Some Physical Properties of the Weeks-Chandler-Andersen Fluid

18 Pages·2017·0.49 MB·English

Some Physical Properties of the
Weeks-Chandler-Andersen Fluid
David Michael Heyes, Hisashi Okumura
To cite this version:
David Michael Heyes, Hisashi Okumura. Some Physical Properties of the Weeks-Chandler-Andersen
Fluid. Molecular Simulation, 2006, 32 (01), pp.45-49. ￿10.1080/08927020500529442￿. ￿hal-00514977￿
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Some Physical Properties of the Weeks-Chandler-Andersen
Fluid
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Journal: Molecular Simulation/Journal of Experimental Nanoscience
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Manuscript ID: GMOS-2005-0102
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Journal: Molecular Simulation
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Date Submitted by the
Author: 18-Drec-2005

Complete List of Authors: Heyes, David; University of Surrey, Chemistry
Okumura, Hisashi; Institute for Molecular Science Okazaki,
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Department of Theoretical Studies
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Keywords: WCA fluids, molecular dynamics, physical properties
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Some Physical Properties of the Weeks-Chandler-Andersen Fluid
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5 David M. Heyes(cid:3)
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Division of Chemistry,
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University of Surrey,
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15 Guildford GU2 7XH, United Kingdom,
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21 Hisashi Okumuray
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Department of Theoretical Studies,
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Okazaki, Aichi 444-8585, Japan,
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31 and Department of Structural Molecular Science,
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33 The Graduate Universityefor Advanced Studies,
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36 Okazaki, Aichi 444-858i5, Japan.
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Abstract
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4 Molecular Dynamics simulations have been carried out of some properties of a Weeks-Chandler-
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Andersen (WCA) system in its (cid:13)uid phase. Data for the potential energy components, mean square
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9 force, in(cid:12)nite frequency elastic moduli and Poissons ratio are presented as a function of density and
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temperature. The scaling behaviour of these quantities using reduced variables, such as an e(cid:11)ective
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14 hard sphere diameter, (cid:27) , was investigated. The in(cid:12)nite frequency Poisson’s ratio, (cid:23) , was found
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to increase with pacFking fraction and temperature towards the incompressible (cid:13)uid limit value of
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evaluated at (cid:27) .
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56 (cid:3)Electronic address: [email protected]
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I. INTRODUCTION
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5 The Weeks-Chandler-Anderson (WCA) potential is a popular pair potential,
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8 4(cid:15)(((cid:27))12 ((cid:27))6)+(cid:15); r 21=6(cid:27)
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This potential is the Lennard-Jones (LJ) potential, shifted upwards by (cid:15) and truncated at the
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16 LJ potential minimum of 21=6(cid:27). Although the total potential is repulsive, it is composed of
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18 repulsive r(cid:0)12 (‘r’) and attractive r(cid:0)6 (‘a’) components. It was originally devised as a reference
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21 (cid:13)uid in a perturbation treat ment for the LJ (cid:13)uid [1, 2]. The Lennard-Jones pair potential is
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attractive. The WCA (cid:13)uid has been examined in various dimensions [3, 4]. The phase diagram
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of the WCA system is relatively simple, in that unlike the LJ potential it does not have a
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30 critical point and liquid-vapour co-existence region. The melting line of the WCA (cid:13)uid has
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been determined [5], and its thermomechanical properties calculated by Molecular Dynamics
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In this study we consider various properties of the WCA (cid:13)uid, including the potential energy,
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42 the mean square force, in(cid:12)nite frequency elastic moduli and Poisson’s ratio. This study follows
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on from our recent molecular dynamics simulation and theory of the generalised soft sphere po-
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[7]. For the soft sphere potential, there is a direct mapping between temperature and density,
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out at a single temperature. In the WCA case, one cannot perform such a temperature-density
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ioroftheWCA(cid:13)uidshouldapproachthatofthesoftspherepotentialwiththeexponentn = 12.
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II. RESULTS AND DISCUSSION
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5 Molecular Dynamics simulations were carried out with N = 500 particles in volume V for
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typically 70000 time steps of 0:005=pT (cid:27)(m=(cid:15))1=2 where T is the ‘reduced’ temperature or
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10 k T=(cid:15), where k is Boltzmann’s constant. All quantities quoted below and on the (cid:12)gures are
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in WCA reduced units, i:e:; (cid:15) (cid:27) m = 1 (m is the mass of the particle). The density
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used in ref.[5]andatdensities uptoandabove the maximum (cid:13)uiddensity ateach temperature.
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One of the main themes of this work is an attempt to collapse the computed quantities onto a
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single master curve in each case. Ineorder to achieve this we need to introduce a prescription
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Although real molecules and the WCA parRticle are not hard spheres, the exercise of mapping
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e(cid:11)ective hard sphere diameter, (cid:27) to the real molecule. The WCA data can be rescaled by
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these do no lead to simple analytic expressions for the usual potential forms. An alternative
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k T (or a factor times the thermal energy), which leads to a simple analytic expression for (cid:27) .
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to solve the quadratic equation, T = 4X2 4X +1 for X, where (in reduced units) X = r(cid:0)6.
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21=6
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on setting r (cid:27) . The formula in Eq. (2) indicates that the e(cid:11)ective hard sphere diameter
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(cid:11)
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where (cid:11) and T are variables that could be density dependent [9, 10].
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In Fig. 1 the potential energy per particle divided by k T , u=k T and the repulsive (u =k T)
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temperatures (even though the total potential energy is always positive). Figure 2 shows the
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Eq. (2)energy perparticle is always k T (this factwas used inderiving the formulain Eq. (2)).
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fraction, (cid:16) de(cid:12)ned with (cid:27) from the formula in Eq. (2). The force is normalised by the
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(cid:27) = ; (4)
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as can be seen in (cid:12)gure 4. The di(cid:11)erence between the de(cid:12)nitions of (cid:27) in Eqs. (2) and (4) is
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de(cid:12)nition of (cid:27) of Ben-Amotz and Herschback [9] given in the formula of Eq. (3). Using
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where g(r) is the radial distribution function and (cid:30)0 d(cid:30)=dr. (cid:26) = N=V is the number density
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G can be computed from Eq. (5) rewritten as a sum over pair interactions,
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< > stands for a simulation time or ensRemble average. Similarly for the in(cid:12)nite frequency
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with the (cid:30)-dependent terms.
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total G , and its repulsive and attractive components are also shown on the (cid:12)gure. The
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formulas for this quantity, given in Eq. (5), one would not expect any simple scaling of the
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term is larger. The (in(cid:12)nite frequency) Poisson’s ratio, (cid:23) can be obtained from the computed
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3K 2G
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which is plotted as a function of equivalent hard sphere packing fraction in Fig. 9. The
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In this report we have explored the density and temperature dependence of some of the less
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temperature and density. We have also made some attempts to scale the various data sets onto
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master curves using an e(cid:11)ective hard sphere diameter treatment. These quantities we (cid:12)nd are,
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complicated functional form of the potential.
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Acknowledgements
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50 DMH and HO thank The Royal Society (London) and the Japan Society for the Promotion
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of Science for funding this collaboration. The authors thank Dr. A.C. Bran(cid:19)ka, Institute for
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Molecular Physics, Polish Academy of Sciences, Poznan(cid:19), Poland, for useful discussions.
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