From cooperative phenomena to synergetic hyperstructures in catalysis

Synergistic and cooperative phenomena in catalysis are defined here via a formal classification of the catalytic systems, using the combination of game theory and hyperstructure theory. Game theory is based on the idea that players are rational decision-makers; therefore, making a transposition is reported as rational, the chemical choice. Three catalytic reactions are considered as characteristic examples: i) the degradation of an azo-dye (Acid Orange 7) with vanadium/hydrogen peroxide/ascorbic acid solutions (homogeneous catalysis); ii) the total oxidation of ethene and iii) the carbon monoxide oxidation over Cu-Ce mixed oxide catalysts (heterogeneous catalysis). According to the game theory, these reactions are paradigms of not-zero sum, asymmetrical and synchronous cooperative-games. The players (i.e. active phases/centres) exhibit a finite number of pure strategies, reflected by their concentrations, and play a strategic game. Moreover, there is the Nash equilibrium and even Pareto equilibrium in the synergistic case. Since the effects of the structural relations among players depend on the catalytic system, a scale of magnitude (in terms of catalytic benefits) is proposed: cooperation < synergetic hyperstructure << strong synergetic hyperstructure. From cooperative phenomena to synergetic hyperstructures in catalysis