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Self-intermediate scattering function of strongly interacting three-dimensional lattice gases: Time- and wave-vector-dependent tracer diffusion coefficient
Phys. Rev. E 89, 053318 – Published 29 May, 2014
DOI: https://doi.org/10.1103/PhysRevE.89.053318
Abstract
We investigate the self-intermediate scattering function (SISF) in a three-dimensional (3D) cubic lattice fluid (interacting lattice gas) with attractive nearest-neighbor interparticle interactions at a temperature slightly above the critical one by means of Monte Carlo simulations. A special representation of SISF as an exponent of the mean tracer diffusion coefficient multiplied by the geometrical factor and time is considered to highlight memory effects that are included in time and wave-vector dependence of the diffusion coefficient. An analytical expression for the diffusion coefficient is suggested to reproduce the simulation data. It is shown that the particles' mean-square displacement is equal to the time integral of the diffusion coefficient. We make a comparison with the previously considered 2D system on a square lattice. The main difference with the two-dimensional case is that the time dependence of particular characteristics of the tracer diffusion coefficient in the 3D case cannot be described by exponentially decreasing functions, but requires using stretched exponentials with rather small values of exponents, of the order of 0.2. The hydrodynamic values of the tracer diffusion coefficient (in the limit of large times and small wave vectors) defined through SIFS simulation results agree well with the results of its direct determination by the mean-square displacement of the particles in the entire range of concentrations and temperatures.
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References (26)
- R. Kutner, K. Binder, and K. W. Kehr, Phys. Rev. B 28, 1846 (1983).
- H. Spohn, Large Scale Dynamics of Interacting Particles (Springer, New York, 1991).
- A. Danani, R. Ferrando, and E. Scalas, J. Mod. Phys. B 11, 2217 (1997).
- G. S. Bokun, Y. G. Groda, C. Uebing, and V. S. Vikhrenko, Physica A 296, 83 (2001).
- E. H. Feng and H. C. Andersen, J. Chem. Phys. 121, 3598 (2004).
- R. Gomer, Rep. Prog. Phys. 53, 917 (1990).
- M. C. Tringides and Z. Choj, Collective Diffusion on Surfaces: Correlation Effects and Adatom Interaction (Springer, New York, 2001).
- A. R. Allnatt and A. B. Lidiard, Atomic Transport in Solids (Cambridge University Press, Cambridge, UK, 2004).
- W. R. McKinnon and R. R. Haering, Modern Aspects in Electrochemistry (Plenum Press, New York, 1983).
- M. D. Levi and D. Aurbach, Electrochim. Acta 45, 167 (1999).
- J. Bisquert, Phys. Chem. Chem. Phys. 10, 49 (2008).
- L. Onsager, Phys. Rev. 65, 117 (1944).
- J. P. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill International, New York, 1980).
- J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic Press, London, 1986).
- A. Serra and R. Ferrando, Surf. Sci. 515, 588 (2002).
- P. A. Fedders and O. F. Sankey, Phys. Rev. B 18, 5938 (1978).
- R. A. Tahir-Kheli and R. J. Elliott, Phys. Rev. B 27, 844 (1983).
- R. A. Tahir-Kheli, Phys. Rev. B 27, 6072 (1983).
- H. van Beijeren and R. Kutner, Phys. Rev. Lett. 55, 238 (1985).
- E. Barsukov and J. R. Macdonald, Impedance Spectroscopy. Theory, Experiment, and Applications (John Wiley and Sons, Inc., Hoboken, NJ, 2005).
- S. Kazlauskas, A. Kezionis, T. Salkus, and A. F. Orliukas, Solid State Ion. 231, 37 (2013).
- R. Kutner and K. W. Kehr, Phys. Rev. B 41, 2784 (1990).
- L. Skarpalezos, N. Tsakiris, P. Argyrakis, and V. S. Vikhrenko, Phys. Rev. B 84, 075476 (2011).
- T. M. Klarke and J. R. Durrant, Chem. Rev. 110, 6736 (2010).
- B. A. Gregg, J. Phys. Chem. Lett. 2, 3013 (2011).
- P. Giazitzidis, P. Argyrakis, J. Bisquert, and V. S. Vikhrenko, Org. Electron. 15, 1043 (2014).