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Relationship between Classical and Quantum Mechanics in Micellar Aqueous Solutions of Surfactants

  • WAVE METHOD OF AQUEOUS SOLUTION RESEARCH
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Abstract

Micellar aqueous solutions of ionic surfactants have been observed to exhibit proton delocalization (the nuclear quantum effect) and to oscillate between a low density (LDL) and a high-density liquid (HDL) state of water at a fixed temperature. It is shown in this paper that such phenomena can be explained with the help of the interpolating Schrӧdinger equation proposed by Ghose. The nuclear quantum effect can be described by the tunneling of a harmonic oscillator in a symmetric double-well potential, and an ensemble of harmonic oscillators can model the LDL-HDL oscillations. The thermodynamics of such harmonic oscillators has been worked out showing continuous transitions between the quantum and classical limits.

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Fig. 1.
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REFERENCES

  1. Yu. A. Mirgorod and T. A. Dolenko, “Liquid polyamorphous transition and self- organization in aqueous solutions of ionic surfactants,” Langmuir 31 (31), 8535–8547 (2015). https://doi.org/10.1021/acs.langmuir.5b00479

    Article  CAS  PubMed  Google Scholar 

  2. T. H. Boyer, “Thermodynamics of the harmonic oscillator: Wien’s displacement law and the Planck spectrum,” Am. J. Phys. 71 (9), 866–870 (2003). https://doi.org/10.1119/1.1566782

    Article  ADS  Google Scholar 

  3. L. de la Peña, A. Valdés-Hernández, and A. M. Cetto, “Statistical consequences of the zero-point energy of the harmonic oscillator,” Am. J. Phys. 76 (10), 947–955 (2008). https://doi.org/10.1119/1.2948780

    Article  ADS  Google Scholar 

  4. Yu. Mirgorod and M. A. Storozhenko, “The role of zero-point energy of water in micelle formation of ionic surfactants” (2020). https://doi.org/10.13140/RG.2.2.21836.44161/1

  5. L. Liu and Q.-X. Guo, “Isokinetic relationship, isoequilibrium relationship, and enthalpy-entropy compensation,” Chem. Rev. 101 (3), 673–696 (2001). https://doi.org/10.1021/cr990416z

    Article  CAS  PubMed  Google Scholar 

  6. K. Schӧnhammer, “Quantum versus thermal fluctuations in the harmonic chain and experimental implications,” ar**v:2008.11005 [quant-ph] (2020). https://arxiv.org/abs/2008.11005

  7. B. O. Koopman, “Hamiltonian systems and transformation in Hilbert space,” Proc. Natl. Acad. Sci. U. S. A. 17 (5), 315–318 (1931). https://doi.org/10.1073/pnas.17.5.315

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  8. J. von Neumann, “Zur Operatorenmethode In Der Klassischen Mechanik,” Ann. Math. 33 (3), 587–642 (1932). https://doi.org/10.2307/1968537

    Article  MathSciNet  Google Scholar 

  9. J. von Neumann, “Zusatze Zur Arbeit “Zur Operatorenmethode …,” Ann. Math. 33 (4), 789–791 (1932). https://doi.org/10.2307/1968225

    Article  MathSciNet  Google Scholar 

  10. D. Mauro, Ph. D. Thesis, ar**v:quant-ph/0301172 and References Therein (2003).

  11. P. Ghose, “A continuous transition between quantum and classical mechanics. I,” Found. Phys. 32 (6), 871–892 (2002). https://doi.org/10.1023/A:1016055128428

    Article  MathSciNet  Google Scholar 

  12. P. Ghose and M. K. Samal, “A continuous transition between quantum and classical mechanics. II,” Found. Phys. 32 (6), 893–906 (2002). https://doi.org/10.1023/A:1016007212498

    Article  MathSciNet  Google Scholar 

  13. H. Goldstein, Classical Mechanics (Addison-Wesley, London, 1950).

    Google Scholar 

  14. A. Benseny, D. Tena, and X. Oriols, “On the classical Schrӧdinger equation,” ar**v:1607.00168 [quant-ph] (2016). https://doi.org/10.48550/ar**v.1607.00168

  15. P. Ghose and K. von Bloh, “Continuous transition between quantum and classical behavior for a harmonic oscillator,” Wolfram Demonstrations Project (January 9, 2017). http://demonstrations.wolfram.com/ContinuousTransitionBetweenQuantumAndClassicalBehaviorForAHa/

  16. P. Ghose and K. von Bloh, “Continuous transitions between quantum and classical motions,” ar**v: 1608.07963v2 [quant-ph] (2017). https://doi.org/10.48550/ar**v.1608.07963

