Statistical Fluctuations along the Lennard-Jones Melting Curve

• Autorzy: Patra R. , Heyes D. M.

Identyfikatory

DOI

10.12921/cmst.2016.22.01.001

• Języki publikacji: EN

Abstrakty

EN

Statistical fluctuations and correlations between thermodynamic properties along the fluid side of the melting line of the Lennard-Jones (LJ) are determined using Molecular Dynamics (MD) computer simulation. Linear regression, the Pearson coefficient and other statistical measures are calculated. The cross correlation between the configurational part of the pressure and potential energy, and the repulsive and attractive parts of the potential energy are focussed on. Regression plots show that at constant temperature and constant total energy the Weeks-Chandler-Andersen (WCA) decomposition of the Lennard-Jones repulsive and attractive potential energy components show a qualitative change along the melting line. At low temperature the two components are correlated, while they are anticorrelated in the high temperature limit. There is an intermediate temperature range in which the two potential energy components are effectively uncorrelated. The various fluctuation trends along the melting line were found to be weakly dependent on the force field used to generate the distribution of states, namely, the LJ potential, inverse power potential with exponent 12, and the repulsive term in the WCA decomposition of the LJ potential.

Słowa kluczowe

EN

Pearson coefficient; fluctuations; molecular simulation

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2016
• Tom: Vol. 22, No. 1
• Strony: 5--17
• Opis fizyczny: Bibliogr. 43 poz., rys.

Twórcy

autor

Patra R.

• Department of Economics, Royal Holloway University of London, Egham, Surrey TW20 0EX, UK

autor

Heyes D. M.

• Department of Physics, Royal Holloway University of London, Egham, Surrey TW20 0EX, UK

