Evidence for a Kinetically Effective Nucleus of Three - ACS Publications

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Nanoparticle Nucleation Is Termolecular in Metal and Involves Hydrogen: Evidence for a Kinetically Effective Nucleus of Three {Ir3H2x·P2W15Nb3O62}6− in Ir(0)n Nanoparticle Formation From [(1,5COD)IrI·P2W15Nb3O62]8− Plus Dihydrogen Saim Ö zkar† and Richard G. Finke*,‡ †

Department of Chemistry, Middle East Technical University, 06800 Ankara, Turkey Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523 United States

‡

S Supporting Information *

ABSTRACT: The nucleation process yielding Ir(0) ∼300 nanoparticles from (Bu4N)5Na3[(1,5-COD)Ir·P2W15Nb3O62] (abbreviated hereafter as (COD)Ir·POM8−, where POM9− = the polyoxometalate, P2W15Nb3O629−) under H2 is investigated to learn the true molecularity, and hence the associated kinetically effective nucleus (KEN), for nanoparticle formation for the first time. Recent work with this prototype transitionmetal nanoparticle formation system (J. Am. Chem. Soc. 2014, 136, 17601−17615) revealed that nucleation in this system is an apparent second-order in the precatalyst, A = (COD)Ir·POM8−, not the higher order implied by classic nucleation theory and its nA ⇌ An, “critical nucleus”, An concept. Herein, the three most reasonable more intimate mechanisms of nucleation are tested: bimolecular nucleation, termolecular nucleation, and a mechanism termed “alternative termolecular nucleation” in which 2(COD)Ir+ and 1(COD)Ir·POM8− yield the transition state of the rate-determining step of nucleation. The results obtained definitively rule out a simple bimolecular nucleation mechanism and provide evidence for the alternative termolecular mechanism with a KEN of 3, Ir3. All higher molecularity nucleation mechanisms were also ruled out. Further insights into the KEN and its more detailed composition involving hydrogen, {Ir3H2xPOM}6−, are also obtained from the established role of H2 in the Ir(0)∼300 formation balanced reaction stoichiometry, from the p(H2) dependence of the kinetics, and from a D2/H2 kinetic isotope effect of 1.2(±0.3). Eight insights and conclusions are presented. A section covering caveats in the current work, and thus needed future studies, is also included.

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Scheme 1. Established Stoichiometry8−10 of Formation of Ir(0)∼300 Nanoparticles from [(1,5-COD)Ir·P2W15Nb3O62]8− under Hydrogen7

INTRODUCTION “Nucleation, in particular its mechanism, continues to be one of the most poorly understood and disputable phenomena in the past half century”, according to Liu.1 Nucleation plus the associated processes of growth and agglomeration in phase changes and self-assembly processes are omnipresent across nature,2−6 nucleation being the important initial process in natural systems as diverse as cloud, rain, and snow formation; other atmospheric processes such as H2SO4 nucleation and aerosol formation; protein aggregation in neurological diseases; crystallization processes of all kinds; pattern formation such as the formation of bones, teeth, or sea shells; bubble formation in the bends that divers can experience; and nanoparticle formation in catalysis and other areas of materials chemistry, to mention just a few among many more examples.2−6 To begin to fill the gap in knowledge regarding the mechanisms of nucleation, we have studied the combined processes of nucleation, growth and agglomeration in the prototype,7 ca. Ir(0)∼300 transition-metal nanoparticle formation system shown in Scheme 1 since 1994.8−11 For readers unfamiliar with the P2W15Nb3O629− polyoxoanion, it is a large, highly charged, excellent nanoparticle stabilizer12 that can be thought of as an enhanced, larger, and higher charge version of © XXXX American Chemical Society

simpler polyoxoanions that are also nanoparticle stabilizers such as PO43−.13 In a 2014 paper,14 we provided kinetic evidence that nucleation is an overall second-order process in the A = [(Bu4N)5Na3(1,5-COD)Ir·P2W15Nb3O62] nanoparticle precursor and not a higher order process via a reversible, nA ⇌ An, larger “critical nucleus” An as postulated by classical nucleation theory (CNT).14 That work led to an update of the classical Finke−Watzky (FW) 2-step mechanism9 to its novel secondorder in A nucleation analog shown in Scheme 2, that secondorder nucleation FW 2-step mechanism serving as a deliberately Received: January 31, 2017

A

DOI: 10.1021/jacs.7b00958 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

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Journal of the American Chemical Society

Scheme 2. Second-Order Nucleation FW 2-Step Mechanism14 and How It Is Conveniently Monitored by Coupling It to a Fast Cyclohexene Hydrogenation Reporter Reactiona

a

A = [(Bu4N)5Na3(1,5-COD)Ir·P2W15Nb3O62]; B = the growing, averaged Ir(0)n nanoparticle.

precision of these nucleation kinetics data will prove useful later in distinguishing two of the three nucleation mechanisms that will be consistent with the additional data and evidence gathered herein. Insights from the 2014 Study14 which Established Net Second-Order Nucleation Kinetics. Fifteen insights and conclusions from the 2014 study, establishing net second-order nucleation in A = [(Bu4N)5Na3(1,5-COD)Ir·P2W15Nb3O62] for Ir(0)n nanoparticle formation, were listed as part of our prior work.14 Three conclusions therein directly relevant to the present work follow:14 (i) “CNT, along with its equilibrium based, theoretical concept of a “critical nucleus”, An, formed from the reversible association of n monomers of A, is therefore disproven for the present Ir(0)n nanoparticle formation system.”;14 (ii) “A new concept of the KEN [kinetically effective nucleus] is needed and therefore postulated...”, namely, the experimentally observed reaction order in the assembling monomer, A.14 “The apparent KEN for Ir(0)n nanoparticle formation, under the identical conditions of those and the present studies, is an apparent KEN = 2, based on the demonstration of second-order nucleation kinetics.”; and (iii) “The FOC [first observable cluster] is an additional needed, new concept that has, therefore, also been postulated as part of this work. Prior literature claims of observation of the putative “critical nucleus” of CNT are, instead, very likely to have actually detected the FOC due to limitation in the sensitivity or timeresolution limitations of even the most powerful physical methods used to date.”14 Literature Relevant to the Concept of a Small, Kinetically Effective Nucleus (KEN) of 2−3. There is a limited set of nucleation literature that provides suggestive, albeit not definitive, evidence for a KEN of 2−3 for systems that, however, span a wide spectrum of nucleation and growth phenomenon across nature.14 Those key systems are (i) a 1989 study reporting rare kinetic evidence for approximately bimolecular (n ≈ 2.2 therein, and thus KEN ≈ 2.2) nucleation in Gelatin R1 renaturation15 (Those data do not, however, allow an unequivocal distinction of a KEN of 2 versus a KEN of 3.); (ii) the detection of Ag2 in the formation of Ag(0)n nanoparticles;16 (iii) a 2012 XAFS study of the formation of rhodium nanocubes suggesting Rh ≈ 2−3 species;17 (iv) protein aggregative nucleation and growth where an n value of 2 used in a global, 5-parameter curve fit (and where a control of letting the n value vary converges at values “close to 2”);18−20 (v) evidence for bimolecular nucleation in H2SO4 relevant to atmospheric droplet formation;.3,21,22 (vi) additional suggestive, albeit not definitive, evidence for second-order, [Pt]2 kinetics in PtIICl42− reduction

minimalistic, Ockham’s razor obeying kinetic model for nucleation and growth phenomena of multiple systems across nature.14 The kinetics data were obtained by a fast cyclohexene reporter reaction method, as shown in Scheme 2, fully documented in our prior publications.9,10 The resultant second-order nucleation FW 2-step mechanism was shown to provide a good fit to the sigmoidal nanoparticle formation kinetics data for the main part of the reaction where the reporter reaction method is still valid, Figure 1. The plot of

Figure 1. Typical nucleation and growth kinetics data obtained by the catalytic reporter reaction method monitoring the cyclohexene loss (Scheme 2). The system consists of 1.5 mM A = [(Bu4N)5Na3(1,5COD)Ir·P2W15Nb3O62] in propylene carbonate under an initial 40 psig H2 and at 22.0 ± 0.1 °C. The fit to the data (blue line) employs the integrated rate equation14 corresponding to the second-order nucleation FW 2-step mechanism in Scheme 2 and was accomplished by nonlinear least-squares curve fitting. Toward the end of hydrogenation, the reporter reaction runs out of cyclohexene and hence is no longer a valid way to monitor the reaction. For this reason, only the first three-fourths of the data are used to obtain the observed fit as detailed elsewhere14 (and as indicated by the blue line in the figure, FIT (3/4)). Note that only one of every five data points is shown for clarity. Reproduced with permission from ref 14. Copyright 2014 American Chemical Society.

k1obs versus A = [(Bu4N) 5Na3(1,5-COD)Ir·P2W15Nb3O62], over the ca. 30-fold concentration of A experimentally accessible for the kinetics, was linear within experimental error, with the resultant slope equal to k1obs(bimol), as shown in Figure 2, vide infra. The kinetics data in Figure 2 reveal a net second-order reaction in the nanoparticle precursor A = [(Bu4N)5Na3(1,5-COD)Ir· P2W15Nb3O62]. Noteworthy here is that such nucleation data are notoriously hard to measure at even the precision achieved, ±21% (k1obs(bimol) = 6.2 ± 1.3 h−1 M−1).14 The relatively high B


