Entropy of a restricted primitive model electrolyte using a mean electrostatic potential approach

Authors

DOI:

https://doi.org/10.5488/cmp.28.13801

Keywords:

electrolytes, restricted primitive model, entropy, thermodynamic integration, Monte Carlo simulations, symmetric and modified Poisson-Boltzmann theories

Abstract

The excess entropy of restricted primitive model electrolytes is calculated using a potential based approach through the symmetric Poisson-Boltzmann and the modified Poisson-Boltzmann theories. The theories are utilized in conjunction with a statistical thermodynamics equation that is shown to be equivalent to thermodynamic integration. Electrolyte systems having ionic valencies 1:1 and 2:2 with diameters 3 × 10−10 m and 4.25 ×10−10 m are treated over a wide range of concentrations. The exact radial distribution functions for the model electrolytes obtained from Monte Carlo simulations in the canonical ensemble are compared with the corresponding theoretical predictions. Furthermore, the radial distribution functions from the theories and the simulations are used in the Laird-Haymet entropy expansion equations [ J. Chem. Phys., 1994, 100, 3775] to estimate the excess entropy of the solutions. These equations take into account multi-particle distribution functions, which are approximated using a “ring” term. In general, the modified Poisson-Boltzmann theory gives results that are more consistent with the simulation data than those from the symmetric Poisson-Boltzmann theory. The results show that the excess entropy is negative with its absolute value increasing for 1:1 electrolytes with increasing concentration. The symmetric Poisson-Boltzmann values are slightly overestimated, while the modified Poisson-Boltzmann values are slightly underestimated relative to the simulations. The curves for 1:1 electrolytes including that from the Laird-Haymet equations are consistent with each other, while only the MPB curves for 2:2 electrolytes at 4.25 × 10−10 m are qualitative relative to the simulations up to about 1 mol/dm3. The 2:2 electrolyte curves reveal a characteristic inflection and plateau. The results obtained in the low concentration range (< 0.01 mol/dm3) are consistent with the predictions of the Debye-Hückel limiting law.

References

Boltzmann L., Sitzungbetichte der Kaiserlichen Akademie der Wissenschaften Mathematisch-Naturwissen Classe. Part II, Vol. LXXVI.76, 1877, 373.

Gibbs J. W., Am. J. Sci., 1878, s3-16, 1875–1978. DOI: https://doi.org/10.2475/ajs.s3-16.96.441

Shannon C. E., Bell Syst. Tech. J., 1948, 27, 379–423. DOI: https://doi.org/10.1002/j.1538-7305.1948.tb01338.x

Hummer G., Soumpasis D. K., J. Chem. Phys., 1993, 98, 581. DOI: https://doi.org/10.1063/1.464600

McQuarrie D. A., Statistical Mechanics, Harper and Row, New York, 1976.

Green H. S., Molecular Theory of Liquids, North-Holland, Amsterdam, 1952.

Laird B. B., Haymet A. D. J., Phys. Rev. A, 1992, 45, 5680. DOI: https://doi.org/10.1103/PhysRevA.45.5680

Hernando J. A., Mol. Phys., 1990, 69, 319. DOI: https://doi.org/10.1080/00268979000100211

Hernando J. A., Mol. Phys., 1990, 69, 327. DOI: https://doi.org/10.1080/00268979000100221

Laird B. B., Haymet A. D. J., J. Chem. Phys., 1994, 100, 3775. DOI: https://doi.org/10.1063/1.466365

Silverstein K. A. T., Dill K. A., Haymet A. D. J., J. Chem. Phys., 2001, 114, 6303. DOI: https://doi.org/10.1063/1.1355997

Lazaridis T., J. Phys. Chem. B, 1998, 102, 3531. DOI: https://doi.org/10.1021/jp9723574

Lazaridis T., Karplus M., J. Chem. Phys., 1996, 105, 4294. DOI: https://doi.org/10.1063/1.472247

Hernando J. A., Blum L., Phys. Rev. E, 2000, 62, 6577. DOI: https://doi.org/10.1103/PhysRevE.62.6577

Laird B. B., Wang J., Haymet A. D. J., Phys. Rev. E, 1993, 47, 2491. DOI: https://doi.org/10.1103/PhysRevE.47.2491

Laird B. B., Wang J., Haymet A. D. J., Phys. Rev. E, 1993, 48, 4145. DOI: https://doi.org/10.1103/PhysRevE.48.4145

Outhwaite C. W., In: Statistical Mechanics, Vol. 2, Singer K. (Ed.), The Royal Society of Chemistry, first edn., 1975, 188–255.

