New Possibilities Provided by the Analysis of the Molecular Velocity Autocorrelation Function in Liquids

  • N. P. Malomuzh I.I. Mechnikov National University of Odessa
  • K. S. Shakun Odessa National Maritime Academy
  • A. A. Kuznetsova Odessa National Maritime Academy
Keywords: self-diffusion coefficient, kinematic shear viscosity coefficient, Maxwell relaxation time, argon spinodal, averaged potential of molecular interaction

Abstract

Long-time tails of the molecular velocity autocorrelation function (VACF) in liquid argon at temperatures higher and lower than the spinodal temperature have been analyzed. By considering the time dependence of the VACF, the self-diffusion and shear viscosity coefficients, and the Maxwell relaxation time are determined, as well as their changes when crossing the spinodal. It is shown that the characteristic changes in the temperature dependences of the indicated kinetic coefficients allow the spinodal position to be determined with a high accuracy. A possibility toapply the proposed method to other low-molecular liquids is considered. As an example, nitrogen and oxygen are used, for which the averaged potential of intermolecular interaction has the Lennard-Jones form.

References


  1. B.J. Alder, T.E. Wainwright. Velocity autocorrelations for hard spheres. Phys. Rev. Lett. 18, 988 (1967).
    https://doi.org/10.1103/PhysRevLett.18.988

  2. B.J. Alder, T.E. Wainwright. Decay of the velocity autocorrelation functions. Phys. Rev. A 1, 18, (1970).
    https://doi.org/10.1103/PhysRevA.1.18

  3. M.H. Ernst, E.H. Hauge, J. van Leewen. Asymptotic time behavior of correlation functions. Phys. Rev. Lett. 25, 1254 (1970).
    https://doi.org/10.1103/PhysRevLett.25.1254

  4. M.H. Ernst, E.H. Hauge, J. van Leewen. Hydrodynamic theory of the velocity correlation function. Phys. Lett. A 34, 419 (1971).
    https://doi.org/10.1016/0375-9601(71)90946-7

  5. M.H. Ernst, E.H. Hauge, J. van Leewen. Asymptotic time behavior of correlation functions. I. Kinetic terms. Phys. Rev. A 4, 2055 (1971).
    https://doi.org/10.1103/PhysRevA.4.2055

  6. K. Kawasaki. Long time behavior of the velocity autocorrelation function. Phys. Lett. A 32, 379 (1970).
    https://doi.org/10.1016/0375-9601(70)90009-5

  7. T. Gaskell, N.H. March. Non-analyticity of frequency spectra in classical liquids. Phys. Lett. A 33, 460 (1970).
    https://doi.org/10.1016/0375-9601(70)90608-0

  8. M.H. Ernst, J.R. Dorfman. Nonanalytic dispersion relations in classical fluids: I. The hard-sphere gas. Physica 61, 157 (1972).
    https://doi.org/10.1016/0031-8914(72)90065-1

  9. J.R. Dorfman, E.G.D. Cohen. Time correlation functions. Phys. Rev. A 12, 292 (1975).
    https://doi.org/10.1103/PhysRevA.12.292

  10. N.N. Bogolyubov. On stochastic processes in dynamic systems. Elem. Chast. At. Yadr. 9, 501 (1978) (in Russian).

  11. P. Resibois, M. De Leener. Classical Kinetic Theory of Fluids (Wiley, 1978).

  12. I.Z. Fisher. Hydrodynamic asymptotic characteristics of the autocorrelation function for the velocity of a molecule in a classical liquid. Sov. Phys. JETP 61, 1647 (1971).

  13. I.Z. Fisher, A.V. Zatovsky, N.P. Malomuzh. Asymptotics of the angular velocities autocorrelation function of a molecule for the liquid argon. Sov. Phys. JETP 65, 297 (1973).