Bibliografia

• [1] J.-P. Hansen and I.R. McDonald, Theory of simple liquids, 4th Ed. Academic Press: 2013.
• [2] D.M. Heyes, D. Dini and A.C. Bra´nka, Scaling of Lennard-Jones liquid elastic moduli, viscoelasticity and other properties along fluid-solid coexistence, Phys. Stat. Solidi B, 252, 1-12 (2015).
• [3] T.S. Ingebrigtsen, T.B. Schrøder and J.C. Dyre, Isomorphs in model molecular liquids, J. Phys. Chem. B 116, 1018-1034 (2012).
• [4] J.C. Dyre, Hidden Scale Invariance in condensed matter, J. Phys. Chem. 118, 10007-10024 (2014).
• [5] N.P. Bailey, T.B. Schrøder and J.C. Dyre, Variation of the dynamic susceptibility along an isochrone, Phys. Rev. E, 90, 042310 (2014).
• [6] N. Gnan, T.B. Schrøder, U.R. Pedersen, N.P. Bailey, J.C. Dyre, Pressure-energy correlations in Liquids. IV. "Isomorphs" in liquid phase diagrams. J. Chem. Phys. 131, 234504 (2009).
• [7] U.R. Pedersen, N.P. Bailey, T.B. Schrøder and J.C. Dyre, Strong pressure-energy correlations in van der Waals liquids, Phys. Rev. Lett. 100, 015701 (2008).
• [8] C. Cortinhas and K. Black, Statistics for Business and Economics, Wiley: 2012.
• [9] M.K. Fung, Are knowledge spillovers driving the convergence of productivity among firms?, Economica 72, 287-305 (2005).
• [10] W.G. Hoover and M. Ross, Statistical theories of melting, Contemp. Phys. 12, 339-356 (1971).
• [11] D. Coslovich and C.M. Roland, Pressure-energy correlations and thermodynamics scaling in viscous Lennard-Jones liquids, J. Chem. Phys. 130, 014508 (2009).
• [12] D.M. Heyes, The liquid state – applications of molecular simulations, John Wiley & Sons: 1998.
• [13] J.R. Morris and X. Song, The melting lines of model systems calculated from coexistence simulations, J. Chem. Phys. 116, 9352-9358 (2002).
• [14] L.V. Woodcock, Isothermal molecular dynamics calculations for liquid salts, Chem. Phys. Lett. 10, 257-261 (1971).
• [15] L.V. Woodcock, Comparison of thermostats, CCP5 Information Quarterly No. 24, March 1987, p. 297.
• [16] S. Nosé, A molecular dynamics method for simulations in the canonical ensemble, Mol. Phys. 52, 255-268 (1984).
• [17] W.G. Hoover, Canonical dynamics: Equilibrium phase-space distributions, Phys. Rev. A 31, 1695-1697 (1985).
• [18] S. Nosé, Constant temperature molecular dynamics methods, Prog. Theor. Phys. Supplement 103, 1-117 (1991).
• [19] M.A. Barroso and A.L. Ferreira, Solid-fluid coexistence of the Lennard-Jones system from absolute free energy calculations, J. Chem. Phys. 116, 7145-7150 (2002).
• [20] A. Ahmed and R.J. Sadus, Solid-liquid equilibria and triple points, J. Chem. Phys. 131, 174504 (2009).
• [21] G.C. McNeil-Watson and N.B. Wilding, Freezing line of the Lennard-Jones fluid: A phase switch Monte Carlo study, J. Chem. Phys. 124 064504 (2006)
• [22] J.-P. Hansen and L. Verlet, Phase transitions of the Lennard-Jones system, Phys. Rev. 184, 151-161 (1969).
• [23] J.D. Weeks, D. Chandler and H.C. Andersen, Role of repulsive forces in determining the equilibrium structure of simple liquids, J. Chem. Phys. 54, 5237-5247 (1971).
• [24] J.D. Weeks, D. Chandler and H.C. Andersen, Relationship between the hard-sphere fluid and fluids with realistic repulsive forces, Phys. Rev. A 4, 1597-1607 (1971).
• [25] H.C. Andersen, D. Chandler and J.D. Weeks, Roles of repulsive and attractive forces in liquids: The optimized Random Phase approximation J. Chem. Phys. 56, 3812-3823 (2006).
• [26] D. Chandler, J.D. Weeks and H.C. Andersen, van der Waals picture of liquids, solids, and phase transformations, Science 220, 787-794 (1983).
• [27] H.C. Andersen, D. Chandler and J.D. Weeks, Roles of repulsive and attractive forces in liquids: The equilibrium theory of classical fluids, Adv. Chem. Phys. 34 105-156 (1976).
• [28] D.M. Heyes and H. Okumura, Equation of state and structural properties of the Weeks-Chandler-Andersen fluid, J. Chem. Phys. 124, 164507 (2006).
• [29] A. de Kuiper, J.A. Schouten and J.P.J. Michels, The melting line of the Weeks-Chandler-Andersen Lennard-Jones reference system, J. Chem. Phys. 93, 3515 (1990).
• [30] S. Pikatan Tan, H. Adidharma and M. Radosz, Weeks-Chandler-Andersen model for solid-liquid equilibria in Lennard-Jones systems, J. Phys. Chem. C 106, 7878-7881 (2002).
• [31] J.-P. Hansen, Phase transition of the Lennard-Jones system. II. High-temperature limit, Phys. Rev. A, 2, 221-230 (1970).
• [32] D.M. Heyes, S.M. Clarke and A.C. Brańka, Soft-sphere soft glasses, J. Chem. Phys. 131, 204506 (2009).
• [33] J.P. Onyango and A.M. Plews, A textbook of basic statistics, East African Publishers : 1987.
• [34] J.M. Wooldridge, Introductory econometrics: A modern approach, South-Western Publishers, 4th Ed.: 2009.
• [35] J.K. Adams, Basic statistical concepts, McGraw-Hill Book Company, Inc.: 1955.
• [36] D.A. McQuarrie, Mathematical methods for scientists and engineers, University science books: 2003.
• [37] D. Ben-Amotz and G. Stell, Hard sphere perturbation theory for fluids with soft-repulsive-core potentials, J. Chem. Phys. 120, 4844-4851 (2004).
• [38] S. Hess, M. Kröger and H. Voigt, Thermomechanical properties of the WCA-Lennard-Jones model system in its fluid and solid states, Physica A 250, 58-82 (1998).
• [39] A. Ahmed and R.J. Sadus, Phase diagram of the Weeks-Chandler-Andersen potential from very to high temperatures and pressures, Phys. Rev. E 80, 061101 (2009).
• [40] R. Zwanzig and R.D. Mountain, High-frequency elastic moduli of simple fluids, J. Chem. Phys. 43, 4464 (1965).
• [41] D.M. Heyes, G. Rickayzen and A.C. Brańka, Static properties and time correlation functions of fluids with steeply repulsive potentials, Mol. Phys. 102, 2057-2070 (2004).
• [42] T.B. Schrøder, N. Gnan, U.R. Pedersen, N.P. Bailey, J.C. Dyre, Pressure-energy correlations in Liquids. V. Isomorphs in generalized Lennard-Jones systems. J. Chem. Phys. 134, 164505(2011).
• [43] © StataCorp. 2001. Statistical Software: Release STATA 12. College Station, TX: Stata Corporation. Statistical Fluctuations along the Lennard-Jones Melting Curve

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.