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Figure 2. k1obs rate constant obtained by the traditional first-order (unimolecular)9 A → B nucleation, 2-step FW mechanism over a 30-fold variation in the concentrations of the initial complex, (Bu4N)5Na3(1,5-COD)Ir·P2W15Nb3O62. The data show a clear linear trend with a slope of 12.2 ± 0.8 h−1 M−1 (R2 = 0.94; y-intercept = (1.3 ± 3.8) × 10−3 h−1).14 The inset shows a close up of the y-intercept and the gray box indicates its uncertainty. Reproduced with permission from ref 14. Copyright 2014 American Chemical Society.

of which can show net second-order kineticswhy we have been careful in the present work to distinguish and use where appropriate the distinct concepts of empirical reaction order versus the intimate-mechanism-derived, theoretical molecularity of a postulated, underlying elementary step.”28 We went on to say that14 “In addition, even for relatively simple bi- to ter-molecular nucleations, possible Ir(0)2, Ir2H, Ir2H2, Ir2+, Ir2H+, or Ir(0)3, Ir3H, Ir3H2, Ir3H3, Ir3+, Ir3H+ and other possible, nominal compositions of the activated complex of the rate-determining, nucleation step remain as important hypotheses awaiting experimental scrutiny.”28 Noteworthy is that the observation of second-order kinetics in precursor A will in general correspond to a molecularity of 2 (bimolecular) only in the simplest, less common of cases where A + A → 2B step is an elementary step, and when A is the actual associating monomer, namely, A + A → A2. This simple situation will not be the case in probably any more complex system, for example, rarely in nanoparticle formation reactions; it is certainly not in the case of the reaction in Scheme 1 where ∼300 A = [(Bu4N)5Na3(1,5-COD)Ir· P2W15Nb3O62] react with 750 H2 to form on average 1 Ir(0)∼300 nanoparticle plus 300 P2W15Nb3O629−, 300 cyclooctanes, and 300 H+ as the experimentally demonstrated, average balanced stoichiometry.9 Indeed, it was the fact that we could write mechanisms termolecular in Ir that, if present, would exhibit apparent net second-order kinetics in the starting A = [(Bu4N)5Na3(1,5COD)Ir·P2W15Nb3O62] which caused us to be very cautious in writing our 2014 paper.14 Therein we were very careful to distinguish the experimental reaction order from the concept of molecularity and to label the k1obs(bimol) and KEN obtained at the time14 as apparent bimolecular rate constants and an apparent KEN of 2. Goal of the Present Study: Uncovering the More Intimate Mechanism and Associated True KEN of Ir(0)n Nanoparticle Nucleation When Starting from the Prototype [(Bu4N)5Na3(1,5-COD)IrI·P2W15Nb3O62] Precatalyst. The goal of the present contribution is to probe more deeply and uncover the more intimate mechanism of nucleation for the [(Bu4N)5Na3(1,5-COD)IrI·P2W15Nb3O62] to Ir(0)n nanoparticle formation reaction shown in Scheme 2. The studies which follow exploit several valuable properties of the [(Bu4N)5Na3(1,5-COD)IrI·P2W15Nb3O62] system,12 including (i) that the (1,5-COD)IrI·P2W15Nb3O629− system (abbreviated

by H2 to Pt(0)n colloids in sodium citrate plus NaOH aqueous solutions from Henglein’s early, important work;23 and (vii) our own 2012 work showing that the formation of an Al2O3supported Ir(0)n heterogeneous catalyst exhibits kinetics secondorder in the Ir-precursor concentration, again suggesting bimolecular nucleation and a KEN of 2.24 That work considered, but was unable to definitively rule out, termolecular nucleation, because the nucleation kinetics data for that heterogeneous catalyst formation system were too noisy to distinguish bi- from ter-molecular nucleation. Computational evidence also exists suggestive of bimolecular nucleation as a preferred process in water condensation in expanding/cooling water plumes25 and in simulated nucleation populations that drop off by ∼107.5 as one goes from dimers to decamers in a glassy solid crystallization system.26 In addition, Stryer has shown in protein aggregations that dimer formation is favored over all other aggregates in the monomer-addition mechanism19 since only dimers grow as a quadratic dependence on [A].27 Hence, and as we noted in our 2014 publication:14 “There is, therefore, every reason to expect that rate-limiting bimolecular to perhaps termolecular nucleation may well apply to many other systems across nature.” However, definitive kinetic evidence for the true molecularity of nucleationand, hence, the true KENgenerally remains undemonstrated unequivocally for most nucleating systems across nature. This claim especially rings true if one includes the necessary task of disproving higherorder nucleations. Indeed, to our knowledge no prior report describes the true, disproof-based molecularity and associated KEN of nucleation of an inorganic or other, nonprotein nanoparticle system. Determining the True Molecularity of Nucleation and Definitive Determination of the True KEN Are Important, Outstanding Problems for Any System across Nature. If the underlying more intimate mechanism of nucleation can be established when beginning with A = [(Bu4N)5Na3(1,5-COD)Ir· P2W15Nb3O62] en route to Ir(0)∼300 nanoparticles so that the true molecularity of nucleation and thus the true KEN becomes known, then that would be a major advance in the area of nucleation kinetics and mechanism compared to any prior study. As we noted in our 2014 paper demonstrating net second-order kinetics in A:14 “Additional studies beyond the scope of the present work are needed to distinguish bimolecular from termolecular mechanisms that we have been able to write, both C


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Scheme 3, is POMadded ≥ 0). Each mechanism yields a related but different expression for the measurable k1obs(bimol) that results from the kinetics data such as that shown back in Scheme 2. Some insights about these three possible nucleation mechanisms and the kinetics they predict are as follows: (i) The associated kinetic derivations for the three nucleation mechanisms make it clear that obtaining a value of the KDiss(apparent) upfront would be invaluable for both simulations and designing the best kinetic experiments, so this is done first in what follows (and using 31P NMR, vide inf ra). (ii) One good test of the three mechanisms is to obtain nucleation kinetics data in the form of k1obs(bimol) as a function of added polyoxometalate, [POM9−]added (and at a constant [(COD)Ir·POM8−]0 = [A]0 value to start) and then curve fit that data to see which of the three mechanisms (i.e., which of the corresponding eqs 1−3 in Scheme 4) best accounts for the observed kinetics data.31 (iii) Using experimentally determined KDiss(apparent) and any initial values of k1(bimol), k1(termol), and k1(alt.termol) (e.g., in what follows from curve fits using eqs 1, 2, or 3 in Scheme 4 to initial POMadded kinetics data), we should be able to predict by simulation the dependence of k1obs(bimol) versus the [A]0 (= [(1,5-COD)Ir· POM8−]0) and as a function of the POMadded. (iv) Additional studies or curve fits of existing data14 can then also be performed using each of the three mechanisms to draw out any additional, expected-to-be-subtle dependence of k1obs(bimol) on [A]0 over and above the net, apparent second-order dependence. In short, which if any of the three mechanisms is favored or perhaps uniquely able to account for the observed kinetics data? Experimental Confirmation that (COD)Ir(solv)2+ Is a Key, Kinetically Competent Intermediate in the Nucleation Process. Since each of the mechanisms in Scheme 4 requires that the dissociated (COD)Ir(solv)2+ be a readily reduced, kinetically competent intermediate, this key point was experimentally checked first via the control experiment reported next. The purpose of the control is to confirm our prior evidence8,9 that dissociation of (COD)Ir·POM8− yields (COD)Ir(solv)2+ as a readily H2-reducible, kinetically competent intermediate. Specifically, in what follows and using authentic, independently prepared [(1,5-COD)Ir(CH3CN)2]BF4, we approximately doubled what will turn out to be the amount of (COD)Ir(solvent)2+ normally present in solution due to the dissociative equilibrium when starting with 1.2 mM (COD)Ir· POM8−. As Figure 3 shows, adding just 0.24 mM (COD)Ir(solv)2+ results in a reduction of induction period from 1.5 to 0.7 h with an increase in the k1obs(bimol) from 5.4 to 11.5 M−1 h−1. The results confirm our prior evidence8,9 that (COD)Ir(solv)2+ is a kinetically competent, readily H2-reducible intermediate in the Ir(0)n nanoparticle formation reaction investigated herein (Scheme 2, vide supra). Determination of KDiss(apparent) Using 31P NMR. Although we had tried unsuccessfully in 1997 to measure directly the KDiss(apparent) value,9 the added signal-to-noise possible for current NMRs and the higher purity [(Bu4N)5Na3(1,5-COD)Ir· P2W15Nb3O62] prepared specifically for these studies in order to obtain the best precision nucleation rate constants possible32 suggested that we might now be able to directly measure KDiss(apparent). Fortunately, the 31P NMR experiments cited in the Experimental Section provided the needed, higher S/N 31P NMR data. Integration of the separate, slow-exchanging peaks33 on the 31P NMR time scale due to the (COD)Ir·POM8− in comparison to the one due to the POM9− polyoxometalate, P2W15Nb3O629−, yielded a KDiss(apparent) of (6.4 ± 1.4) × 10−5 M in

again as (COD)Ir·POM8−) is monomeric (i.e., unaggregated) in solution according to ultracentrifugation molecular weight measurements,29 a point that is important for writing the dissociative equilibrium in Scheme 3 and the interpretation of the Scheme 3. Dissociative Equilibrium of the [(1,5-COD)IrI· P2W15Nb3O62]8− Precursor, Abbreviated as (COD)Ir·POM8−, and Associated Definitions of KDiss(apparent)a

a The counter cations present, [(Bu4N)5Na3]8+, are omitted for convenience to simplify the kinetic equations and derivations to their essential features.