  14. A.R. Dexter, A.J. Matheson. Elastic moduli and stress relaxation times in liquid argon. J. Chem. Phys. 54, 203 (1971).
    https://doi.org/10.1063/1.1674594

  15. T.V. Lokotosh, N.P. Malomuzh. Lagrange theory of thermal hydrodynamic fluctuations and collective diffusion in liquids. Physica A 286, 474 (2000).
    https://doi.org/10.1016/S0378-4371(00)00107-2

  16. T.V. Lokotosh, N.P. Malomuzh. Manifestation of the collective effects in the rotational motion of molecules in liquids. J. Mol. Liq. 93, 95 (2001).
    https://doi.org/10.1016/S0167-7322(01)00214-8

  17. T.V. Lokotosh, N.P. Malomuzh, K.S. Shakun. Nature of oscillations for the autocorrelation functions for translational and angular velocities of a molecule J. Mol. Liq. 96-97, 245 (2002).
    https://doi.org/10.1016/S0167-7322(01)00351-8

  18. L.A. Bulavin, D.A. Gavryushenko, and V.M. Sysoev, Molecular Physics (Znannya, 2006) (in Ukrainian).

  19. L.A. Bulavin, Neutron Diagnostics of Liquid Matter State (Institute for Safety Problems of Nuclear Power Plants, 2012) (in Ukrainian).

  20. D. Zubarev, V. Morozov, G. Ropke. Statistical Mechanics of Nonequilibrium Processes (Wiley, 1997).

  21. D. van der Spoel, E. Lindahl, B. Hess, G. Groenhof, A.E. Mark, H.J.C. Berendsen. Gromacs: fast, flexible and free. J. Comp. Chem. 26, 1701 (2005).
    https://doi.org/10.1002/jcc.20291

  22. W.F. van Gunsteren, S.R. Billeter, A.A. Eising, P.H. Hunenberger, P. Kruger, A.E. Mark, W.R.P. Scott, I.G. Tironi. Biomolecular Simulation: The GROMOS96 Manual and User Guide (Hochschulverlag AG an der ETH, 1996).

  23. C. Oostenbrink, A. Villa, A.E. Mark, W.F. van Gunsteren. A biomolecular force field based on the free enthalpy of hydration and solvation: The GROMOS forcefield parameter sets 53A5 and 53A6. J. Comput. Chem. 25, 1656 (2004).
    https://doi.org/10.1002/jcc.20090

  24. D. Frenkel, B. Smit. Understanding Molecular Simulation: from Algorithms to Applications (Academic Press, 2001).

  25. S. Nos’e. A molecular dynamics method for simulations in the canonical ensemble. Mol. Phys. 52, 255 (1984).
    https://doi.org/10.1080/00268978400101201

  26. W.G. Hoover. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 31, 1695 (1985).
    https://doi.org/10.1103/PhysRevA.31.1695

  27. A.Yu. Kuksin, I.V. Morozov, G.E. Norman, V.V. Stegailov, I.A. Valuev. Standards for molecular dynamics modelling and simulation of relaxation. Mol. Simulat. 31, 1005 (2005).
    https://doi.org/10.1080/08927020500375259

  28. P.M. Morse, H. Feshbach. Methods of Theoretical Physics (McGraw-Hill, 1953), Vol. 1.

  29. O.A. Grechanyi. Stochastic Theory of Irreversible Processes (Naukova Dumka, 1989) (in Russian).

  30. Yu.V. Slyusarenko. Influence of fluctuations on hydrodynamic asymptotics of Green's functions. Ukr. Fiz. Zh. 28, 774 (1983) (in Russian).

  31. A.I. Sokolovsky. Projection formulation of the Bogolyubov reduced description method and its application to fluctuation kinetics. Ukr. J. Phys. 45, 545 (2000).

  32. A.I. Sokolovsky. Reduced description of nonequilibrium processes and correlation functions. Divergences and non-analyticity. Condens. Matter Phys. 9, 415 (2006).
    https://doi.org/10.5488/CMP.9.3.415

  33. S.V. Peletminsky, Yu.V. Slusarenko. On the theory of long wave nonequilibrium fluctuations. Physica A 210, 412 (1994).
    https://doi.org/10.1016/0378-4371(94)00065-4

  34. S.V. Peletminskii, Yu.V. Slyusarenko, A.I. Sokolovsky. Kinetics and hydrodynamics of long-wave fluctuations under external random force. Physica A 326, 412 (2003).
    https://doi.org/10.1016/S0378-4371(03)00255-3

