Distribution patterns due to diffusion in a coagulation-fragmentation process with cluster-wall interactions

The chemical reactivity of metal nanoclusters is determined mainly by their size and their oxidation state. The control of metal particle size is essential in order to manipulate their reactivity and interfacial behavior. Uniformity of size and spatial distribution of the metal nanoclusters is essential in the study of their properties and can be achieved primarily by conducting their synthesis in the presence of stabilizers. These materials, such as surfactants or polymers, adsorb onto the surfaces of growing clusters and create a "shielding effect," a chemical barrier that prevents the effects of van der Waals interactions between particles, thus inhibiting particle aggregation. Polymers are frequently used as stabilizers for metal clusters because they are transparent, permeable, and nonconductive, and as such, do not interfere with and/or mask the potential optical, electrical, and catalytic properties of these clusters. When the concentration of the polymer in the reaction solution is above its critical coil overlap, entanglements occur, and hence the polymer may be viewed as a dynamically cross-linked network. Since the metal precursors can interact with the polymer via weak polar interactions, the metal cluster formation will therefore occur within the confines of these closed polymeric domains. In this work we will show, both theoretically and experimentally, the consequences of these interactions in the confines of the polymeric domains on metal particle size and particle size distribution.