From cooperative phenomenato 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.
In catalysis there are several characteristic examples in which the presence of two, or more, components may influence the catalytic activity of a catalyst by changing its solid-state chemistry (1). Many solid catalysts are multicomponent materials (e.g. bismuth molybdates, perovskites, heteropolyanions, vanadium phosphate, and so on) with active phases and promoters mutually-interacting each other over different domains (2-3). Thus, either cooperative or synergistic phenomena may appear and the catalytic behavior typically results in a non-linear combination of complexity structures of active sites (4-6).
For instance, it has been shown through X-ray photoelectron spectroscopy (XPS) and electrical conductivity mea