Skip to main content
SpringerLink
Log in

Essentials of kinetics and thermodynamics for understanding chemical oscillations

  • Published:
Foundations of Chemistry Aims and scope Submit manuscript

Abstract

This paper presents a numerical study of the reaction A ↔ B in the presence of an intermediate and destabilizing step in its dynamics. After introducing a direct autocatalytic destabilizing process, namely quadratic autocatalysis (\(X + Y \to 2Y\)) and cubic autocatalysis (\(X + 2Y \to 3Y\)), a thermodynamic analysis of the evolution of the reaction in closed and open systems was performed. In addition, the Gibbs free energy, the thermodynamic affinity, and the entropy generation of the overall reaction were evaluated for each of the autocatalytic steps, in order to analyze the behavior of these thermodynamic quantities when the system moved towards equilibrium or towards oscillatory non-equilibrium states.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Aris, R., Gray, P., Scott, S.K.: Modelling cubic autocatalysis by successive bimolecular steps. Chem. Eng. Sci. 43, 207 (1988)

    Article  Google Scholar 

  • Borckmans, P., Metens, S.: An excursion in theoretical nonlinear chemistry: from oscillations to turing patterns. In: Borckmans, P., de Kepper, P., Khokhlov, A.R., Métens, S. (eds.) Chemomechanical Instabilities in Responsive Materials. Springer, Netherlands, pp. 57–94 (2009)

  • Cook, G.B., Gray, P., Knapp, D.G., Scott, S.K.: Bimolecular routes to cubic autocatalysis. J. Phys. Chem. 93, 2749 (1989)

    Article  Google Scholar 

  • de Groot, S.R., Mazur, P.: Non-equilibrium Thermodynamics. Dover, New York (2011)

    Google Scholar 

  • Demirel, Y.: Nonequilibrium Thermodynamics: Transport and Rate Processes in Physical, Chemical and Biological Systems. Elsevier, North Holland (2007)

    Google Scholar 

  • Demirel, Y.: Nonequilibrium thermodynamics modeling of coupled biochemical cycles in living cells. J. Non Newton. Fluid. 165, 953 (2010)

    Article  Google Scholar 

  • Epstein, I.: Oscillating chemical reactions and nonlinear dynamics. J. Chem. Educ. 66, 195 (1989)

    Article  Google Scholar 

  • Epstein, I.R., Pojman, J.: An introduction to nonlinear chemical dynamics: oscillations, waves, patterns, and chaos. Oxford University Press, Oxford (1998)

    Google Scholar 

  • Field, R.J., Koros, E., Noyes, R.M.: Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate–cerium–malonic acid system. J. Am. Chem. Soc. 94, 8649 (1972)

    Article  Google Scholar 

  • Garcia-Colín, L.S., Piña, E., de la Selva, S.M.T.: On the thermodynamic basis of the affinity decay rate. J. Chem. Phys. 92, 3545 (1990)

    Article  Google Scholar 

  • Garfinkle, M.: The thermodynamic natural path in chemical reaction kinetics. Discret. Dyn. Nat. Soc. 4, 145 (2000)

    Article  Google Scholar 

  • Gray, P., Scott, S.K.: Chemical Oscillations and Instabilities, Nonlinear Chemical Kinetics. Clarendon, Oxford (1990)

    Google Scholar 

  • Irvin, B.R., Ross, J.: Calculation of the rate of entropy production for a model chemical reaction. J. Chem. Phys. 89, 1064 (1988)

    Article  Google Scholar 

  • Kay, S.R., Scott, S.K., Tomlin, A.S.: Quadratic autocatalysis in a non-isothermal CSTR. Chem. Eng. Sci. 44, 1129 (1989)

    Article  Google Scholar 

  • Kondepudi, D.K., Prigogine, I.: From Heat Engines to Dissipative Structures. Wiley, New York (1998)

    Google Scholar 

  • Lefever, R., Nicolis, G., Borckmans, P.: The Brusselator: it does oscillate all the same. J. Chem. Soc. Faraday Trans. 84, 1013 (1988)

