Introduction to self-organization in chemical and electrochemical systems

Abstract

The world around us, and including us, is a huge dynamical system composed of dynamical subsystems in which, in course of irreversible processes, spontaneous organization of matter into patterns of different complexity, or simply— SHAPES, takes place. Since we believe that the second law of thermodynamics cannot be violated, the entropy decrease assist ing the formation of every pattern must be overcompensated by the entropy increase in simultaneously occurring dissipative processes. Since however not every irreversible process is a source of dynamic self-organization, in addition to this general thermodynamic condition, also, some additional strict kinetic criteria must be fulfilled: namely—the nonlinearity of the system’s dynamics and the presence of appropriately operating feedback loops in the kinetic mechanism. Finally, the control parameters, like, e.g., rate constants, initial concentrations of reactants, electrode potential or electric current, or temperature have to be tuned up to the values that throw the system out of its trivial stable steady-state towards self-organized instabilities, like the oscillations of the entire system’s state or spatial/spatiotemporal patterns. The concept of stability is thus crucial: the Bexotic^ selforganized dynamics is a consequence of a loss of stability of the Btrivial^ steady-state. The pulsations of our heart, the conduction of electric impulse along the axon, the oscillatory activity of our brain, the visually attractive patterns on the skins of animals, like zebras or snakes belong to the rich set of natural phenomena, the understanding of which is possible in terms of an interdisciplinary science, termed nonlinear dynamics. You might think that such impressive and crucial, for functioning of living matter, phenomena should attract the attention of many researchers, as it was the case, among others, for the Nobel Prize winners: I. Prigogine, M. Eigen, and more recently G. Ertl. However, this is evidently not the case for the majority of chemical community and the main reason for that lack of interest seems to be an insufficient education. Principles of nonlinear dynamics are in fact being taught only at those few universities, where people are working who have a serious interest in this topic and who share their knowledge and enthusiasm with the students. In consequence, the vast majority of chemists of all generations, who received only traditional education in chemistry, even if they heard something about oscillations or related phenomena, are not familiar at all with their fascinating scientific background. Moreover, a conservative way of education favors perception of nonlinear dynamics as a rather difficult and exotic discipline, for which ordinary chemists are not prepared. This is of course not true since the education in this area, as in all other disciplines, is only a question of an appropriate effort and motivation. In consequence of all these reservations of the chemical community, limited interest in chemical nonlinear dynamics manifests itself also in the area of interfacial electrochemistry, for which it is even easier than in homogeneous chemistry to drive the systems smoothly out from equilibrium, by simply varying the electrode potential or imposed current. Since most (electro)chemists are thus not familiar with nonlinear dynamics, it is useful to introduce here some of the basic concepts [1–9], in order to facilitate the reading of the contributions to this topical issue. If similar dynamic phenomena occur in different systems, they must have common mechanistic basis. From the physical point of view, the essential reason for the occurrence of the oscillatory behavior is the alternate domination of the positive and negative feedback loops in the system’s dynamics. From the mathematical point of view, the transition from the non-oscillatory, steady-state to * Marek Orlik morlik@chem.uw.edu.pl