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No Access Submitted: 02 May 2001 Accepted: 11 December 2001 Published Online: 05 March 2002

  • Theoretical equations of state for temperature and electromagnetic field dependence of fluid systems, based on the quasi-Gaussian entropy theory

J. Chem. Phys. 116, 4437 (2002); https://doi.org/10.1063/1.1448291
A. Amadei
  • Department of Chemical Sciences and Technology, University of Rome “Tor Vergata,” Via della Ricerca Scientifica 1, 00133, Rome, Italy
    • M. E. F. Apol
  • Department of Chemistry, University of Rome “La Sapienza,” P. le A. Moro 5, 00185, Rome, Italy
  • Department of Biophysical Chemistry, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
    • G. Brancato and A. Di Nola
  • Department of Chemistry, University of Rome “La Sapienza”, P. le A. Moro 5, 00185, Rome, Italy
    • more...View Contributors
    • A. Amadei
    • M. E. F. Apol
    • G. Brancato
    • A. Di Nola
  • See also: The Journal of Chemical Physics 116, 4426
    • ABSTRACT
    The quasi-Gaussian entropy (QGE) theory employs the fact that a free-energy change can be written as the moment-generating function of the appropriate probability distribution function of macroscopic fluctuations of an extensive property. By modeling this distribution, one obtains a model of free energy and resulting thermodynamics as a function of one state variable. In this paper the QGE theory has been extended towards theoretical models or equations of state (EOS’s) of the thermodynamics of semiclassical systems as a function of two state variables. Two “monovariate” QGE models are combined in the canonical ensemble: one based on fluctuations of the excess energy (the confined gamma state giving the temperature dependence) and the other based on fluctuations of the reduced electromagnetic moment [various models as derived in the preceding paper [Apol, Amadei, and Di Nola, J. Chem. Phys. 116, 4426 (2002)], giving the external field dependence]. This provides theoretical EOS’s for fluid systems as a function of both temperature and electromagnetic field. Special limits of these EOS’s are considered: the general weak-field EOS and the limit to a Curie’s law behavior. Based on experimental data of water and simulation data using the extended simple point charge (SPC/E) water model at 45.0 and 55.51 mol/dm3, the specific EOS based on a relatively simple combination of the confined gamma state model with a discrete uniform state field model accurately reproduces the dielectric properties of water at constant density, as the temperature dependence of the weak-field dielectric constant for gases and liquids, and the field dependence of the dielectric constant of liquids.

    REFERENCES
    Section:
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    1. 1. A. Amadei, M. E. F. Apol, and H. J. C. Berendsen, J. Chem. Phys. 106, 1893 (1997). Google ScholarScitation
    2. 2. A. Amadei, M. E. F. Apol, and H. J. C. Berendsen, J. Chem. Phys. 109, 3004 (1998). Google ScholarScitation
    3. 3. M. E. F. Apol, A. Amadei, H. J. C. Berendsen, and A. Di Nola, J. Chem. Phys. 111, 4431 (1999). Google ScholarScitation
    4. 4. M. E. F. Apol, A. Amadei, H. J. C. Berendsen, and A. Di Nola (unpublished). Google Scholar
    5. 5. M. E. F. Apol, A. Amadei, and H. J. C. Berendsen, J. Chem. Phys. 109, 3017 (1998). Google ScholarScitation
    6. 6. M. E. F. Apol, A. Amadei, and A. Di Nola, J. Chem. Phys. 116, 4426 (2002), preceding paper. Google ScholarScitation
