ted lmes are shown m fig. 4b: the parameters are from ref. [ 181. .... Chem. 91. (1987) 5103. [ 131 J. Ross and L.S. Garcta-Cohn,. J. Phys. Chem. 93 (1989). 2091.
Chemical Physics North-Holland
152 (1992)
265-270
Equilibrium and nonequilibrium Oregonator model
steady states in the reversible
Arun K. Dutt ’ Physrcal Chernrstry Dmxon, Natronal Chewcal Laboratory, Poona 411008, India and Pure Chemstrv Department, Calcutta L~nrverslty.92.4.P.C. Road, Calcutta 700009, India Received
26 November
1991. in final form 22 January
1992
For the reversible Oregonator model a relationship between noneqmlibnum steady states and the eqtnlibnum state has been established using the thermodynamic formulation of chermcal affinity. which 1s also a measure of the distance from equilibrium of the system. In tlus mode1 the distance from equihbnum is found to be a function of the constant concentrations of reactant and product and a stoicluometnc factor between them for an overall open system reaction in wiuch there is no accumulation of the intermediates for each instant of time or over a complete cycle of the oscillations. Assummg that the system is initially m a far from equilibnum situation for certain values of the stolchiometric factor and the concentrations of reactant and product, the equilibnum state can be attamed in many cases merely by changing the blfurcatlon parameters (the concentrations of reactant and product and the stoichiometnc factor between them) suitably.
1. Introduction The thermodynamic formulation of closed and open isothermal systems greatly displaced from equilibrium is a subject of recent interest. The classical theory of irreversible processes was originally developed by Onsager [ 11, Prigogine [ 2 1, Haase [ 3 1, de Groot and Mazur [4]. There were attempts to extend the classical formalism by Garcia-Colin and coworkers [ 5-8 ] in the framework of the so-called extended irreversible thermodynamics [ 9- 141. The thermodynamics and mechanistic basis of the affinity decay of closed isothermal systems has been studied by Garfinkle, Garcia-Colin et al. and by Hjelmfelt et al. Gafinkle [ 15 ] claims that “A stoichiometric chemical reaction in a closed system traverses a unique natural path from reaction initiation to equilibrium. Along such a natural path the time rate of the charge of the thermodynamic functions can be analytically described independently of phenomenological or mechanistic consideration”. Garcia-Colin Present address: Max-Planck-Institut Fiir Emlhrungsphysiologie, Rheinlanddamm 20 I, W-4600 Dortmund I, Germany. 0301-0104/92/$05.00
0 1992 Elsevier Science Publishers
et al. [ 161 and Hjelmfelt et al. [ 171 have criticized Garfinkle’s claim and have proved that the affinity decay rate in general depends on the chemical reaction mechanism. The present work considers an open multistep chemical mechanism (reversible Oregonator [ 18 ] ) with parameters chosen such that the system is initially greatly displaced from equilibrium and which undergoes a Hopf bifurcation generating limit cycle oscillations. While moving back and forth between the oscillatory and nonoscillatory nonequilibrium regions, it is attempted to study how the distance from equilibrium changes due to these motions and also how the equilibrium state of the system can be attained by changing the parameters in different ways. One way is to stop the flow of the chemicals between the system and the surrounding as a result of which the concentrations of the reactants and products in the system, being driven by chemical kinetics, evolve in a direction such that finally the equilibrium state is reached. The second way to obtain the equilibrium state is to vary the bifurcation parameters suitably. In the present work a detailed study of the reversible Oregonator has been made in terms of the distance from equilibrium (chemical affinity multi-
B.V. All nghts reserved.
266
A.K. Dutt /Steady states rn the revewble Oregonator model
plied by a known factor at constant temperature) as a function of the bifurcation parameters and an effort has been made to obtain a relationship between nonequilibrium steady states and the equilibrium state. Moreover, the conceptual bases regarding nonequilibrium steady states and the equilibrium state in this model have been discussed.
