r) = 0$ for $r > σ_{i j}$ .
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Figure 5
Structure of the two leading poles for additive BHS mixtures with a size ratio $σ_{s} / σ_{b} = 0.648$ and a total packing fraction $η = 0.5$ . Here, $α$ and $ω$ denote the damping coefficient and the oscillation frequency, respectively [see Eq. (3)]. Big (green) circles are results from the WM-scheme [for each $η_{s}$ , $α$ and $ω$ were obtained by solving Eqs. (21)], small (red) circles are simulation results from Statt et al. [26], black solid lines are from the RFA, and gray solid lines are from the PY approximation. The horizontal blue double-sided arrow indicates the location of the structural crossover, which takes place near $η_{s} = 0.29$ and $α σ_{b} = 2.4$ . The left and right poles are denoted as $Π_{1}$ (first) and $Π_{2}$ (second), respectively (see the main text).
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Figure 6
Small-small correlation function $h_{s s} (r)$ for additive BHS mixtures with $σ_{s} / σ_{b} = 0.648$ , $η = 0.5$ , and (a) $η_{s} = 0.1$ and (b) $η_{s} = 0.4$ . The open (red) circles are the MD data, while the solid (blue) and dot-dashed (black) lines represent the contribution of the $Π_{1}$ and $Π_{2}$ pole, respectively. Note a change in the type of the leading pole describing the decay of the function at $η_{s} = 0.1$ ( $Π_{1}$ ) and $η_{s} = 0.4$ ( $Π_{2}$ ).
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