    7. 7. D. Roccatano, A. Amadei, M. E. F. Apol, A. Di Nola, and H. J. C. Berendsen, J. Chem. Phys. 109, 6358 (1998). Google ScholarScitation
    8. 8. A. Amadei, M. E. F. Apol, G. Chillemi, H. J. C. Berendsen, and A. Di Nola, Mol. Phys. 96, 1469 (1999). Google ScholarCrossref
    9. 9. A. Amadei, G. Chillemi, M. A. Ceruso, A. Grottesi, and A. Di Nola, J. Chem. Phys. 112, 9 (2000). Google ScholarScitation
    10. 10. L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1, 3rd ed. (Pergamon, Oxford, 1980). Google Scholar
    11. 11. L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 2, 3rd ed. (Pergamon, Oxford, 1980). Google Scholar
    12. 12. Note that the classical potential energy and the mass tensors for a given configuration, as well as the integration limits, are in principle different for different quantum vibrational states. However, in Eq. (2) such differences can be in general safely neglected. It should be also noted that at zero field, Eq. (2) reduces to the usual expression [Eqs. (2) and (3) of Ref. 1], valid for semirigid molecules, if Πj=1N(det M̃j)1/2 is constant over the configurations. Hence the integral over the momenta can be considered independent of the coordinates, although the integrand generally is not. In that case the partition function can be factorized into two independent integrals: one over the coordinates involving the potential energy and another over the momenta involving the kinetic energy (Refs. 1, 10, and 11). Google Scholar
    13. 13. N. I. Johnson, S. Kotz, and A. W. Kemp, Univariate Discrete Distributions, 2nd ed. (Wiley, New York, 1992). Google Scholar
    14. 14. A. Stuart and J. K. Ord, Kendall’s Advanced Theory of Statistics, 5th ed. (Griffin, London, 1987), Vol. 1. Google Scholar
    15. 15. M. Aschi, R. Spezia, A. Di Nola, and A. Amadei, Chem. Phys. Lett. 344, 374 (2001). Google ScholarCrossref
    16. 16. M. Raynaud, C. Reynaud, Y. Ellinger, G. Hennico, and J. Delhalle, Chem. Phys. 142, 191 (1990). Google ScholarCrossref
    17. 17. C. Kittel, Introduction to Solid State Physics, 5th ed. (Wiley, New York, 1976). Google Scholar
    18. 18. B. I. Bleaney and B. Bleaney, Electricity and Magnetism, 3rd ed. (Oxford University Press, Oxford, 1976). Google Scholar
    19. 19. P. W. Selwood, Magnetochemistry, 2nd ed. (Interscience, New York, 1956). Google Scholar
    20. 20. K.-H. Hellwege, Einführung in die Festkörperphysik (Springer-Verlag, Berlin, 1976). Google Scholar
    21. 21. Note that a more general Gaussian [U′]+Gaussian [M′] expression of χ0(T), treating also the effect of sample shape, is given by Eq. (46) where in that case z(T)=T0/T. Google Scholar
    22. 22. H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem. 91, 6269 (1987). Google ScholarCrossref, ISI
    23. 23. D. P. Fernández, A. R. H. Goodwin, E. W. Lemmon, J. M. H. Levelt Sengers, and R. C. Williams, J. Phys. Chem. Ref. Data 26, 1125 (1997). Google ScholarScitation, ISI
    24. 24. W. Wagner and A. Kruse, Properties of Water and Steam (Springer-Verlag, Berlin, 1998). Google Scholar
    25. 25. D. P. Fernández, Y. Mulev, A. R. H. Goodwin, and J. M. H. Levelt Sengers, J. Phys. Chem. Ref. Data 24, 33 (1995). Google ScholarScitation, ISI
    26. 26. A. Amadei, Ph.D. thesis, Rijksuniversiteit Groningen, The Netherlands, 1998. Also available from http://docserver.ub.rug.nl/eldoc/dis/science/a.amadei/ Google Scholar
