CHEMICAL ENGINEERING AND COMPLEXITY, AN UNDISSIPATED STRUCTURE...YET.

Abstract

One of the main contributions of Ilya Prigogine, Nobel Prize in Chemistry in 1977, was the understanding of the three fields of thermodynamics, that is, the thermodynamics of systems in equilibrium, near equilibrium, and far from equilibrium. This last field, which is called the complexity sciences (CC), opened the understanding of creating order out of chaos with Prigogine’s Dissipative Structures. This paper presents the basics of the CC with the perspective of Chemical Engineering, presenting its utility in unstable simple reactions and in reactive distillation. All within the framework of education and training of chemical engineers, with the view that the Sciences of Complexity, more than a tool, constitute an approach that can transform the performance of engineering and the role we engineers play in the society. 1. DISSIPATIVE STRUCTURES The concept of Dissipative Structures was proposed by Ilya Prigogine in 1930 as a consequence of unexplained phenomena found in chemical reactions, such as the production of enantiomers, or oscillatory reactions. His explanation was in terms of that far from equilibrium, nature tends to find new forms of organization that seem to be unpredictable, but that in the end by self-organization, a new ordered structure is created, dissipating energy 9 . 1.1. Stability Criteria The basic foundation for the Dissipative Structures is that, since for a system in a stationary state (that could be an equilibrium state) its entropy must not be changing in time, so that the stability under perturbation for this stationary state is determined by the nature of second order variations in entropy, that is, if the second derivative is positive, then the system is under an unstable state, and a perturbation will take it out of it. For chemical reactions, the entropy change can be expressed as: 1 For the second order change we have: Area tematica: Engenharia das Separacoes e Termodinâmica 1 1 1 For chemical reactions is convenient to use the reaction coordinate: dN ν de. For U and V constant, the expressions become: 1 Where ∑ is called the Affinity of the reaction. It may be also expressed as: ,! For the second order change in entropy: 2 #  $ %& , 2 For the change in entropy after a perturbation, considering the second order term. ∆ ( ) 12 If the initial state was an equilibrium state, then the first order δS must vanish, since the entropy in equilibrium states reaches a maximum. Moreover, for the second order variation to be a stable change, must be negative, in order to be necessary an increase in entropy to come back in equilibrium, that is, for perturbations in systems under stable equilibrium: 12 1 2  , 0 To use this expression for the analysis of stationary states, is necessary to derivate with respect of time, obtaining for one simple reaction: 12 . ./  0 0 Where A RTln R6/R8 , υ R6 ( R8 and with Rf and Rr being the forward and reverse velocities of reaction. Consider for instance the autocatalitic reaction: Area tematica: Engenharia das Separacoes e Termodinâmica 2