Relationship between Diffusion Coefficients in Nonideal Binary Lennard-Jones Mixtures and Entropy

I. P. Anashkin; Анашкин И. П.; S. G.  Dyakonov; Дьяконов С. Г.; A. V. Klinov; Клинов А. В.

doi:10.31857/S0040357123020045

Relationship between Diffusion Coefficients in Nonideal Binary Lennard-Jones Mixtures and Entropy

Authors: Anashkin I.P.¹, Dyakonov S.G.¹, Klinov A.V.¹
Affiliations:
1. FSBEI HPE Kazan National Research Technological University
Issue: Vol 57, No 2 (2023)
Pages: 202-208
Section: Articles
Published: 01.03.2023
URL: https://journal-vniispk.ru/0040-3571/article/view/138447
DOI: https://doi.org/10.31857/S0040357123020045
EDN: https://elibrary.ru/EIVFWO
ID: 138447

Cite item

Full Text

Open Access
Restricted Access

Access granted
Restricted Access

Subscription Access

Abstract
About the authors
References
Supplementary files
Statistics

Abstract

The simulation of nonideal Lennard-Jones mixtures is carried out by the method of molecular dynamics. The values of pressure, internal energy, chemical potential, and diffusion coefficients are determined depending on the composition and density. The nonideal behavior of the mixtures is specified by the parameters in the mixing rules for the intermolecular interaction potential. Four options for the values of such parameters are considered. The thermodynamic consistency of the calculated thermodynamic properties is verified using the Gibbs–Duhem expression. The value of excess entropy is calculated, and its connection with the Einstein diffusion coefficients is shown. A parameter is determined in the regression equation that relates the excess entropy to the Einstein diffusion coefficients. Its value is 0.8, which is close to the values in similar expressions for other substances.

Keywords

entropy, diffusion coefficient, Lennard-Jones potential

References

Taylor R., Krishna R. Multicomponent mass transfer. New York: Wiley, 1993. 579 p.
The Stokes-Einstein law for diffusion in solution // Proc. R. Soc. Lond. Ser. Contain. Pap. Math. Phys. Character. 1924. V. 106. № 740. P. 724–749.
Shabarova L.V. et al. Modeling Thermal Gas Dynamic Processes of the Production of Silicon from Its Halides // Theor. Found. Chem. Eng. 2020. V. 54. № 4. P. 631–640.
Rosenfeld Y. Relation between the transport coefficients and the internal entropy of simple systems // Phys. Rev. A. 1977. V. 15. № 6. P. 2545–2549.
Dyre J.C. Perspective: Excess-entropy scaling // J. Chem. Phys. 2018. V. 149. № 21. P. 210901.
Dehlouz A. et al. Entropy Scaling-Based Correlation for Estimating the Self-Diffusion Coefficients of Pure Fluids // Ind. Eng. Chem. Res. 2022. V. 61. № 37. P. 14033–14050.
Novak L. Self-Diffusion Coefficient and Viscosity in Fluids // Int. J. Chem. React. Eng. 2011. V. 9. № 1.
Novak L.T. Fluid Viscosity-Residual Entropy Correlation // Int. J. Chem. React. Eng. 2011. V. 9. № 1.
Bell I.H. Entropy Scaling of Viscosity– I: A Case Study of Propane // J. Chem. Eng. Data. 2020. V. 65. № 6. P. 3203–3215.
Bell I.H. Entropy Scaling of Viscosity– II: Predictive Scheme for Normal Alkanes // J. Chem. Eng. Data. 2020. V. 65. № 11. P. 5606–5616.
Nikitiuk B.I. et al. Pair entropy and universal viscosity scaling for molecular systems via molecular dynamics simulations // J. Mol. Liq. 2022. V. 368. P. 120714.
Yang X. et al. Entropy Scaling of Viscosity– III: Application to Refrigerants and Their Mixtures // J. Chem. Eng. Data. 2021. V. 66. № 3. P. 1385–1398.
Bell I.H. et al. Modified Entropy Scaling of the Transport Properties of the Lennard–Jones Fluid // J. Phys. Chem. B. 2019. V. 123. № 29. P. 6345–6363.
Bell I.H. et al. Modified Entropy Scaling of the Transport Properties of the Lennard–Jones Fluid // J. Phys. Chem. B. 2019. V. 123. № 29. P. 6345–6363.
Viet T.Q.Q. et al. Mass effect on viscosity of mixtures in entropy scaling framework: Application to Lennard–Jones mixtures // Fluid Phase Equilibria. 2022. V. 558. P. 113459.
Yokoyama I. A relationship between excess entropy and diffusion coefficient for liquid metals near the melting point // Phys. B Condens. Matter. 1998. V. 254. № 3–4. P. 172–177.
Anashkin I., Dyakonov S., Dyakonov G. Relationship between the Transport Coefficients of Polar Substances and Entropy // Entropy. 2019. V. 22. № 1. P. 13.
Bell I.H., Dyre J.C., Ingebrigtsen T.S. Excess-entropy scaling in supercooled binary mixtures // Nat. Commun. 2020. V. 11. № 1. P. 4300.
Abraham M.J. et al. GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers // SoftwareX. 2015. V. 1–2. P. 19–25.
Van Der Spoel D. et al. GROMACS: Fast, flexible, and free // J. Comput. Chem. 2005. V. 26. № 16. P. 1701–1718.
Pronk S. et al. GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit // Bioinformatics. 2013. V. 29. № 7. P. 845–854.
McQuarrie D.A. Statistical mechanics. Sausalito, Calif: University Science Books, 2000. 641 p.
Widom B. Some Topics in the Theory of Fluids // J. Chem. Phys. 1963. V. 39. № 11. P. 2808–2812.
articles [Online]. URL: https://github.com/KSTU/articles/tree/master/entropy-diffusion-mixture.
Johnson J.K., Zollweg J.A., Gubbins K.E. The Lennard-Jones equation of state revisited // Mol. Phys. 1993. V. 78. № 3. P. 591–618.
Demirel Y. Calculation of Excess Entropy for Binary Liquid Mixtures by the NRTL and UNIQUAC Models // Ind. Eng. Chem. Res. 1994. V. 33. № 11. P. 2875–2878.