  35. L.A. Bulavin, T.V. Lokotosh, N.P. Malomuzh. Role of the collective self-diffusion in water and other liquids. J. Mol. Liq. 137, 1 (2008).
    https://doi.org/10.1016/j.molliq.2007.05.003

  36. T.V. Lokotosh, M.P. Malomuzh, K.M. Pankratov, K.S. Shakun. New results in the theory of collective self-diffusion in liquids. Ukr. Fiz. Zh. 60, 697 (2015) (in Ukrainian).
    https://doi.org/10.15407/ujpe60.08.0697

  37. M.E. Soloviev, M.M. Soloviev. Computer Chemistry (Solon-Press, 2005) (in Russian).

  38. L.A. Bulavin, N.V. Vygornitskii, N.I. Lebovka. Computer Modeling of Physical Systems (Intellekt, 2011) (in Russian).

  39. L.D. Landau, E.M. Lifshitz. Statistical Physics (Pergamon Press, 1980).

  40. J. Naghizadeh, S.A. Rice. Kinetic theory of dense fluids. X. Measurement and interpretation of self-diffusion in liquid Ar, Kr, Xe, and CH4. J. Chem. Phys. 36, 2710 (1962).
    https://doi.org/10.1063/1.1732357

  41. R. Laghaei, A.E. Nasrabad, Byung Chan Eu. Generic van der Waals equation of state, modified free volume theory of diffusion, and viscosity of simple liquids. J. Phys. Chem. B 109, 5873 (2005).
    https://doi.org/10.1021/jp0448245

  42. B.A. Younglove, H.J.M. Hanley. The viscosity and thermal conductivity coefficients of gaseous and liquid argon. J. Phys. Chem. Ref. Data 15, 1323 (1986).
    https://doi.org/10.1063/1.555765

  43. R. Hartkamp, P.J. Daivis, B.D. Todd. Density dependence of the stress relaxation function of a simple fluid. Phys. Rev. E 87, 032155 (2013).
    https://doi.org/10.1103/PhysRevE.87.032155

  44. P.S. van der Gulik. The linear pressure dependence of the viscosity at high densities Physica A 256, 39 (1998).
    https://doi.org/10.1016/S0378-4371(98)00197-6

  45. NIST Standard Reference Database 69: NIST Chemistry WebBook; http://webbook.nist.gov/chemistry/fluid/

  46. B.P. Nikolskiy. Chemical Handbook (Chemistry, 1965), Vol. 1.

  47. N.P. Malomuzh, K.S. Shakun. Specific properties of argon- like liquids near their spinodals. J. Mol. Liq. 235, 155 (2017).
    https://doi.org/10.1016/j.molliq.2017.01.079

  48. W.T. Laughlin, D.R. Uhlmann. Viscous flow in simple organic liquids. J. Phys. Chem. 76, 2317 (1972).
    https://doi.org/10.1021/j100660a023

  49. A.R. Ubbelohde. Melting and Crystal Structure (Oxford Univ. Press, 1965).

  50. A.Yu. Kuksin, G.E. Norman, V.V. Stegailov. The phase diagram and spinodal decomposition of metastable states of Lennard-Jones system. High Temp. 45, 37 (2007).
    https://doi.org/10.1134/S0018151X07010063

  51. P.V. Makhlaychuk, V.N. Makhlaychuk, N.P. Malomuzh. Nature of the kinematic shear viscosity of low-molecular liquids with averaged potentials of Lennard-Jones type. J. Mol. Liq. 225, 577 (2016).
    https://doi.org/10.1016/j.molliq.2016.11.101

  52. N. Ohtori, Y. Ishii. Explicit expression for the Stokes-Einstein relation for pure Lennard-Jones liquids. Phys. Rev. E 91, 012111 (2015).
    https://doi.org/10.1103/PhysRevE.91.012111
Published
2018-06-18
How to Cite
Malomuzh, N., Shakun, K., & Kuznetsova, A. (2018). New Possibilities Provided by the Analysis of the Molecular Velocity Autocorrelation Function in Liquids. Ukrainian Journal of Physics, 63(4), 317. https://doi.org/10.15407/ujpe63.4.317
Section
Physics of liquids and liquid systems, biophysics and medical physics