    27. 27. P. Schiebener, J. Straub, J. M. H. Levelt Sengers, and J. S. Gallagher, J. Phys. Chem. Ref. Data 19, 677 (1990). Google ScholarScitation
    28. 28. P. Schiebener, J. Straub, J. M. H. Levelt Sengers, and J. S. Gallagher, J. Phys. Chem. Ref. Data 19, 1617 (1990). Google ScholarScitation
    29. 29. F. Booth, J. Chem. Phys. 19, 391 (1951). Google ScholarScitation, ISI
    30. 30. F. Booth, J. Chem. Phys. 19, 1327 (1951). Google ScholarScitation, ISI
    31. 31. F. Booth, J. Chem. Phys. 19, 1615 (1951). Google ScholarScitation, ISI
    32. 32. H. A. Kolodziej, G. Parry Jones, and M. Davies, J. Chem. Soc., Faraday Trans. 2 71, 269 (1975). Google ScholarCrossref
    33. 33. Y. Marcus, The Properties of Solvents (Wiley, New York, 1998). Google Scholar
    34. 34. Y. Marcusand G. Hefter, J. Solution Chem. 28, 575 (1999). Google ScholarCrossref
    35. 35. I.-C. Yehand M. L. Berkowitz, J. Chem. Phys. 110, 7935 (1999). Google ScholarScitation, ISI
    36. 36. D. van der Spoel, P. J. van Maaren, and H. J. C. Berendsen, J. Chem. Phys. 108, 10220 (1998). Google ScholarScitation, ISI
    37. 37. S.-B. Zhu, S. Sing, and G. W. Robinson, Adv. Chem. Phys. 85, 627 (1994). Google Scholar
    38. 38. T. Darden, D. York, and L. Pedersen, J. Chem. Phys. 98, 10089 (1993). Google ScholarScitation, ISI
    39. 39. U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pederson, J. Chem. Phys. 103, 8577 (1995). Google ScholarScitation, ISI
    40. 40. S. W. de Leeuw, J. W. Perram, and E. R. Smith, Proc. R. Soc. London, Ser. A 373, 27 (1980). Google ScholarCrossref, ISI
    41. 41. M. Neumann, Mol. Phys. 50, 841 (1983). Google ScholarCrossref, ISI
    42. 42. H. J. C. Berendsen, D. van der Spoel, and R. van Drunen, Comput. Phys. Commun. 91, 43 (1995). Google ScholarCrossref, ISI
    43. 43. E. Lindahl, B. Hess, and D. van der Spoel, J. Mol. Model. [Electronic Publication] 7, 306 (2001). Google ScholarCrossref, ISI
    44. 44. D. van der Spoel, A. R. van Buuren, E. Apol et al., Gromacs User Manual Version 3.0 (Nijenborgh, Groningen, The Netherlands, 2001). Internet: http://www.gromacs.org, Google Scholar
    45. 45. H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. Di Nola, and J. R. Haak, J. Chem. Phys. 81, 3684 (1984). Google ScholarScitation, ISI
    46. 46. D. J. Evansand G. P. Morris, Comput. Phys. Rep. 1, 297 (1984). Google ScholarCrossref
    47. 47. T. Morishita, J. Chem. Phys. 113, 2976 (2000). Google ScholarScitation
    48. 48. S. Miyamotoand P. A. Kollman, J. Comput. Chem. 13, 952 (1992). Google ScholarCrossref, ISI
    49. 49. M. P. Allen and D. J. Tildesly, Computer Simulation of Liquids (Oxford University Press, Oxford, 1989). Google Scholar
    50. 50. T. P. Straatsma, H. J. C. Berendsen, and A. J. Stam, Mol. Phys. 57, 89 (1986). Google ScholarCrossref
    51. 51. M. Bishopand S. Frinks, J. Phys. Chem. 87, 3675 (1987). Google ScholarScitation
    52. 52. I. M. Svishchevand P. G. Kusalik, J. Phys. Chem. 98, 728 (1994). Google ScholarCrossref, ISI
    53. 53. L. Onsager, J. Am. Chem. Soc. 58, 1486 (1936). Google ScholarCrossref
    54. 54. D. C. Grahame, J. Chem. Phys. 21, 1054 (1953). Google ScholarScitation, ISI
    55. 55. W. Feller, An Introduction to Probability Theory and Its Application, 3rd ed. (Wiley, New York, 1968), Vol. 1. Google Scholar
    56. 56. A. Sauland W. Wagner, J. Phys. Chem. Ref. Data 18, 1537 (1989). Google ScholarScitation, ISI
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