Gold Nanocluster Agglomeration Kinetic Studies: Evidence for Parallel Bimolecular Plus Autocatalytic Agglomeration Pathways as a Mechanism-Based Alternative to an Avrami-Based Analysis

Abstract

The most extensive and highest quality Au0n nanocluster agglomeration size vs time TEM data set yet obtained are analyzed by a nanoparticle size vs time equation that is derived herein for parallel bimolecular (B + B → C, rate constant k3) and autocatalytic (B + C → 1.5C, rate constant k4) agglomeration steps of preformed nanoclusters, B. The results show that the size vs time data are well fit by the new size vs time equation. The fits and resultant k3 and k4 rate constants yield several interesting insights that are presented and discussed, including the finding that to date k4 > k3, that is, that the autocatalytic agglomeration rate constant is faster than the bimolecular rate constant, at least for the cases examined to date. The results of the effects of added TOABr (tetraoctylammonium bromide) on the 180 °C agglomeration k3 and k4 rate constants in unstirred diphenylmethane solvent are also presented and discussed, the TOABr being added originally to compact the nanoclusters double layer thereby helping induce agglomeration. The observed different [TOABr] effects on k3 vs k4 also provide prima facie evidence that the two agglomeration steps are fundamentally different and unique. Literature size vs time data, from El-Sayed et al. for Pd nanocluster agglomeration, are also fit as a further test of the new, mechanism-based size vs time equation. The combined results, showing good fits by the k3 and k4 steps to the Au0n as well as literature Pd, Pt, and Ir nanocluster data, provide good support for the underlying B + B → C and B + C → 1.5C agglomeration steps themselves as well as for the assumptions and math behind the new size vs time equation. The significance of the results in general, as well as for future measurements of k3 and k4 rate constants as a preferred way to quantitate nanocluster stability in solution, are also presented and discussed. Most significant, however, is that as a result of the present work one can now use chemical equations and associated, mechanistically rigorously defined concepts of bimolecular (B + B → C; rate constant k3) and autocatalytic (B+ C → 1.5C; rate constant k4) agglomeration to analyze and describe nanoparticle agglomeration rather than the harder to interpret, more obscure n and k parameters from an Avrami-type, semiempirical curve fit.