kinetic order in Ir as the molecularity in Ir in what follows, vide inf ra. Other valuable properties of the (COD)Ir·POM8− system include the following: (ii) Nucleation is carefully controlled and placed in a convenient time frame for measurement at room temperature as a result of the dissociative equilibrium shown in Scheme 3. That dissociative, prior equilibrium provides a small, controlled amount of (1,5-COD)Ir(solvent)2+ that is then readily reduced under H2 and is critical in controlling the rate of the Ir(0)n nanoparticle nucleation reaction.30 Uncontrolled formation of bulk metal quickly results if one places only (1,5COD)Ir(solvent)2+ under H2 and in the absence of the POM9− stabilizer and nucleation and growth controller. The presence of the dissociative equilibrium in turn herein will allow us (iii) to exploit the dependence of the rate law on added [POM9−] to probe how many dissociated (COD)Ir(solv)2+ are involved in the nucleation event, and (iv) to examine in closer detail the observed, net (apparent) second-order dependence on the starting A = (COD)Ir·POM8− precursor. (v) Those kinetics insights then additionally will allow us to test bi-, tri- (i.e., ter), as well as all higher order and all implied molecularity nucleation rate laws in the prototype (COD)Ir·POM8− system. The results provide the first definitive test of the true nuclearity of the KEN, in a complex nucleation and growth system such as a nanoparticle in which higher-order nucleation beyond termolecular has been specifically considered and can be ruled out. The results also provide important evidence for the role of hydrogen in a KEN of {Ir3H2xPOM}6− and hence initial evidence for the long-standing hypothesis that metal hydrides are important in the nucleation of transition-metal nanoclusters under H2-asreductant conditions.

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RESULTS AND DISCUSSION Three Main Alternative Nucleation Mechanisms, Their Associated Kinetic Expressions, and Optimization of the Kinetic and Mechanistic Experiments Aimed at Distinguishing These Mechanisms. The three most plausible alternative nucleation mechanisms, shown in Scheme 4, are tested and as a group comprise mechanisms in which the molecularity in Ir is bimolecular and termolecular and one that we term an “alternative termolecular mechanism”. The kinetic equation associated with each possible mechanism is given below that scheme. Each equation is general for the cases where the amount of extra, externally added POM9− ranges from zero to nonzero values (i.e., where the added POM9− over and above that formed from the dissociative equilibrium, KDiss(apparent), as in D


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Scheme 4. Three Alternative Nucleation Mechanisms: A True Bimolecular Mechanism, a Termolecular Mechanism, and an “Alternative Termolecular Mechanism”a

a

These mechanisms involve elementary steps in so far as the Ir precursor is concerned up to the rate-determining step so that the kinetics of any supported (i.e., could not be disproved) mechanism will provide the molecularity of Ir in the KEN.14 Derivations of the kinetic expressions associated with each mechanism (eqs 1−3) are provided in the Supporting Information. bAbbreviation used here and in the Supporting Information: POMadded = concentration of extra, added POM9−; [A]0 = initial concentration of (COD)Ir·POM8−; KDiss(apparent) = KDiss[solv]2 as defined in Scheme 3.

propylene carbonate solution at 25 °C. (31P NMR spectra are available in Figure S5.) Note that the value of KDiss(apparent) and hence the iridium(0) nanoparticles formation have been shown to be highly sensitive to the experimental conditions.34 Therefore, the 31P NMR determination of KDiss(apparent) was performed in the presence of both propylene carbonate solvent and 1.65 M cyclohexene in order to mimic the conditions of the kinetic reporter reaction as closely as possible (but do not include the presence of H2, since an attempt to measure KDiss(apparent)

under H2 failed (as expected) due to the rapid formation of Ir(0)n under those conditions as detailed in the Experimental Section). With the KDiss(apparent) of (6.4 ± 1.4) × 10−5 M in hand, the percentages of (COD)Ir(solvent)2+ versus (COD)Ir·POM8− present at equilibrium as a function of the starting concentration, [A]0 = [(COD)Ir·POM8−]0 in propylene carbonate solution at 25 °C are readily computed as shown in Figure 4. As expected, the percentage of (COD)Ir(solvent)2+ rapidly decreases to an asymptotic value as the initial concentration of the precursor complex increases. E


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Figure 3. Reporter reaction (Scheme 2, vide supra) nucleation and growth kinetic curve starting with 1.2 mM A = [(COD)Ir·POM8−] in propylene carbonate at 22.0 ± 0.1 °C under an initial 40 psig H2 (□) and under the same conditions but now with 0.24 mM (20% of the initial [(COD)Ir·POM8−]) of added, authentic solvate complex, [(1,5COD)Ir(CH3CN)2]BF4 (○). Note that only one of every five data points is shown for clarity.

Figure 4. Calculated percentages of (COD)Ir(solvent)2+ (red circles) and (COD)Ir·POM8− (blue squares) present at equilibrium as a function of the starting concentration, [A]0 = [(COD)Ir·POM8−]0, and using the experimentally determined KDiss(apparent) of 6.4 × 10−5 M.

Figure 5. Curve fits of k1obs(bimol) versus added polyoxometalate [POM]added at constant concentration of precursor [(COD)Ir· POM8−]0 = [A]0 = 1.2 mM, with the error estimates for each k1obs(bimol) representing the standard deviation from 3 independent experiments. The curve fits shown are for the mechanisms in Scheme 4: (a) the bimolecular nucleation mechanism, eq 1, (b) the termolecular nucleation mechanism, eq 2, and (c) the alternative termolecular nucleation mechanism, eq 3. The take-way message from this figure is that all three fits are visually equally good as also judged by an equivalent R2 value of 0.96 for each.

Kinetic Studies at Constant [A]0 But with Varying [POM]added, from 0 to 2.1 mM. As a first set of initial added POM nucleation and growth experiments, kinetic runs were performed at constant initial concentration of precursor complex [(COD)Ir·POM8−]0 = [A]0 = 1.2 mM, but varying the [POM] added from 0.15−2.1 mM. Each experiment was performed under the otherwise standard conditions of 22.0 ± 0.1 °C and 40 ± 1 psig initial H2 pressure. The resultant kinetics data were fit to the bimolecular 2-step mechanism, using eq S13, to yield k1obs(bimol). The resulting k1obs(bimol) versus [POM]added plots are provided in Figure 5, along with fits to the data by the bimolecular, termolecular, and alternative termolecular mechanisms (eqs 1−3, respectively, in Scheme 4) given in Figure 5a−c, respectively. The resulting table of the fits, their associated errors, and the kinetically determined KDiss(apparent) values in comparison to the 31P experimental value of KDiss(apparent) are given in Table 1. Several observations from Figure 5 and Table 1 are noteworthy: In each case, the anticipated inverse dependence of the nucleation rate constant, k1obs(bimol), upon the added, excess P2W15Nb3O629− polyoxometalate is seen, confirming our 1997

observation9 of a lengthened induction period with added polyoxometalate and a resultant slowed nucleation step.35 In addition, each fit is visually good, as well as indistinguishable by its R2 = 0.96 value. However, the fits yield different KDiss(apparent) values of (8.0 ± 0.2) × 10−5, (2.1 ± 0.5) × 10−4, and (8.0 ± 0.2) × 10−5 M, for the bimolecular, termolecular, and alternative termolecular mechanisms, respectively (Table 1). Since the experimentally independently determined KDiss(apparent) by 31P NMR is (6.4 ± 1.4) × 10−5 M at 25 °C, the termolecular mechanism can be tentatively ruled out as it yields a KDiss(apparent) that does not match the value determined by 31P NMR within experimental error. F


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Journal of the American Chemical Society Table 1. Results of the Three Fits of k1obs(bimol) versus Added Polyoxometalate Concentration Data by the Bimolecular, Termolecular, and Alternative Termolecular Nucleation Mechanisms fit KDiss(apparent)

nucleation mechanism +

bimolecular nucleation {2(COD)Ir } termolecular nucleation {3(COD)Ir+} alternative termolecular nucleation {2(COD)Ir+ + 1(COD)Ir·POM8−}