  17. S. Chakravarty, “Quantum fluctuations in the tunneling between superconductors,” Phys. Rev. Lett. 49 (9), 681–684 (1982). https://doi.org/10.1103/PhysRevLett.49.681

    Article  ADS  CAS  Google Scholar 

  18. S. Chakravarty and A. J. Leggett, “Dynamics of the two-state system with Ohmic dissipation,” Phys. Rev. Lett. 52 (1), 5–8 (1984). https://doi.org/10.1103/PhysRevLett.52.5

    Article  ADS  Google Scholar 

  19. D. Bohm, “A suggested interpretation of the quantum theory in terms of “hidden” variables. I,” Phys. Rev. 85 (2), 166–179 (1952). https://doi.org/10.1103/PhysRev.85.166

    Article  ADS  MathSciNet  CAS  Google Scholar 

  20. D. Bohm, “A suggested interpretation of the quantum theory in terms of “hidden” variables. II,” Phys. Rev. 85 (2), 180–193 (1952). https://doi.org/10.1103/PhysRev.85.180

    Article  ADS  MathSciNet  CAS  Google Scholar 

  21. C. Huang, K. T. Wikfeldt, T. Tokushima, D. Nordlund, Y. Harada, U. Bergmann, M. Niebuhr, T. M. Weiss, Y. Horikawa, M. Leetmaa, M. Ljungberg, O. Takahashi, A. Lenz, L. Ojamäe, P. Lyubartsev, S. Shin, L. G. M. Pettersson, and A. Nilsson, “The inhomogeneous structure of water at ambient conditions,” Proc. Natl. Acad. Sci. U. S. A. 106 (36), 15214–15218 (2009). https://doi.org/10.1073/pnas.0904743106

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  22. Yu. Mirgorod, “Quantum nuclear effect in aqueous ionic surfactant and polyelectrolytes solutions,” Nat. Conf. “Bio-Inspired Nanomaterials” (Seoul, South Korea, November 14–15, 2021). https://doi.org/10.13140/RG.2.2.32364.08325

  23. Yu. A. Mirgorod, S. G. Emelyanov, and M. A. Pugachesky, RF Patent No. 2730433, Byull. Izobret., No. 24 (2020).

  24. I. A. Shcherbakov, “Influence of external impacts on the properties of aqueous solution,” Phys. Wave Phenom. 29 (2), 89–93 (2021). https://doi.org/10.3103/S1541308X21020114

    Article  ADS  Google Scholar 

  25. G. A. Lyakhov, V. I. Man’ko, and I. A. Shcherbakov, “Action of classical fields on quantum systems within the Schrödinger–Robertson uncertainty relation,” Phys. Wave Phenom. 30 (3), 169–173 (2022). https://doi.org/10.3103/S1541308X22030049

    Article  ADS  Google Scholar 

  26. G. A. Lyakhov, V. I. Man’ko, N. V. Suyazov, I. A. Shcherbakov, and M. A. Shermeneva, “Physical mechanisms of activation of radical reactions in aqueous solutions under mechanical and magnetic effect: Problem of singlet oxygen,” Phys. Wave Phenom. 30 (3), 174–181 (2022) https://doi.org/10.3103/S1541308X22030050

    Article  ADS  Google Scholar 

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ACKNOWLEDGMENTS

The authors are grateful to Anirban Mukherjee for collaborating to develop the double-well potential section, to Partha Nandi for plotting Figs. 2 and 3, and Alexander Pribylov for his help in preparing the manuscript.

Funding

Study was financially supported by the Ministry of Education and Science of the Russian Federation (2020, no. 0851-2020-0035). For Y.M. the study was carried out as a part of the Strategic Academic Leadership Program “Priority 2030” (Agreement no. 075-15-2021-1213, Russian Federation).

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Authors and Affiliations

  1. Tagore Centre for Natural Sciences and Philosophy, Rabindra Tirtha, New Town, 700156, Kolkata, India

    Partha Ghose

  2. Southwest State University, 305040, Kursk, Russia

    Yuri Mirgorod

Authors
  1. Partha Ghose
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  2. Yuri Mirgorod
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Contributions

Y.M. designed and directed the research, and contributed to the interpretation of the results. P.G. carried out applications of the interpolating Schrӧdinger equation and developed the thermodynamics of harmonic oscillators for micellar solutions. The authors made equal contributions to the writing of the article.

Corresponding author

Correspondence to Yuri Mirgorod.

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The authors declare that they have no conflicts of interest.

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Ghose, P., Mirgorod, Y. Relationship between Classical and Quantum Mechanics in Micellar Aqueous Solutions of Surfactants. Phys. Wave Phen. 32, 34–42 (2024). https://doi.org/10.3103/S1541308X24010072

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