    Article  Google Scholar 

  • Li, Y., Qian, H., Yi, Y.: Oscillations and multiscale dynamics in a closed chemical reaction system: second law of thermodynamics and temporal complexity. J. Chem. Phys. 129, 154505 (2008)

    Article  Google Scholar 

  • Martyushev, L.M., Seleznev, V.D.: Maximum entropy production principle in physics, chemistry and biology. Phys. Rep. 426, 1 (2006)

    Article  Google Scholar 

  • Pacault, A., Hanusse, P., De Kepper, P., Vidal, C., Boissonade, J.: Phenomena in homogeneous chemical systems far from equilibrium. Acc. Chem. Res. 9, 438 (1976)

    Article  Google Scholar 

  • Prigogine, I., Defay, R.: Chemical Thermodynamics. Longmans, London (1954)

    Google Scholar 

  • Prigogine, I.: Introduction to Thermodynamics of Irreversible Processes. Interscience, New York (1967)

    Google Scholar 

  • Rastogi, R.P., Mathur, P.: Open systems in non-equilibrium: complexity, dynamics, modeling and mechanism. J. Sci. Ind. Res. 71, 453 (2012)

    Google Scholar 

  • Rastogi, R.P.: Introduction to Non-equilibrium Physical Chemistry. Elsevier, Ámsterdam (2007)

    Google Scholar 

  • Ross, J., García-Colín, L.S.: Thermodynamics of chemical systems far from equilibrium. J. Phys. Chem. 93, 2091 (1989)

    Article  Google Scholar 

  • Ross, J., Vlad, M.O.: Exact solutions for the entropy production rate of several irreversible processes. J. Phys. Chem. A 109, 10607 (2005)

    Article  Google Scholar 

  • Sagués, F., Epstein, I.: Nonlinear chemical dynamics. Dalton Trans. 7, 1201 (2003)

    Article  Google Scholar 

  • Saikhanov, M.B.: On the thermodynamic and kinetic stability of nonequilibrium systems. Russ. J. Phys. Chem. A 80, 1170 (2006)

    Article  Google Scholar 

  • Scott, S.K.: Oscillations in simple models of chemical systems. Acc. Chem. Res. 20, 186 (1987)

    Article  Google Scholar 

  • Tyson, J.J.: Classification of instabilities in chemical reaction systems. J. Chem. Phys. 62, 1010 (1975)

    Article  Google Scholar 

  • Van Rysselberghe, P.: The fundamentals of chemical thermodynamics. Chem. Rev. 16, 37 (1935)

    Article  Google Scholar 

  • Vellela, M., Qian, H.: Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlögl model revisited. J. R. Soc. Interface 6, 925 (2009)

    Article  Google Scholar 

  • Wilhelm, T., Heinrich, R.: Smallest chemical reaction system with Hopf bifurcation. J. Math. Chem. 17, 1 (1995)

    Article  Google Scholar 

  • Wang, J.: Modern Thermodynamics, pp. 1–18. Springer, Berlin (2012)

    Google Scholar 

Download references

Acknowledgments

In memory of Dr. Alfredo Gómez O. (1943–2011), our friend, colleague and professor for many years in the Departamento de Química, Facultad de Ciencias, Universidad Nacional de Colombia Sede Bogotá. Financial support by the DIME-Universidad Nacional de Colombia (grant 201010013024) is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Facultad de Ciencias, Escuela de Química, Universidad Nacional de Colombia, Núcleo El Volador, Bloque 16, Oficina 413, Calle 59A No 63-20, Medellín, Colombia

    Daniel Barragán

Authors
  1. Daniel Barragán
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Barragán.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barragán, D. Essentials of kinetics and thermodynamics for understanding chemical oscillations. Found Chem 17, 93–106 (2015). https://doi.org/10.1007/s10698-015-9221-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10698-015-9221-4

Keywords

Search

Navigation