Journal of Mathematical Chemistry

, Volume 42, Issue 4, pp 859–891 | Cite as

Model hysteresis dimer molecule I: Equilibrium properties

  • Christopher G. Jesudason

A Hamiltonian system describing hysteresis behavior in a dimeric chemical reaction is modeled in a MD simulation utilizing novel two-body potentials with switches that is particularly suitable for numerical thermodynamical investigations. It is surmized that such reaction mechanisms could exist in nature on the basis of recent experiments, which indicate that electromagnetic hysteresis behavior is exhibited at the molecular level, although experimental interpretations tend to construct models that avoid such mechanisms. Numerical results of various common equilibrium thermodynamical and kinetic properties are presented together with new algorithms that were implemented to compute these quantities, where no unusual thermodynamics was observed for the chemical reaction which might be interpreted as not being “time reversible invariant” and therefore susceptible to manifesting unusual thermodynamical phenomena, which might contradict any of the known laws of thermodynamics. A revision of the concept of “time reversibility” to accommodate the above results is suggested. The general design of the reaction mechanism also allows for the use of conventional potentials and by the utilization of switches, overcomes the bottleneck of computations which involves multi-body interactions.


hysteresis chemical reaction model thermodynamics of reaction kinetic properties 

2000 AMS mathematics classification

65-{04,Z05} 68-{04,W01} 70-{08,F01,F16} 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hendrickson D.N, Single-molecule magnets, in: Abstracts of Papers, 225th ACS National Meeting 2003 (American Chemical Society, Washington DC, 2003).Google Scholar
  2. 2.
    Gatteschi D, (2001) From molecular magnets to magnetic molecules, Actual. Chimique. 6: 21–26Google Scholar
  3. 3.
    Sanudo E, Carolina E, Wernsdorfer W, Abboud K.A., Christou G, (2004) Synthesis, structure, and magnetic properties of a Mn21 single-molecule magnet, Inorg. Chem. 43(14): 4137–4144CrossRefGoogle Scholar
  4. 4.
    Jesudason C.G, (1999) I. Time’s Arrow, detail balance, Onsager reciprocity and mechanical reversibility: Basic Considerations. Apeiron 6(1–2): 9–24Google Scholar
  5. 5.
    Jesudason C.G, (1999) II Time’s Arrow, detail balance, Onsager reciprocity and mechanical reversibility: Thermodynamical Illustrations. Apeiron 6(1–2): 172–185Google Scholar
  6. 6.
    Allen M.P, Schofield P, (1980) Molecular dynamics simulation of a chemical reaction in solution. Mol Phys. 39(1): 207–215CrossRefGoogle Scholar
  7. 7.
    Zeiri Y, Hood E.S, (1985) Nonequilibrium distributions in reactive systems. Phys. Rev. Letts. 55(6): 634–637CrossRefGoogle Scholar
  8. 8.
    Gorecki J, Gryko J, (1989) Molecular dynamics simulation of a chemical reaction. Comput. Phys. Commun. 54: 245–249CrossRefGoogle Scholar
  9. 9.
    Stillinger F.H., Weber T.A, (1988) Molecular dynamics simulation for chemically reactive substances. fluorine. J. Chem. Phys. 88(8): 5123–5133Google Scholar
  10. 10.
    Benjamin I, Gertner B.J, Tang N.J, Wilson K.R, (1990) Energy flow in an atom exchange chemical reaction in solution. J. Am. Chem. Soc. 112: 524–530CrossRefGoogle Scholar
  11. 11.
    Bergsma J.P, Reimers J.R, Wilson K.R, Hynes J.T, (1986) Molecular dynamics of the A+BC reaction in a rare gas solution. J. Chem. Phys. 85(10): 5625–5643CrossRefGoogle Scholar