−5

(8.0 ± 0.2) × 10 (2.1 ± 0.5) × 10−4 (8.0 ± 0.2) × 10−5

R2 (χ2)

k1 rate constant

0.96 (0.13) 0.96 (0.16) 0.96 (0.13)

k1(bimol) = (1.2 ± 0.3)×102 M−1 h−1 k1(termol) = (8.6 ± 3.0) × 104 M−2 h−1 k1(alt.termol) = (6.4 ± 1.6) × 104 M−2 h−1

the curve fits.) The attempted fits by the bimolecular and termolecular mechanisms, Figure 7a,b, respectively, yield nonsensical values for the coefficient of determination and residual (Table 2) as well as values for the rate constant k1 (Table 2) that are not within experimental error of the values listed in Table 1. Furthermore, for both the bimolecular and termolecular mechanisms, the fit tries to force the data toward approaching infinitely large values of k1obs(bimol) as the initial concentration of precursor, [A]0, goes to zero, as the simulations using the respective eqs 1 and 2 in Figure 7a,b, respectively, predicted, all while the actual data tends the opposite way with k1obs(bimol) decreasing as [A]0 decreases. However, Figure 7c shows that the data are reasonably well fit and, more importantly, only fit by the alternative termolecular mechanism using eq 3 in Scheme 4 (R2 = 0.70 and residual = 0.069, Table 2). In addition, a value for the rate constant of k1(alt.termol) = (7.7 ± 0.3) × 104 M−2 h−1 is within experimental error of the Table 1 value of k1(alt.termol) = (6.4 ± 1.6) × 104 M−2 h−1 obtained from the fit to the POMadded kinetic data, providing confidence in at least the internal consistency of the kinetics data. In short, the very important insight here is that the data are fit only by the alternative termolecular mechanism. The highly intriguing insight here is that nucleation is termolecular in Ir but hides under a net, apparent second-order dependence of the kinetics on the initial [(COD)Ir·POM8−]0 = [A]0 concentration until and unless the additional, subtle dependence of k1obs(bimol) versus [A]0 is teased out as it has been herein. The reader interested in a more intuitive feeling for how nucleation termolecular in Ir exhibits apparent second-order kinetics is referred to the Supporting Information for an explanation of that interesting kinetics detail. The take-home message is, however, clear: Only when the fuller rate law and more intimate mechanism are known is one then in a position to recognize the true rate-determining step and molecularity of the nucleation process under consideration. H2 Pressure Dependence of the Rate Law and the D2 Kinetic Isotope Effect: Evidence for the Involvement of Ir−H Species in the Nucleation. We have long suspected, and have commented in the literature several times,11e,36,37 that Ir−H species are probable intermediates in nucleation of our (1,5COD)Ir(I)+ containing precatalyst A = [Bu4N]5Na3(1,5-COD)Ir·P2W15Nb3O62 and probably also other metal nanoparticle systems made under H2 or with hydridic reducing agents. To provide evidence for or against this now long-standing, but previously little tested, hypothesis, the H2 dependence of the nucleation and growth rate law was examined next. The only prior evidence on this point for the present Ir(0)n system dates back to our 1997 demonstration that the observed induction period varies inversely with the initial H2 pressure.9 Those data are kinetically nondefinitive, however, as demonstrated by our recent publication showing that the induction time is, mathematically and for the FW 2-step mechanism, a function of each of k1, k2, and the starting concentration of precatalyst, [A]0.38 That is, the induction time is not just a function of the

However, based on the POMadded kinetic data and fits in Figure 5, the bimolecular and alternative termolecular mechanisms cannot be distinguished. Hence, simulations were undertaken next, with the hope of providing insight into how to disprove one (or perhaps both) of the two remaining mechanisms. The needed simulations are made possible by employing the (different, curve-fit-derived) k1 rate constants in Table 1 for the different mechanisms plus the 31P NMR determined KDiss(apparent) of ∼6.4 × 10−5 and lead to the needed additional experiments and analysis that could distinguish the remaining two mechanisms. Simulations Using KDiss(apparent). Simulations of the dependence of k1obs(bimol) on the initial concentrations of (COD)Ir·POM and POMadded were done for all three mechanisms using the 31P NMR determined KDiss(apparent) of ∼6.4 × 10−5 M and using the rate constants determined from the curve fits in Figure 5 of k1(bimol) = (1.2 ± 0.3) × 102 M−1 h−1, k1(termol) = (8.6 ± 3.0) × 104 M−2 h−1, and k1(alt.termol) = (6.4 ± 1.6) × 104 M−2 h−1. The mechanistic logic here is that if a given mechanism of the three is correct, then the curve fit k1 should be correct so that use of that k1 value (along with the KDiss(apparent) and eqs 1, 2, or 3 in Scheme 4) should predict the kinetics one should see as a function of the other two variables in eqs 1, 2, or 3 in Scheme 4, namely, k1obs(bimol) versus the starting (COD)Ir·POM concentration, [A]0, and versus the POMadded concentration. The results of those numerical integration simulations are given in Figure 6. The simulations show how k1obsv(bimol) is predicted to vary for each of the three mechanisms as a function of the amount of starting [(COD)Ir·POM8−]0 = [A]0, with each curve being for a constant amount of added POM over a range of 0−2.1 mM POMadded. The simulations are informative, revealing that the most striking difference is expected at zero concentration of added polyoxometalate, as the initial concentration of precursor [(COD)Ir·POM8−]0 = [A]0 goes to zero. The simulations further reveal that only for the alternative termolecular mechanism does the k1obs(bimol) value become zero at [POM]added = 0. In the bimolecular and termolecular mechanisms, k1obs(bimol) tends differently toward an increasingly large value. Hence, the next set of experiments needed to distinguish the remaining two mechanisms, bimolecular vs alternative termolecular, became clear: to go back and see if we could not tease out the expected, additional subtle dependence of k1obs(bimol) on the starting [(COD)Ir·POM8−]0 = [A]0 concentration, with no added polyoxometalate, [POM]added = 0. Kinetic Studies Varying [A]0 with No [POM]added. Figure 7 shows the curve fits of the k1obs(bimol) data obtained14 as a function of the initial [(COD)Ir·POM8−]0 = [A]0 concentration without added P2W15Nb3O629− polyoxometalate stabilizer ([POM]added = 0). The fits shown are to mechanisms given in Scheme 4: (a) to the bimolecular mechanism (eq 1), (b) to the termolecular mechanism (eq 2) (i.e., as a control and even though it has already been ruled out), and (c) to the alternative termolecular nucleation mechanism (eq 3). (The 31P NMR measured KDiss(apparent) = 6.4 × 10−5 M is the only other input into G


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Figure 6. Plots of the expected (calculated) k1obs(bimol) values versus the initial concentration of the precursor [(COD)Ir·POM8−]0 = [A]0 at various constant concentrations of the added polyoxometalate, [POM]added, for the (a) bimolecular, (b) termolecular, and (c) alternative termolecular mechanisms. The numerical integration simulations that lead to these figures were performed using eqs 1, 2, and 3 in Scheme 4, plus the experimentally determined KDiss(apparent) = (6.4 ± 1.4) × 10−5 M and rate constants k1(bimol) ≅ 1.2 × 102 M−1 h−1, k1(termol) ≅ 8.6 × 104 M−2 h−1, and k(alt.termol) ≅ 6.4 × 104 M−2 h−1 obtained from the curvefits of the data collected in Table 1. The important point from these simulations is that they predict a way to distinguish the three mechanisms that Figure 6a−c represent, notably at zero added POM, the top blue curve in each figure.

either a first-order, or perhaps a saturation-kinetics, dependence of k1obs(bimol on the initial p(H2) (Figure S8a). As a check or control, the induction period for the same kinetics curves was plotted versus the initial H2 pressure, and a linear decrease with increasing p(H2) is seen over the range of 29−69 psi, tinduction = −0.024 p(H2) + 2.48 (Figure S9a), similar, albeit not exactly

nucleation rate constant, k1, as our original, 1997 evidence seemed to suggest.10 The details of our present study on the effect of initial H2 pressure on the nucleation and growth kinetics are given in the Supporting Information. A rather scattered plot is observed for k1obs(bimol) versus the initial H2 pressure, but is consistent with H


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threshold of 23.4 psi before a non-zero k2 value is seen (Figure S8b). There is no significant change in the particles size and size distribution of iridium(0) nanoparticles generated starting with various initial H2 pressure in the range 29−69 psi (Figure S10). A set of kinetic isotope effect (KIE) experiments was also done under the same standard conditions as those of the cyclohexene hydrogenation experiment, but using D2 instead of H2 at several initial pressures. The data are again somewhat scattered and showed an average k1(D2) value of 1.2(±0.3) (Figure S11 and k1(H 2)

Table S6).39 Significantly, one can write the following, minimalistic equation in Scheme 1 (and in a general way using xH2 in eq 4) if one combines the four lines of evidence: (i) that the nucleation step is, based on the present work, now known to be termolecular in Ir(I)+ and contains 1 POM9− (i.e., based on the kinetic evidence presented herein); (ii) that there is a p(H2) dependence in the kinetics; (iii) that there is a

k1(D2 ) k1(H 2)

= 1.2 ± 0.3; and

importantly, (iv) that there is the established evidence for H2 as the reductant for the (COD)Ir(I)+ precursor in the reaction stoichiometry:8−11 3Ir(I)+ + POM9 − + x H 2 ⇌ {Ir3H 2xPOM}6 −→→ 3Ir(0) + POM9 − + 2x H+

(4)

