Investigations Of Complex Coupled Effect In BZ Reaction

Classical thermodynamics has perfectly explained the behavior of complex systems that tend to equilibrium and disordered states spontaneously,however,a large number of examples of spontaneous processes leading to order found in both the living and non-living worlds cannot be interpreted by it,so the nonlinear and non-equilibrium thermodynamics came into being.Prigogine introduced the concept of dissipative structure in the 1950 s and the Brussels School was established.Since then,the theory of dissipative structure has been extensively developed.As the dissipative structure is an ordered structure that may appear after a system is unstable.Therefore,the conditions under which the system loses its stability must first be determined.In this article,we mainly discussed the influence of complex coupling on the instability of the system and the appearance of dissipative structure.Firstly,the influence of compound coupling in the Brusselator model was discussed.In our studies,the compound coupling term in the thermodynamic flow was found through the thermodynamic analyses,and then it was used to analyze the excess entropy production of the system.And we found that,the larger compound coupling in the system is,the easier the excess entropy production of the system will turn to be less than zero.Obviously,in this case,the easier the system is to lose its stability,and the more likely a dissipative structure will appear.In addition,the dynamics of this system was also studied to find the possibility of system instability from the dynamics of the system.By comparing the analysis results from two different angles,we found that the results are consistent with each other,in other words,only when there is a strong complex coupling factor the system is more prone to be instability,and the dissipative structure will be easier to appear.It is noted that above analysis is based on ideal models.Therefore,in order to make the discussions more meaningful,the specific chemical reaction such as B-Z reaction should be included in our studies.It is well known that,in B-Z reaction,the malonic acid is oxidized by sodium salt under the condition of metal cerium ion as a catalyst,which can result in orderly chemical oscillation.We first analyzed it from the perspective of thermodynamics.By analyzing the relationship between the generalized thermodynamic flow and the generalized thermodynamic force,the complex coupling factor in the reaction was found out.Next,by analyzing its excess entropy production,it was found that the contribution of the complex coupling factor to the excess entropy production is negative,and this means that the greater the complex coupling effect is,the easier the excess entropy production is less than zero,and the easier the dissipative structure to appear.And this conclusions were further verified by the dynamic analyses.To sun up,it is clear that,in a non-equilibrium system,the complex coupling effect plays the most important roles for the instability of the steady-state,so the stronger complex coupling effect is helpful for a dissipative structure to appear.