  12. 12.
    Hafskjold B, Ikeshoji T,(1995) Partial specific quantities computed by nonequilibrium dynamics, Fluid Phase Equilibr. 104, 173–184CrossRefGoogle Scholar
  13. 13.
    Jesudason C.G, (2005) The Clausius inequality: implications for non-equilibrium thermodynamic steady states with NEMD corroboration. Nonlinear Anal. 63(5–7): e541–e553CrossRefGoogle Scholar
  14. 14.
    Levine R.D, Bernstein R.B, Molecular Reaction Dynamics and Chemical Reactivity (Oxford University Press, Oxford, 1987) esp. pp. 375–376 and figure 6.60.Google Scholar
  15. 15.
    Ikeshoji T, Hafskjold B, (1994) Non-equilibrium molecular dynamics calculation of heat conduction in liquid and through liquid gas interface. Mol. Phys, 81(2): 251–261CrossRefGoogle Scholar
  16. 16.
    Levine I.N, (2003). Physical Chemistry, 5th ed. McGraw-Hill, SingaporeGoogle Scholar
  17. 17.
    Jesudason C.G, (2006) An energy interconversion principle applied in reaction dynamics for the determination of equilibrium standard states. J. Math. Chem. (JOMC) 39(1): 201–230CrossRefGoogle Scholar
  18. 18.
    Laidler K.J., Chemical Kinetics, 3rd ed. (Harper & Row, New York 1987) esp. pp. 74–75.Google Scholar
  19. 19.
    Debye P, (1945). Polar Molecules-1929 reprint edn. Dover Publications Inc, New YorkGoogle Scholar
  20. 20.
    O’Konski C.T., Haltner A.J,(1956) Characterization of the monomer and dimer of tobacco mosaic virus by transient elastic birefringence relaxation of optically anisotropic crystals. J. Am. Chem. Soc. 78, 3604–3610CrossRefGoogle Scholar
  21. 21.
    Broersma S, (1960) Rotational Diffusion constant of a cylindrical particle. J. Chem. Phys. 32(6): 1626–1631CrossRefGoogle Scholar
  22. 22.
    Moog R, Bankert D, Maroncelli M, (1993) Rotational diffusion of Coumarin 102 in Trifluoroethanol: the case for solvent attachment. J. Phys. Chem. 97: 1496–1501CrossRefGoogle Scholar
  23. 23.
    Srivastava A, Doraiswamy S., (1995) Rotational diffusion of Rose Bengal. J. Chem. Phys. 103(14): 6197–6205CrossRefGoogle Scholar
  24. 24.
    Pathria R.K, (2001). Statistical Mechanics (2/e). Butterworth-Heinemannm, OxfordGoogle Scholar
  25. 25.
    Lynden-Bell R.M., (1984) Comparison of the results from simulations with the predictions of models for molecular reorientation. In: Barnes A.J, Orville Thomas W.J., Yarwood J. (eds). Molecular Liquids—Dynamics and Interactions. D. Reidel Publishing Co, Dordrecht/Boston/ Lancaster, pp. 501–518Google Scholar
  26. 26.
    Levesque D, Verlet L., (1970) Computer “experiments” on classical fluids, III. time dependent self-correlation functions. Phys. Rev. A 2(6): 2514–2528CrossRefGoogle Scholar
  27. 27.
    Nakanishi K, Toukubo K, Watanabe N, (1978) Molecular dynamics studies of Lennard-Jones liquid mixtures: further calculation on the behavior of one different particle as a model of real fluid systems. J. Chem. Phys. 68(5): 2041–2045CrossRefGoogle Scholar
  28. 28.
    Jesudason C.G, Examples Include W.C.N.A 2004 (Orlando, Florida, U.S.A, 2004) and in presentation entitled Equilibrium properties of a hysteresis dimer molecule from MD simulations using two-body potentials, in: International Conference on Numerical Analysis and Applied Mathematics 2005, eds. Simos T.E, G. Psihoyios and Ch. Tsitouras (Wiley-VCH, Weinheim, 2005) pp. 287–290Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Chemistry DepartmentUniversity of MalayaKuala LumpurMalaysia

Personalised recommendations