Proving Cooperativity of a Catalytic Reaction by Means of Nanoscale Geometry: The Case of Click Reaction.

Establishing whether a reaction is catalyzed by a single-metal catalytic center or cooperatively by a fleeting complex encompassing two such centers may be an arduous pursuit requiring detailed kinetic, isotopic, and other types of studies─as illustrated, for instance, by over a decade-long work on single-copper versus di-copper mechanisms of the popular "click" reaction. This paper describes a method to interrogate such cooperative mechanisms by a nanoparticle-based platform in which the probabilities of catalytic units being proximal can be varied systematically and, more importantly, independently of their volume concentration. The method relies on geometrical considerations rather than a detailed knowledge of kinetic equations, yet the scaling trends it yield can distinguish between cooperative and non-cooperative mechanisms.