The deliberately minimalistic reaction in eq 4 is able to rationalize the observed data, including the small, negligible KIE ≈ 1 as perhaps most likely compensating inverse and regular isotope effects38 in the prior equilibrium and follow-up steps, respectively. A bit more discussion of how this minimal scheme was arrived at is provided along with Figure S8 of the Supporting Information. Overall, the composite data allow us to suggest an {Ir3H2xPOM}6− species as the more detailed KEN en route to the formation of polyoxometalate-stabilized Ir(0)∼300 nanoparticles. As such, the data are the most detailed information presently available for the composition of the activated complex and associated KEN for nucleation of a transition-metal nanoparticle. The results also provide rare evidence for the role of hydrogen and by implication metal-hydrides40 in KENs of transition-metal nanoclusters formed under H2-as-reductant conditions. These results are significant in comparison to all of the extant literature of nucleation in the level of insight and detail they offer for a KEN in a transition-metal nanoparticle catalyst formation reaction. The results are furthermore significant in that they continue and fortify the case made elsewhere14 against the applicability of CNT to strong-bonding systems such as those herein involving Ir−Ir or Ir−H−Ir bonds. Specifically, the KEN is not a CNT-type “critical nucleus” of Irn, n ≫ 2−3, for a reversibly assembling, nA ⇌ An system as postulated by CNT. Recent Literature Evidence Consistent with Low Molecularity, Possibly Termolecular, Nucleation. An intriguing study in the context of the results presented herein

Figure 7. Plot of k1obs(bimol) versus initial concentration of precursor [A]0 = [(COD)Ir·POM8−]0 without added P2W15Nb3O629− polyoxometalate stabilizer ([POM9−]added = 0) and its fit by the equations in Scheme 4: (a) the bimolecular (eq 1), (b) the termolecular (eq 2), and (c) the alternative termolecular nucleation (eq 3) mechanisms using as input only the 31P NMR measured KDiss(apparent) = 6.4 × 10−5 M. Each datum point at no added excess polyoxometalate is the average of 3 experiments.14 The key point is that the data are fit reasonably well only by the alternative termolecular mechanism (bottom, Figure 7c).

identical, to the nonlinear dependence seen in 1997,9 thereby establishing at least the reproducibiltiy of the p(H2) dependence over the intervening 20 year period. The autocatalytic surface growth rate constant, k2, increases linearly with increasing initial H2 pressure (Figure S8b) and shows a minimum pressure

Table 2. Results of the Three Fits of the Data of k1obs(bimol) versus Initial Concentrations of Precursor Complex [A]0 = [(COD)Ir· POM8−]0 without Added P2W15Nb3O629− Polyoxometalate Stabilizer ([POM]added = 0) by the Three Nucleation Mechanisms nucleation mechanism +

bimolecular nucleation {2(COD)Ir } termolecular nucleation {3(COD)Ir+} alternative termolecular nucleation {2(COD)Ir+ + 1(COD)Ir·POM8} a

R2 (χ2)

k1 rate constant

[30 (−39)]a [8.6 (−10)]a 0.70 (0.069)

k1(bimol) = (6.1 ± 3.1)×101 M−1 h−1 k1(termol) = (4.2 ± 0.7)×105 M−2 h−1 k1(alt.termol) = (7.7 ± 0.3)×104 M−2 h−1

The values given are nonsensical. I


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Figure 8. Particle size distribution of neat silver nanoparticles formed in a cetyltrimethylammonium bromide solution containing Na3Citrate and NaBH4 reductant, calculated from the ultracentrifugation data using the bulk density of silver. The presented particle sizes are those of the silver core. Reproduced with permission.41 Copyright 2015 Royal Society of Chemistry.

KENs could in principle build up to levels that might be detected spectroscopically in general the KEN is expected to be close in, if not equal to, energy of the rate-determining transition-state structure for nucleation, with the latter being implied for the present KEN of {Ir3H2xPOM}6− as it is defined kinetically via Scheme 4. This in turns means that KENs will generally be detectable most readily, if not primarily only, by kinetic studies. Homogeneous versus Heterogeneous Nucleation. On the basis of the implied {Ir3H2xPOM}6− for the KEN, one could envisage that in some real sense the polyanionic POM9− polyoxoanion is serving as an assembly framework for the 2Ir(I)+ perhaps analogous to the role of “dust” in assembling and thereby involved in nucleating the best studied and weakly bonding organic-molecule crystallizations.44 This also raises an important question: Is dust or other (e.g., glass surface-area) heterogeneous nucleation a part of the present, as well as most other, ostensibly “homogeneously nucleating” systems? As discussed in our prior publication,14 the y-intercept in Figure 2 herein is 1.3 × 10−3 ± 3.8 × 10−3, that is “0” within experimental error, arguing against any detectable parallel path heterogeneous or other nucleation, k1,hetero,parallel‑path ≤ 0.001 (±0.004) h−1, again within experimental error. That said, studies are in progress to test our current hypothesis, based on a careful reading of seminal nucleation literature,44 so that dust should be tested to see if it is important kinetically in any nucleations not performed under clean-room conditions. In short, even with the advances herein and other evidence for low-molecularity nucleation in at least strong-bonding systems like Ir(0)n nanoparticles,14 it is not yet clear whether or not nature has given up even a fraction of its secrets about the nucleation phenomenon that are so critical and widespread across nature.

centrifugation data and using the bulk density of silver as a necessary first approximation, has been attributed to either [Ag3]0/n+ or [Ag1]0/+. (The charge on the clusters is not known with certainty; AgH species could also conceivably be involved.) While a definitive distinction between [Ag3]0/n+ and [Ag1]0/+ is not possible at present for this still state-of-the-art data (due to the assumptions made about the size-dependent particle density and a lack of knowledge of the amount of cetyltrimethylammonium bromide or citrate3− on the surface that will influences the particle size in solution), these intriguing results do demonstrate: (i) 8 discrete, small, detectable Agn clusters; (ii) evidence that either [Ag3]0/n+ or [Ag1]0/+ is present as the dominant species under the reaction conditions; and (iii) evidence that the ∼0.7 and ∼1.2 nm species are the early full-shell, “magic number”42 Ag∼13 and Ag∼55 clusters (with, again, some uncertainty due to the unknown density change and surface ligation as a function of particle size). In short, strong if not compelling evidence continues to accumulate for small, metal1−3 (therein Ag1−3, herein definitively Ir3) nanoclusters as kinetically, even directly detectable, species in nanoparticle formation reactions.14 Caveats and Needed Future Studies.43 More Intimate Mechanism and the Issue of the Timing of Steps. As is wellknown, kinetics alone cannot distinguish mechanisms that differ only in their timing of steps. Hence, even the valuable, more intimate mechanism provided herein is, however and once again by design,10,14 a minimalistic, Ockham’s razor obeying mechanism consistent with the available data. The kinetics do not tell us the order that these components are assembled, nor do they convey the structure of the transition state of the indicated minimal composition, {Ir3H2xPOM}6−. Note also that while

CONCLUSIONS The following are the primary conclusions resulting from the present study: (i) Compelling evidence has been obtained for nucleation termolecular in Ir, evidence that includes a detailed consideration of, and experimental disproving of, tetra- and all higher-molecularity nucleations when one includes all the available evidence.14 (ii) No prior study of any nucleation system in nature has, to our knowledge, provided evidence for net termolecular nucleation while also definitively ruling out both bimolecular as well as higher-order nucleation mechanisms. (iii) The results again14 provide evidence disproving the higher molecularity nucleation processes postulated by CNT and its implied reversible, thermochemically controlled associations of nA ⇌ An, where An is the elusive, arguably never actually detected,14 “critical nucleus” concept of CNT.11e (iv) The results demonstrate that only when the fuller form of the rate law and more intimate mechanism is known is one then in a position to determine the true molecularity and KEN of a complex nanoparticle formation reaction when the nanoparticle formation reaction typically involves reagents that are not just a simple association of strictly monomeric precursor, nA ⇌ An. (v) The results herein provide evidence for a perhaps more general paradigm for nucleation in at least stronger bonding,14 one in which a small, KEN of close to 2−3 governs the rate of nucleation in a kinetically controlled process. (vi) The results provide evidence consistent with a minimalistic KEN of composition {Ir3H2xPOM}6−, for the formation of Ir(0)∼300 nanoclusters under the present conditions. That said, neither the timing of steps leading to nor the precise structure of this transition-state composition for the {Ir3H2xPOM}6− KEN are presently known. (vii) It follows that rate-determining low-order (e.g., second- or

is the formation of Ag(0)n nanoparticles by the reduction of Ag(NO3) by NaBH4 in aqueous solution in the presence of cetyltrimethylammonium bromide and Na3citrate as stabilizers.41 This Ag(0)n formation system was examined by synthetic boundary crystallization ultracentrifugation combined with a multiwavelength detector and a specialized titration assay. The highest intensity peak observed in the particle size distribution of the core Agn nanoparticles (Figure 8), calculated from ultra-

