Structural behavior of fluids from the vapor and liquid region to the supercritical phase

James Losey and Richard J. Sadus

Phys. Rev. E 100, 052132 – Published 22 November 2019

Abstract

A metric ( $χ$ ) is introduced to quantify the relative proportion of particles having a specified number of near neighbors that are characteristic of liquid-phase properties. It can be used as a simple alternative to other methods for the investigation of some aspects of percolation behavior. Values of $χ$ are obtained from molecular-dynamics simulations spanning the heterogeneous vapor and liquid region and the supercritical phase of the Lennard-Jones fluid. The supercritical phase can be delineated into regions of different structural properties. At different isochoric subcritical conditions, the temperature versus $χ$ behavior shows evidence of inflections, which are associated with the onset of transitions from the vapor and liquid region to the supercritical phase. The analysis suggests a phenomenological requirement for the critical point in terms of a near-equal proportion of near neighbors with gaslike and liquidlike characteristics.

Received 3 June 2019
Revised 10 October 2019

DOI:https://doi.org/10.1103/PhysRevE.100.052132

Physics Subject Headings (PhySH)

Critical phenomena Phase separation Phase transitions

Statistical Physics & Thermodynamics

Authors & Affiliations

James Losey and Richard J. Sadus ^*

Centre for Computational Innovations, Swinburne University of Technology, PO Box 218, Hawthorn, VIC, 3122, Australia

^*rsadus@swin.edu.au

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Vol. 100, Iss. 5 — November 2019

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Images

Figure 1
Comparison of the (a) Stillinger and (b) TWF approaches for determining near neighbors. The colored circles represent particles at a given instance of time. In (a) the solid gray reference particle ( $i$ ) has five neighbors inside the threshold distance of $r_{S}$ and the four red particles (outside of the dashed circle) are not counted as neighbors. In (b), the $i$ particle has the same five neighbors but only the green particle ( $j$ ) has five neighbors within its own $r_{S}$ radius, which now involves two of the red particles excluded in (a).
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Figure 2
Comparison of the fraction of $N = 2000$ LJ particles with respect to the number of near neighbors obtained from the (a) Stillinger and (b) TWF methods at $T = 1.65$ and from left to right $ρ = 0.3$ (blue line), 0.4 (orange line), 0.5 (green line), and 0.6 (red line). The vertical dashed line represents the division between gaslike ( $\leq 4$ neighbors) and liquidlike ( $> 4$ neighbors) properties.
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Figure 3
Comparison of Stillinger (upper blue circles) and TWF (lower orange circles) $χ$ values for 2000 LJ particles as a function of $ρ$ for a liquidlike state ( $> 4$ near neighbors) at $T = 1.65$ .
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Figure 4
The behavior of $T$ with respect to $χ$ at different isochores using the (a) Stillinger and (b) TWF methods. The different circles represent from left to right $ρ = 0.3$ (blue), 0.316 (orange), 0.35 (green), 0.4 (red), 0.5 (purple), and 0.75 (brown, very close to the $χ = 1$ region) isochores. The horizontal dashed line represents $T_{c} = 1.312$ [34]. The squares are the supercritical maximum (minimum) values [8] of $C_{v}$ (lower aquamarine squares) and $C_{p}$ (upper brown squares), with the extremum for these properties given by the diamond of the same color.
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Figure 5
$χ − ρ$ behavior at critical $(T_{c} = 1.312)$ and supercritical $(T > 1.312)$ values of $T$ the (a) Stillinger and (b) TWF methods. The different circles represent from left to right $T = 1.312$ (green), 1.5 (blue), 2.0 (purple), 2.5 (lime), 3.0 (black), and 3.5 (gray). The values corresponding to the minimum (maximum) [8] of both $C_{v}$ (aquamarine squares) and $C_{p}$ (red squares) are illustrated. The vertical dashed line represents $ρ_{c} = 0.316$ .
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Figure 6
$T − ρ$ behavior of the LJ fluid at constant values of $χ$ obtained for the (a) Stillinger and (b) TWF methods. Results are illustrated from left to right for $χ = 0.2$ (blue line), 0.5 (aquamarine line), 0.8 (orange line), and 0.95 (brown line). Also illustrated are VLE (upper black dashed line) and spinodal (lower dashed red line) boundaries calculated from the Johnson et al. [40] equation of state; the critical point (black circle); and the supercritical maximum (minimum) values [8] of $C_{v}$ (lower aquamarine squares) and $C_{p}$ (upper brown squares), with the extremum for these properties given by the diamond of the same color.
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