Quiñones A. O., Bhuiyan L. B., Abbas Z., Outhwaite C. W., Condens. Matter Phys., 2018, 21, 23802. DOI: https://doi.org/10.5488/CMP.21.23802

Quiñones A. O., Bhuiyan L. B., Abbas Z., Outhwaite C. W., J. Mol. Liq., 2023, 371, 12119. DOI: https://doi.org/10.1016/j.molliq.2022.121119

Molero M., Outhwaite C.W., Bhuiyan L. B., J. Mol. Liq., 2023, 390, 123025. DOI: https://doi.org/10.1016/j.molliq.2023.123025

Molero M., Outhwaite C. W., Bhuiyan L. B., Phys. Chem. Chem. Phys., 2024, 26, 10029. DOI: https://doi.org/10.1039/D3CP05808E

Ruas A., Moisy P., Simonin J.-P., Bernard O., Dufreche J.-F., Turq P., J. Phys. Chem. B, 2005, 109, 5243. DOI: https://doi.org/10.1021/jp0450991

Blum L., Mol. Phys., 1975, 30, 1529. DOI: https://doi.org/10.1080/00268977500103051

Høye J. S., Blum L., Mol. Phys., 1978, 78, 299. DOI: https://doi.org/10.1080/00268977800100221

Sanchez-Castro C., Blum L., J. Phys. Chem. B, 1989, 93, 7478. DOI: https://doi.org/10.1021/j100358a043

Outhwaite C. W., Chem. Phys. Lett., 1978, 53, 599. DOI: https://doi.org/10.1016/0009-2614(78)80078-5

Outhwaite C. W., J. Chem. Soc., Faraday Trans. 2, 1987, 83, 949. DOI: https://doi.org/10.1039/F29878300949

Outhwaite C. W., Molero M., Bhuiyan L. B., J. Chem. Soc., Faraday Trans., 1991, 87, 3227. DOI: https://doi.org/10.1039/FT9918703227

Outhwaite C. W., Molero M., Bhuiyan L. B., J. Chem. Soc., Faraday Trans., 1993, 89, 1315. DOI: https://doi.org/10.1039/FT9938901315

Outhwaite C. W., Molero M., Bhuiyan L. B., J. Chem. Soc. Faraday Trans., 1994, 90, 2002.

Outhwaite C. W., Condens. Matter Phys., 2004, 7, 719. DOI: https://doi.org/10.5488/CMP.7.4.719

Hansen J. -P., McDonald I. R., Theory of Simple Liquids, 2nd Edn., Academic Press, London, 1990.

Hribar Lee B., Vlachy V., Bhuiyan L. B., Outhwaite C. W., Molero M., Mol. Phys., 2003, 101, 2969. DOI: https://doi.org/10.1080/00268970310001608441

Reščič J., Vlachy V., Bhuiyan L. B., Outhwaite C. W., Langmuir, 2004, 21, 481. DOI: https://doi.org/10.1021/la049285+

Lamperski S., Mol. Simul., 2007, 33, 1193. DOI: https://doi.org/10.1080/08927020701739493

Frenkel D., Smit B., Understanding Molecular Simulation, From Algorithms to Applications, Academic Press, San Diego, 1996.

Kjellander R., Mitchell D. J., J. Chem. Phys., 1994, 101, 603. DOI: https://doi.org/10.1063/1.468116

Mitchell D. J., Ninham B. W., Chem. Phys. Lett., 1978, 53, 397. DOI: https://doi.org/10.1016/0009-2614(78)85426-8

Carnie S. L., Torrie G. M., Valleau J. P., Mol. Phys., 1984, 53, 253. DOI: https://doi.org/10.1080/00268978400102261

Harned H. S., Owen B. B., The Physical Chemistry of Electrolyte Solutions, 3rd ed., Reinhold, New York, 1958.

Robinson R. A., Stokes R. H., Electrolyte Solutions, 2nd ed., Dover, New York, 2002.

Guggenheim E. A., Stokes R. H., The International Encyclopedia of Physical Chemistry and Chemical Physics, Vol. 1, Equilibrium Properties of Aqueous Solutions of Single Strong Electrolytes, Pergammon Press, Oxford, 1969.

Bjerrum N., Dansk K., Videnskab. Selskab, Math.-Fys. Medd., 1926, 7, 1.

Barthel J., Krienke H., Kunz W., Physical Chemistry of Electrolyte Solutions: Modern Aspects, Topics in Physical Chemistry, Vol. 5, Springer, New York, 1998.

Holovko M., In: Ionic Soft Matter: Modern Trends in Theory and Applications, Henderson D., Holovko M., Trokhymchuk A. (Eds.), NATO Science Series II. Mathematics, Physics and Chemistry, Vol. 206, Springer, Dordrecht, 2005.

Rossky P. J., Dudowicz J. B.,Tembe B. L., Friedman H. L., J. Chem. Phys., 1980, 73, 3372. DOI: https://doi.org/10.1063/1.440533

Rogde S. A., Hafskjold B., Mol. Phys., 1983, 48, 1241. DOI: https://doi.org/10.1080/00268978300100891

Malatesta F., J. Solution Chem., 2020, 49, 1536. DOI: https://doi.org/10.1007/s10953-020-01041-8

Published

2025-03-28

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[1]
S. Lamperski, L. B. Bhuiyan, C. Outhwaite, and R. Gorniak, “Entropy of a restricted primitive model electrolyte using a mean electrostatic potential approach”, Condens. Matter Phys., vol. 28, no. 1, p. 13801, Mar. 2025, doi: 10.5488/cmp.28.13801.

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