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was then used in an Ir(0)n nanoparticle formation kinetics experiment, vide inf ra, all according to our prior detailed descriptions.9,10,14 Experimentally Determined KDissociation Constant for [(1,5-COD)Ir· P 2 W 15 Nb 3 O 62 ] 8− Dissociation to (1,5-COD)Ir(solvent) 2 + and P2W15Nb3O629−. In order to measure KDissociation under the same solvent conditions as the hydrogenation reactions (or more precisely to measure KDiss(apparent) which includes the solvent term in KDissociation; see eq S21), 31 P NMR spectra were obtained unlocked (due to the absence of deuterated solvent) on a series of solutions with successively larger ratios of (1,5-COD)Ir+ to P2W15Nb3O629−. In these spectra, the peaks from both free P 2 W 15 Nb 3 O 62 9− and coordinated [(1,5-COD)Ir· P2W15Nb3O62]8− were visible, and their integrated areas were used to calculate ratio of the two species. From that ratio, the empirical KDiss(apparent) was determined to be 6.4(±1.4) × 10−5. The dissociative equilibrium is under slow exchange conditions compared to the 31P NMR time scale.33 A 10 mM solution of P2W15Nb3O629− in propylene carbonate and cyclohexene was prepared in a drybox by adding 188.2 mg of (Bu4N)9[P2W15Nb3O62] to a 50 mL round-bottomed flask with a 5/8 in. × 5/16 in. magnetic stir bar along with 2.5 mL of propylene carbonate and 0.5 mL of cyclohexene. The 10 mM solution of polyoxometalate was completely dissolved by stirring for 5−10 min. A 1 mL sample of this solution was added to a 5 mm o.d. NMR tube using a 1 mL gastight syringe, and the NMR tube was capped with a rubber stopper. Next, 58.7 mg of [(1,5-COD)Ir(CH3CN)2]BF4 was added to a 2 mL GC sample vial and dissolved in 1 mL of propylene carbonate to form a 0.125 M solution. An airtight cap with a rubber septum was crimped onto the vial, and both the sealed vial and NMR tube were removed from the drybox. A base line 3 1 P NMR a nalysis was pe rfor med on the (Bu4N)9[P2W15Nb3O62] solution, and then a 10 μL syringe was used to add [(1,5-COD)Ir(CH3CN)2]BF4 solution to the NMR tube through the rubber septum. After each drop of [(1,5-COD)Ir(CH3CN)2]BF4 solution, the NMR tube was vigorously shaken for 5 min. 31P NMR spectra were obtained at 25 °C held constant by the NMR software. Spectra were obtained after the successive addition of 72, 76, 78, and 80 μL. The resulting succession of 31P NMR spectra at 0, 90, 95, 97.5, and 100% titrated by [(1,5-COD)Ir(CH3CN)2]BF4 showed the two main peaks of the uncoordinated P2W15Nb3O629− species at −11.5 and −18.4 ppm being replaced by peaks from the coordinated [(1,5-COD)Ir·P2W15Nb3O62]8− at −12.0 and −18.2 ppm. The four measurements implied an average dissociation constant of (6.4 ± 1.4) × 10−5. An attempt was also made to measure the KDiss(apparent) under the full reaction conditions, which include 40 psi H2 along with cyclohexene and propylene carbonate, using a J. Young NMR tube. However, and as expected, H2 was consumed and Ir(0)n nanoparticles began forming during the ca. 30−60 min NMR scans, obscuring the desired peaks; hence, the attempt to determine KDiss(apparent) under H2 had to be abandoned. We also attempted to measure the KDiss(apparent) by using UV−vis electronic absorption spectroscopy starting with 0.90 mM solution of (Bu4N)9[P2W15Nb3O62] in propylene carbonate and adding [(1,5COD)Ir(CH3CN)2]BF4 in various concentrations in the range 0.27− 0.90 mM. However, the intense charge transfer bands of polyoxoanion do not allow the detection of changes in the weak d-d bands of iridium(I). Simulations of k1obs(bimol as a Function of Initial Precursor Concentration at Various Constant Concentration of Added Polyoxometalate. The numerical integration simulations of k1obs(bimol) depending on the initial concentrations [(COD)Ir·POM8−]0 and [POM]added were performed on Microsoft Excel for Mac 2011 Version 14.5.0 using eqs 1−3 given in Scheme 4 for the bimolecular, termolecular, and alternative termolecular nucleation mechanisms, respectively. The k1obs(bimol) values were calculated by incrementally varying the initial concentration of the precursor [(COD)Ir·POM8−]0 = [A]0 at various constant concentrations of the added polyoxometalate, [POM]added, for each of the three mechanisms using the respective equation and the experimentally determined KDiss(apparent) = (6.4 ± 1.4) × 10−5 M plus the rate constants k1(bimol) ≅ 1.16 × 102 M−1 h−1, k1(termol) ≅ 8.59 × 104 M−2 h−1, and k1(alt.termol) ≅ 6.44 × 104 M−2 h−1 obtained

third-order) nucleation and the implied low-molecularity nucleation should now serve as the dominant starting hypothesis for subsequent studies to attempt the disproving of nucleation phenomena in stronger bonding systems across nature. (iix) Caveats in the current study, and thus needed future studies, include a range of additional, needed work: further evidence for (or against) hydridic species such as {Ir3H2xPOM}6− in other nucleating metal systems; studies aimed at providing evidence for or against dust or other heterogeneous nucleation phenomena; studies of the nucleation kinetics and associated KEN in other, prototype nucleation systems across nature;44 and any and all efforts that can lead to an even more detailed and intimate description of omnipresent nanoparticle nucleation, growth, and agglomeration pathways throughout nature.

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EXPERIMENTAL SECTION

This section and associated experimental details parallel almost exactly our most recent paper, where extensive experimental details are given. Hence, experimental sections that are identical to our prior work simply cite those prior experimental sections. New experimental details or procedures are, however, provided in what follows. Reagents. This section is identical to that in our recent report,14 except deuterium (D2, 99.9 atom % D, in 0.451 L cylinder under 945 psig pressure, ISOTEC) was purchased from Sigma-Aldrich and used as received. Instrumentation. This section is identical to that in our recent report,14 with exception of the TEM instrument: JEOL JEM2100F Transmission Electron Microscope operating at 200 kV was used to take bright field STEM images of iridium(0) nanoparticles deposited on an ultrathin 20 nm carbon coated copper grid (Ted Pella, Inc.). (Bu4N)5Na3[(1,5-COD)Ir·P2W15Nb3O62] Synthesis. This section is identical to that in our recent report,14 including the underlying syntheses of [(1,5-COD)Ir(CH3CN)2]BF4, K6[α-P2W18O62], Na12[αP2W15O56], (Bu4N)9[P2W15Nb3O62], and (Bu4N)5Na3[(1,5-COD)Ir· P2W15Nb3O62].14 Preparation of Precatalyst Solutions. The solutions for the kinetic experiments were prepared from (Bu4N)5Na3[(1,5-COD)Ir· P2W15Nb3O62] isolated as detailed in our previous work.14 Monitoring Ir(0)n Nanoparticle Formation Kinetics and Extraction of the k1obs(bimol.curvefit) and k1obs(bimol) Rate Constants. This section is identical to that in our recent report.14 Typically, one extra significant error is retained in reporting the derived rate constants in order to avoid round-off errors in their subsequent use. Kinetic Data Analysis. Analysis of the kinetic data was accomplished by nonlinear least-squares curve fitting of the appropriate integrated rate equation to the kinetic data, all precisely as detailed in our prior paper.14 Excess Added P2W15Nb3O629− Stabilizer Experiments Starting with Isolated (Bu4N)5Na3[(1,5-COD)Ir·P2W15Nb3O62]. Precatalyst samples in these experiments were prepared in a ≤ 1 ppm of O2, N2-filled drybox using excess (Bu4N)9[P2W15Nb3O62] stabilizer. For each sample, 20.2 mg (1.2 mM concentration) of (Bu 4 N) 5 Na 3 [(1,5-COD)Ir· P2W15Nb3O62] were added to a 1 dram vial, and dissolved in 1 mL of propylene carbonate along with 1 equiv of Proton Sponge. The solution was transferred to a 22 mm × 175 mm disposable pyrex culture tube containing a 5/8 in. × 5/16 in. magnetic stir bar, and 0.25 mL of propylene carbonate was used to wash the 1 dram vial and was then added to the culture tube. The desired equivalents of (Bu4N)9[P2W15Nb3O62] were weighed out in a separate 1 dram vial and dissolved in 1 mL of propylene carbonate. The solution was then added dropwise (∼1 drop per 2 s) to the stirring solution in the culture tube. Next, 0.25 mL of propylene carbonate was used to wash out the second 1 dram vial and that wash was added to the culture tube for a total of 2.5 mL of propylene carbonate. Finally, 0.5 mL of cyclohexene was added and stirred for ∼30 s. The culture tube containing the precatalyst solution was then placed in a Fischer−Porter bottle modified with Swagelock TFE-sealed Quick-Connects, sealed, and transferred out of the drybox, all as before.9,10,14 That Fischer−Porter bottle and apparatus K


