Nucleation Kinetics and Molecular Mechanism in Transition-Metal Nanoparticle Formation: The Intriguing, Informative Case of a Bimetallic Precursor, {[(1,5-COD)Ir^I·HPO₄]₂}^2–

Abstract

Following a summary of the relevant literature on nucleation and applicable nucleation and growth models and mechanisms, the kinetics and molecular mechanism of nucleation are investigated in detail starting from [(1,5-COD)­IrI(NCCH3)2]­[BF4], 1, which upon addition of HPO4 2– to 1 forms a neutral, phosphate-bridged species, {[(1,5-COD)­IrI(NCCH3)]2·HPO4}0, 2, en route to {[(1,5-COD)­IrI·HPO4]2[Bu4N]2}, 3. Post a list of the seven advantages of the {[(1,5-COD)­IrI·HPO4]2}2– precatalyst as a novel bimetallic precursor for kinetic and mechanistic studies of nucleation, six important, previously unanswered questions are raised about the ill-understood but exceedingly broad and important topic of nucleation. 1H NMR solution speciation and Signer apparatus solution molecular weight studies establish that in situ prepared {[(1,5-COD)­IrI·HPO4]2}2–, 3, exists predominantly in its indicated, dimeric form. The NMR studies also identify {[(1,5-COD)­IrI(NCCH3)]2·HPO4}0, 2, as an important, metastable species with one less HPO4 2–, formed in a dissociative equilibrium of 3 to 2 plus HPO4 2–. Kinetic studies reveal a first-order dependence of nucleation on the concentration of 3 and hence rule out the higher-order dependence implied by classical nucleation theory. Additional kinetic studies reveal a telling, inverse, quadratic dependence on added HPO4 2–, results that unveil the previously unavailable insights that a simple bimetallic, Ir2 precursor is sufficient to enable low-molecularity nucleation via {[(1,5-COD)­IrI(NCCH3)]2·HPO4}0, 2, as a kinetically competent intermediate, a unique example of a nucleation mechanism known in molecular detail from a precisely defined molecular precursor that also includes spectroscopic detection of a kinetically competent intermediate. The results with {[(1,5-COD)­IrI·HPO 4 ]2}2– in comparison to previous results with {[(1,5-COD)­IrI·POM]}8– (POM = the polyoxometalate P2W15Nb3O62 9–) allow insights into the details of nucleation, notably that Ir2 versus Ir3 kinetically effective nuclei are controlled by the different HPO 4 2– and POM 8– anion’s surface charge and resultant 2 versus 3 IrI(1,5-COD)+ moieties they are able to bind to achieve surface-charge neutrality. The state-of-the-art nucleation results allow a total of nine insights, conclusions, and two new working hypotheses, insights that promise to help drive a deeper understanding of nucleation, not just in transition-metal nanoparticle formation but hopefully more broadly across nature.

LaMer's 1950 model of particle formation: a review and critical analysis of its classical nucleation and fluctuation theory basis, of competing models and mechanisms for phase-changes and particle formation, and then of its application to silver halide, semiconductor, metal, and metal-oxide nanoparticles

“…25 Critical to understanding CNT and where it should or should not be applied is to realize that CNT is a thermodynamic-based theory-a hypothesis-for nucleation that we now know is more generally a kinetically controlled process. 2,3,5,6,[10][11][12][13][14]16,17,26,27 In the thermodynamically based CNT, the free energy change of the particle formation is defined/assumed to be the sum of the free energy changes of the phase transformation and formation of the surface, Fig. 1.…”

“…What is experimentally measurable is the kinetics of nucleation, including the reaction order, n, in the precursor concentration (i.e., [A] n ) of the nucleation step, 3,17,26,27 that reaction order nominally giving one the nuclearity (A n ) of the what has recently been defined as the kinetically effective nucleus (KEN). 17 Such an experimental measurement of the nucleation reaction order also looks to be one version of the so-called ''Nucleation Theorem''; see p.…”

“…There the kinetically effective nucleus composition has been determined via classical kinetics dependence on [A] and other experiments to be {Ir I 3 H 2x ÁPOM} 6À . 26 Hence, the stronger metal-hydride, M-H-M, bond is involved, 17,26,27 for reference a single Ir-H bond energy is on the order of B75 kcal mol À1 . 17 In this system the evidence is strong that nucleation does not involve a reversible, nA " A n system but, instead, involves a low nuclearity 17,26,27 KEN with a n = 3.…”

“…26 Hence, the stronger metal-hydride, M-H-M, bond is involved, 17,26,27 for reference a single Ir-H bond energy is on the order of B75 kcal mol À1 . 17 In this system the evidence is strong that nucleation does not involve a reversible, nA " A n system but, instead, involves a low nuclearity 17,26,27 KEN with a n = 3. 26 This is a good example of where classical experimental kinetics, but now of nucleation, are both necessary and powerful, kinetics generally giving one the composition of the transition state of the rate-determining step in all but a few special cases.…”

“…2 Moreover, in terms of realizing where CNT should or should not be applied, it helps to realize that CNT is a macroscopic to microscopic (but not atomic), ''top-down'' theory-again, really just a hypothesis expressed as one possible mathematical model-brought down to the size of a still large ''droplet'' via the capillary approximation. CNT theorists likely had no idea at the time if they would need to treat 1000s of atoms, or o10 or (as it now appears) r3 atoms 17,26,27 in the ''critical nucleus'' of at least some strong bonding systems, borrowing CNT language for a moment. Even for H 2 O, the best current computations suggest there are no more than 10-50 water molecules in the, therefore, (H 2 O) B10-50 ''critical cluster''.…”