Autocatalytic cluster growth

Actually, the kinetics study of the redox potential of transient clusters (Section 20.3.2) has shown that beyond the critical nuclearity, they receive electrons without delay from an electron donor already present. The critical nuclearity depends on the donor potential and then the autocatalytic growth does not stop until the metal ions or the electron donor are not exhausted (Fig. 8c). An extreme case of the size development occurs, despite the presence of the polymer, when the nucleation induced by radiolytic reduction is followed by a chemical reduction. The donor D does not create new nuclei but allows the supercritical clusters to develop. This process may be used to select the cluster final size by the choice of the radiolytic/chemical reduction ratio. But it also occurs spontaneously any time when even a mild reducing agent is present during the radiolytic synthesis. The specificity of this method is to combine the ion reduction successively ... 

Figure 6.15. Schematic of the four-step mechanism for transition metal (e.g., Pt) nanocluster formation. Shown are (i) nucleation to a desired cluster size (ii) autocatalytic growth onto the cluster surface (hi) diffusive agglomerative growth of two nanoclusters and (iv) autocatalytic agglomeration into bulk metal particulates. Reproduced with permission from Besson, C. Finney, E. E. Einke, R. G. J. Am. Chem. Soc. 2005,127, an9. Copyright 2005 American Chemical Society.

Although the environment ofthe clusters is different in solutions and at the surface of silver halide crystals, we proposed to extend the same growth mechanism, which was demonstrated by pulse radiolysisfor Ag J clusters free in solution, to a theoretical explanation ofthe development process in photography [7] (Fig. 10). The development occurs in both cases at the interface between an aqueous solution of an electron donor and a silver cluster acting as an autocatalytic growing site alternately accepting electrons and silver ions. 

Cluster properties, mostly those that control electron transfer processes such as the redox potential in solution, are markedly dependent on their nuclearity. Therefore, clusters of the same metal may behave as electron donor or as electron acceptor, depending on their size. Pulse radiolysis associated with time-resolved optical absorption spectroscopy is used to generate isolated metal atoms and to observe transitorily the subsequent clusters of progressive nuclearity yielded by coalescence. Applied to silver clusters, the kinetic study of the competition of coalescence with reactions in the presence of added reactants of variable redox potential allows us to describe the autocatalytic processes of growth or corrosion of the clusters by electron transfer. The results provide the size dependence of the redox potential of some metal clusters. The influence of the environment (surfactant, ligand, or support) and the role of electron relay of metal clusters in electron transfer catalysis are discussed. 

Electron Transfer Mechanism. Thus, the first oxidation step of the hydroquinone occurs, provided the nuclearity is supercritical, n> nc, which means when the potential °(Ag, + i-Ag +i) becomes higher than the threshold °(Q "-QH2). Then the supercritical cluster acts as a nucleus for its own growth through an autocatalytic electron transfer (reactions 5,6) according to the mechanism that was summarized by reaction 12 ... 

Figure 6. Transient optical absorption signals of the electron donor decay (reduced form of sulfonato-propyl viologen SPV at 650 nm) and of the autocatalytic growth of silver clusters (at 420 nm), after a critical time. Single pulse in a mixed solution of silver ions and SPY. ...

Pulse radiolysis allows one to observe directly some catalytic electron transfer reactions other than the autocatalytic growth (reactions (25-27). Indeed the clusters are so small that they may be considered as diffusing molecular systems. The electron transfer from MV to protons in water requires the presence of a catalyst, for example radiolytically formed gold or platinum clusters ... 

If the concentration of is high, the reactions depicted by Eqs. (29)-(31) are faster than the coalescence reactions (Eqs. 10 and 11) with a fixed total concentration of atoms and the clusters now grow mostly by successive additions of supplementary reduced atoms (electron plus ion). It has been shown that once formed, a critical cluster, of silver for example,indeed behaves as a growth nucleus. Alternate reactions of electron transfer (Eqs. 32 and 34) and adsorption of surrounding metal ions (Eq. 33) make its redox potential more and more favorable to the transfer (Fig. 8), and autocatalytic growth is observed.The observation of an effective transfer therefore implies that the potential of the critical cluster is at least slightly more positive than that of the electron-donor system, i.e. °(M +/M ) > °(S/S-). 

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