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and our prior8,9,14 studies has been 2.0 ± 0.3 nm, which corresponds to on-average Ir(0)∼300 nanoparticles. The Ir(0)n nanoparticles formed herein and in our most recent study14 averaged a bit smaller, 1.7−1.8 nm, respectively, which correspond to Ir(0)∼182−215, but are still within experimental error of our prior studies.8,9,14 Hence, we retain the nomenclature of Ir(0)∼300 for the nanoparticles in the present study for the sake of simplicity and since our prior and the present studies provide the same size particles within experimental error. (8) Lin, Y.; Finke, R. G. J. Am. Chem. Soc. 1994, 116, 8335−8353. (9) Watzky, M. A.; Finke, R. G. J. Am. Chem. Soc. 1997, 119, 10382− 10400. (10) Watzky, M. A.; Finke, R. G. Chem. Mater. 1997, 9, 3083−3095. (11) (a) Hornstein, B. J.; Finke, R. G. Chem. Mater. 2004, 16, 139−150. (b) Besson, C.; Finney, E. E.; Finke, R. G. J. Am. Chem. Soc. 2005, 127, 8179−8184. (c) Besson, C.; Finney, E. E.; Finke, R. G. Chem. Mater. 2005, 17, 4925−4938. (d) Finney, E. E.; Finke, R. G. Chem. Mater. 2008, 20, 1956−1970. (e) Finney, E. E.; Finke, R. G. J. Colloid Interface Sci. 2008, 317, 351−374. (f) Ott, L. S.; Finke, R. G. Chem. Mater. 2008, 20, 2592−2601. (g) Finney, E. E.; Finke, R. G. Chem. Mater. 2009, 21, 4468−4479. (h) Finney, E. E.; Finke, R. G. Chem. Mater. 2009, 21, 4692−4705. (i) Finney, E. E.; Shields, S.; Buhro, W. E.; Finke, R. G. Chem. Mater. 2012, 24, 1718−1725. (12) (a) One special property of the (Bu4N)5Na3(1,5-COD)Ir· P2W15Nb3O62 system is the high stabilization provided by the highcharge, large-size, so-called “electrosteric” and overall “gold-standard” P2W15Nb3O629− stabilizer.12b The resultant nanoparticle stabilization is sufficient to permit isolable, redissolvable nanoparticles,8−10 nanoparticles that form without detectable bulk Ir(0) metal formation and according to the known balanced stoichiometry shown in Scheme 1 of the main text. (b) Starkey-Ott, L.; Finke, R. G. Coord. Chem. Rev. 2007, 251, 1075−1100. (13) Ö zkar, S.; Finke, R. G. Langmuir 2003, 19, 6247−6260. In this paper, simple HPO42− is shown to have most, but not all, of the desirable nanoparticle-stabilizing properties of the larger and more complex P2W15Nb3O629− polyoxoanion stabilizer. (14) Laxson, W. W.; Finke, R. G. J. Am. Chem. Soc. 2014, 136, 17601−17615, and references cited therein. (15) Busnel, J. P.; Morris, E. R.; Ross-Murphy, S. B. Int. J. Biol. Macromol. 1989, 11, 119−125. (16) (a) Evidence for Ag2+: Henglein, A.; Giersig, M. J. Phys. Chem. B 1999, 103, 9533−9539. (b) Evidence for Ag(0)2, but where the authors considered, and argue they can rule out, a Ag(0) + Ag+ to Ag2+ step: Stamplecoskie, K. G.; Scaiano, J. C. J. Am. Chem. Soc. 2011, 133, 3913− 3920. (17) Yao, S.; Yuan, Y.; Xiao, C.; Li, W.; Kou, Y.; Dyson, P. J.; Yan, N.; Asakura, H.; Teramura, K.; Tanaka, T. J. Phys. Chem. C 2012, 116, 15076−15086. (18) Meisl, G. University of Cambridge, Cambridge, U.K. Personal communication, 2017. We thank Georg Meisl and Profs. Dobson and Knowles for sharing this information in response to our query about how the reported n ≃ 2 values were obtained.. (19) Morris, A. M.; Watzky, M. A.; Agar, J. N.; Finke, R. G. Biochemistry 2008, 47, 2413−2427. (20) Meisl, G.; Yang, X.; Hellstrand, E.; Frohm, B.; Kirkegaard, J. B.; Cohen, S. I. A.; Dobson, C. A.; Linse, S.; Knowles, T. P. J. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 9384−9389. (21) Zhang, R. Science 2010, 328, 1366−1267. See the interesting discussion therein, highly relevant to the concepts proposed herein of a kinetically effective nucleus (KEN) and first-observable cluster (FOC),14 of the most recent nucleation studies by more sensitive methods that suggest a “critical nucleus” for H2SO4 droplet nucleation of 2 (what we call herein the KEN). Note also the discussion therein pointing out that prior studies (by less sensitive methods) previously reported a “critical nucleus” of four-to-nine, (H2SO4)4−9, that “...agreed with predictions from Classical Nucleation Theory...”, but probably are, instead, what we define herein as the FOC, the true KEN = 2 seemingly having been missed. (22) Atmospheric nucleation is obviously complex, as the following paper, detailing the large effects of NH3 on atmospheric H2SO4

from the curvefits of the data collected in the initial kinetic studies given in Table 1. D2 Kinetic Isotope Effect Experiments. The possible D2 kinetic isotope effect was investigated by performing standard conditions cyclohexene hydrogenation and concomitant Ir(0) nanoparticles formation in the same way as described above, but using D2 instead of H2 as the reducing agent. In the drybox, a 1.2 mM solution of (Bu4N)5Na3[(1,5-COD)Ir·P2W15Nb3O62] precursor in 2.5 mL of propylene carbonate plus 0.5 mL of cyclohexene was transferred to a new culture tube with a 22 mm × 175 mm disposable pyrex culture tube containing a 5/8 in. × 5/16 in. magnetic stir bar. The culture tube containing the precatalyst solution was then placed in a Fischer−Porter bottle modified with Swagelock TFE-sealed Quick-Connects, which was then sealed and taken out of the drybox. The Fischer−Porter bottle was connected to the hydrogenation line via Swagelock TFE-sealed Quick connector all according to our prior detailed descriptions.9,10,14 The hydrogenation line was connected to a deuterium cylinder (99.9 atom % D, ISOTEC, Sigma-Aldrich). Standard conditions cyclohexene hydrogenation was started at various initial pressures of D2 and 22.0 ± 0.1 °C following the procedure as detailed elsewhere.9,10,14

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b00958. Treatment of the kinetic data, reporter reaction method details, comparison of hydrogentation fits, equations for attempted fitting kinetics data, 31P NMR details, derivations, explanation of nucleation, kinetic data, effects of varying H2 pressure, investigation of kinetic isotope effect, analysis of ref 6 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] ORCID

Richard G. Finke: 0000-0002-3668-7903 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support of this research by the above-noted DOE grant FG0203ER15453 to R.G.F. and Colorado State University is gratefully acknowledged.

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REFERENCES

(1) Zhang, T. H.; Liu, X. Y. Angew. Chem., Int. Ed. 2009, 48, 1308− 1312. (2) Kashchiev, D. Nucleation: Basic Theory with Applications; Butterworth-Heinemann: Oxford, U.K., 2000. (3) Sipilä, M.; Berndt, T.; Petäjä, T.; Brus, D.; Vanhanen, J.; Stratmann, F.; Patokoski, J.; Mauldin, R. L.; Hyvärinen, A.-P.; Lihavainen, H.; Kulmala, M. Science 2010, 327, 1243−1246. (4) Chen, S.; Ferrone, F. A.; Wetzel, R. Proc. Natl. Acad. Sci. U. S. A. 2002, 99, 11884−11889. (5) Dauer, W.; Przedborski, S. Neuron 2003, 39, 889−909. (6) Thanh, N. T. K.; Maclean, N.; Mahiddine, S. Chem. Rev. 2014, 114, 7610−7630. This review unfortunately looks to have been written by researchers without the needed kinetic nor especially mechanistic background to write a critical, reliable review in the title area. As a result, the resultant review is, in our opinion, superficial, often uncritical, and misses key literature. Five specific examples to back up this opinion are provided as part of the Supporting Information for the interested reader. (7) Previously, the size of the Ir(0)n nanoparticles formed under the general concentration, solvent, and other conditions of both the current L


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given the chemical shift difference of 0.5 ppm between the peaks being 1 1 monitored, can be estimated to be: Δt = 2π Δυ = . 8

nucleation, demonstrates. Kirkby, J.; Curtius, J.; Almeida, J.; Dunne, E.; Duplissy, J.; Ehrhart, S.; Franchin, A.; Gagné, S.; Ickes, L.; Kürten, A.; Kupc, A.; Metzger, A.; Riccobono, F.; Rondo, L.; Schobesberger, S.; Tsagkogeorgas, G.; Wimmer, D.; Amorim, A.; Bianchi, F.; Breitenlechner, M.; David, A.; Dommen, J.; Downard, A.; Ehn, M.; Flagan, R. C.; Haider, S.; Hansel, A.; Hauser, D.; Jud, W.; Junninen, H.; Kreissl, F.; Kvashin, A.; Laaksonen, A.; Lehtipalo, K.; Lima, J.; Lovejoy, E. R.; Makhmutov, V.; Mathot, S.; Mikkilä, J.; Minginette, P.; Mogo, S.; Nieminen, T.; Onnela, A.; Pereira, P.; Petäjä, T.; Schnitzhofer, R.; Seinfeld, J. H.; Sipilä, M.; Stozhkov, Y.; Stratmann, F.; Tomé, A.; Vanhanen, J.; Viisanen, Y.; Vrtala, A.; Wagner, P. E.; Walther, H.; Weingartner, E.; Wex, H.; Winkler, P. M.; Carslaw, K. S.; Worsnop, D. R.; Baltensperger, U.; Kulmala, M. Nature 2011, 476, 429−433. (23) Henglein, A.; Ershov, B. G.; Malow, M. J. Phys. Chem. 1995, 99, 14129−14136. (24) Mondloch, J. E.; Finke, R. G. ACS Catal. 2012, 2, 298−305. (25) Li, Z.; Zhong, J.; Levin, D. A.; Garrison, B. J. J. Chem. Phys. 2009, 130, 174309. (26) Lee, B.-S.; Burr, G. W.; Shelby, R. M.; Raoux, S.; Rettner, C. T.; Bogle, S. N.; Darmawikarta, K.; Bishop, S. G.; Abelson, J. R. Science 2009, 326, 980−984. See Figure 3 therein. (27) Goldstein, R. F.; Stryer, L. Biophys. J. 1986, 50, 583−599. An interesting comment that Stryer makes on p. 593 based on his results and earlier results of others, that strikes a cord in light of our current termolecular nucleation studies, is “...the pre-equilibrium assumption is highly suspect. Why was this not discovered earlier?”. (28) The rest of the relevant full quote14 is: “Mechanistic science is by its very nature stepwise, cautious and highly evolutionary, building piece-by-piece and step-by-step to more complex mechanismsbut only as the data demand! In addition, even for relatively simple bi- to termolecular nucleations, possible Ir(0)2, Ir2H, Ir2H2, Ir2+, Ir2H+, or Ir(0)3, Ir3H, Ir3H2, Ir3H3, Ir3+, Ir3H+ and other possible, nominal compositions of the activated complex of the rate-determining, nucleation step remain as important hypotheses awaiting experimental scrutiny. (29) Pohl, M.; Lyon, D. K.; Mizuno, N.; Nomiya, K.; Finke, R. G. Inorg. Chem. 1995, 34, 1413−1429. See p. 1416, top right-hand column where the ultracentrifugation MW data is given and note 21 therein that explains that this MW measurement followed the absorbance due to the POM. (30) Even in our 1994 paper8 (p. 8345−8346 and Scheme 2 therein) we noticed a dependence of the induction period on amount of added [P2W15Nb3O629−]. Then, in our 1997 paper9 reporting P2W15Nb3O629− polyoxoanion-stabilized Ir(0)∼900 nanoparticles, we demonstrated an inverse dependence of k1obs on the amount of added [P2W15Nb3O629−] (see Figure 10a and footnote 42 therein; k1obs ≈ 1/tinduction, as in Figure S6).9 Controls done back in 19979 show that addition of authentic (1,5COD)Ir(solvent)2+ BF4− to the reaction conditions results in rapid nucleation and growth to, in that case, largely bulk metal product, a result confirmed via the control in Figure 3 in the present contribution. (31) Additional derivations given in the Supporting Information, intended to reveal the “intuitive approximate inverse order in [[POM9−]added]x” (eqs S47, S50, and S53 for the bimolecular, termolecular, and alternative termolecular mechanisms, respectively), show that under the more restrictive conditions of [POM9−]added ≫ [POM9−]dissociated (i.e., from the KDiss(appt)) and also if [POM]added ≫ KDiss(appt), then at least the bimolecular mechanism should be discernible from the two termolecular mechanisms by its inverse [[POM]added]x, x = −3 versus −2 dependences, respectively. The curve fits using the less restrictive equations (eqs 1−3 in Scheme 4) showed that this is in fact the case, as discussed in the main text. (32) Laxson, W.; Ö zkar, S.; Finke, R. G. Inorg. Chem. 2014, 53, 2666− 2676. (33) As a check, the following analysis supports the (i) slow exchange and (ii) thereby the 31P NMR assignments of two intense singlet peaks to the (COD)Ir·POM8− precursor used in the KDiss(apparent) determik1 k −1 −1 −1

nation. Specifically, KDiss(apparent) =

2π(0.5 × 1.62 × 10 Hz)

Hence, slow exchange with respect to the 31P NMR time scale is both expected and observed. (34) Ott, L. S.; Finke, R. G. J. Nanosci. Nanotechnol. 2008, 8, 1551− 1556. (35) Note that k1obs(bimol) is then and necessarily a pseudo-order rate constant in which any dependence on H2 of the nucleation step is buried in this (composite; apparent) rate constant. Note, however, that the H2 pressure (and thus solution concentration of H2) is constant to a high approximation during the induction period so that this dependence is not needed for the purposes of the present study which is designed to provide evidence for the kinetic molecularity of Ir in the nucleation process. (36) Widegren, J. A.; Finke, R. G. J. Mol. Catal. A: Chem. 2003, 198, 317−341. (37) Yih, K.-H.; Hamdemir, I. K.; Mondloch, J. M.; Bayram, E.; Ö zkar, S.; Vasic, R.; Frenkel, A. I.; Anderson, O.; Finke, R. G. Inorg. Chem. 2012, 51, 3186−3193. (38) Bentea, L.; Watzky, M.; Finke, R. G. J. Phys. Chem. C 2017, 121, 5302−5312. (39) (a) Collman, J. P.; Finke, R. G.; Matlock, P. L.; Wahren, R.; Komoto, R. G.; Brauman, J. I. J. Am. Chem. Soc. 1978, 100, 1119−1140. This paper reports an early example of an inverse D/H KIE in organotransition-metal chemistry. See also (b) Parkin, G. Acc. Chem. Res. 2009, 42, 315−325. (40) Ben-Eliyahu, Y.; Brill, M.; Mintz, M. H. J. Chem. Phys. 1999, 111, 6053−6060. (41) Völkle, C. M.; Gebauer, D.; Cölfen, H. Faraday Discuss. 2015, 179, 59−77. (42) Teo, B. K.; Zhang, H. In Metal Nanoparticles: Synthesis, Characterization, and Applications; Feldheim, D. L., Foss, C. A., Jr., Eds.; Marcel Dekker: New York, 2002; Chapter 3, pp 55−87. (43) (a) An observant referee wondered if we had plans to study the rigorously different, but interesting and related system, suggested by our termolecular nucleation mechanism finding, namely, the system of 2(COD)Ir(solv)2+X− + 1(COD)Ir·POM8−. The answer is that we do not have any such plans, in part because we know that in the absence of good stabilizers such as the POM9− that insoluble bulk metal (i.e., not a narrow dispersion of soluble, well-formed nanoparticles) tends to result.8,43b Hence, the mechanism of that different system almost surely will involve agglomeration phenomena and, hence, will necessarily be more complex and harder to establish. The rate will also be faster, perhaps requiring stopped-flow kinetic methods, since two-thirds of the POM9− rate-inhibiting effect demonstrated herein, and which is crucial to slowing down the nucleation and growth en route to achieving the final, narrow size, soluble Ir(0)n nanoparticles, will be absent in that (COD)Ir(solv)2++ 1 (COD)Ir(solv)2·POM8− system (that lacks twothirds of the POM9− stabilizer). There is also the question of what anion “X−”, to pick, and what its influence will be. However, our hope is that the present study will give ideas and impetus to others for their own future studies of nucleation, growth and agglomeration kinetics and mechanism(s). (b) Lin, Y.; Finke, R. G. Inorg. Chem. 1994, 33, 4891. (44) (a) The following, state-of-the-art paper 44b describes isonicotinamide crystallization from EtOH stirred at 700 rpm, in which 144 repeat heat/cooling to 25 °C cycles of crystallization are followed for a given sample in this weakly bonded system using a “Crystal16” multiple sample reactor that detects turbidity by measuring light transmission through the sample. In that work, dust particles and resultant heterogeneous nucleation are shown to dominate >2/3 of the nucleation data. The authors report a “nucleus size”, n* = 11−50, but what they are actually monitoring is the first-observable cluster (FOC)14 via their light-transmission threshold value, and not the kinetically effective nucleus (KEN). In short, in 2/3 of the 144 repeat crystallizations, solid crystalline organic product is formed predominantly as a result of dust-mediated, heterogeneous nucleation. The inescapable prediction from that important paper is, in our opinion, that at least for such organic molecule nucleations and possibly much more

= 6.4 × 10−5 M and one can

estimate that k−1 should be >10 M s so that k1 = 6.4 × 103 s−1 can be estimated as well. The NMR time scale in our 31P NMR experiment, 8

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Journal of the American Chemical Society generally, nucleations not done under clean room conditions need to be experimentally tested for involvement of a dust-mediated, heterogeneous component. Efforts are in progress to test just this hypothesis for the present (COD)Ir·POM8− nanoparticle formation system. (b) Kulkarni, S. A.; Kadam, S. S.; Meekes, H.; Stankiewicz, A. I.; ter Horst, J. H. Cryst. Growth Des. 2013, 13, 2435−2440.

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Evidence for a Kinetically Effective Nucleus of Three - ACS Publications

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