Article pubs.acs.org/JACS
Nucleation is Second Order: An Apparent Kinetically Effective Nucleus of Two for Ir(0)n Nanoparticle Formation from [(1,5COD)IrI·P2W15Nb3O62]8− Plus Hydrogen William W. Laxson and Richard G. Finke* Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, United States S Supporting Information *
ABSTRACT: Nucleation initiates phase changes across nature. A fundamentally important, presently unanswered question is if nucleation begins as classical nucleation theory (CNT) postulates, with n equivalents of monomer A forming a “critical nucleus”, An, in a thermodynamic (equilibrium) process. Alternatively, is a smaller nucleus formed at a kinetically limited rate? Herein, nucleation kinetics are studied starting with the nanoparticle catalyst precursor, [A] = [(Bu4N)5Na3(1,5-COD)IrI·P2W15Nb3O62], forming soluble/dispersible, B = Ir(0) ∼300 nanoparticles stabilized by the P2W15Nb3O629− polyoxoanion. The resulting sigmoidal kinetic curves are analyzed using the 1997 Finke−Watzky (hereafter FW) two-step mechanism of (i) slow continuous nucleation (A → B, rate constant k1obs), then (ii) fast autocatalytic surface growth (A + B → 2B, rate constant k2obs). Relatively precise homogeneous nucleation rate constants, k1obs, examined as a function of the amount of precatalyst, A, reveal that k1obs has an added dependence on the concentration of the precursor, k1obs = k1obs(bimolecular)[A]. This in turn implies that the nucleation step of the FW two-step mechanism actually consists of a second-order homogeneous nucleation step, A + A → 2B (rate constant, k1obs(bimol)). The results are significant and of broad interest as an experimental disproof of the applicability of the “critical nucleus” of CNT to nanocluster formation systems such as the Ir(0)n one studied herein. The results suggest, instead, the experimentally-based concepts of (i) a kinetically effective nucleus and (ii) the concept of a first-observable cluster, that is, the first particle size detectable by whatever physical methods one is currently employing. The 17 most important findings, associated concepts, and conclusions from this work are provided as a summary.
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A Brief Review of Classical Nucleation Theory and Its “Critical Nucleus” Concept. Classical nucleation theory (CNT) is the firstand currently still the most popular theoretical model for nucleation.6 CNT is, inherently, a thermodynamic, equilibrium-based model in which n equivalents of monomer, A, are implied to be in associative equilibria up to a putative “critical nucleus”, An, that is then postulated to be stable enough to grow rather than dissociate back to A. CNT postulates a balance of thermodynamic forces of favorable bonding or other associations between the precursor A vs the increasingly unfavorable interfacial surface energy associated with the creation of a new interface between the nucleus, An, and the solution. CNT has been widely used to try to explain nucleation6 since its earliest formulation by Volmer8,9 and Becker and Döring.10 LaMer then adopted CNT as part of his widely cited, but still little supported, “burst nucleation and diffusion-controlled particle growth” mechanism dating back to the 1950s.11 One fundamental problem with CNT from a kinetic perspective is the statistical improbability of a kinetically facile, higher-order, reversible n > 3 nucleus; true termolecular (concerted) reactions being rare and documented primarily only in gas-phase reactions.12
INTRODUCTION The Generality and Hence Broad Importance of Nucleation and Growth Across Nature. Nucleation and growth phenomena are essential components of phase changes for many chemical and physical systems in areas as diverse as materials science, atmospheric and climate research,1,2 degenerative neurological diseases,3,4 and many other important systems throughout nature. It is, therefore, critical to have an accurate mechanistic model of nucleationthose crucial first events governing the formation of the new phase5to be able to rationally design reproducible, size- and shape-specific syntheses of nanoparticulate and larger systems formed by nucleation and growth processes. Unfortunately, a consensus view of nucleation, and especially its mechanism, has not emerged. Indeed, Liu has commented that “Nucleation, in particular its mechanism, continues to be one of the most poorly understood and disputable phenomena in the past half century”.5 In nanoparticle chemistry in particular, the mechanism of nucleation has been a long sought goal,6 given that nucleation greatly influences5 the size, shape, and resultant electronic, optical, and catalytic properties6,7 of the resultant new phase. A kinetic and mechanistic understanding of nucleation is, therefore, a critical gap in our fundamental understanding of phase changes throughout nature. © XXXX American Chemical Society
Received: October 8, 2014
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processes.6,28 If so, then such MxHy or other kinetic intermediates along the nucleation pathway would be profound in signaling that CNT does not apply and should not be used, as the system is not a nA →An type system, since A is highly soluble so that CNT and its notion of supersaturation in A are inapplicable. Our second hypothesis for some time now has been that, in at least strongly bonding/strongly associating systems (and maybe many if not most others), nucleation will generally be under kinetic control and not the equilibrium control implied by CNT. As part of the present work we in turn define the more readily experimentally measurable kinetically effective nucleus (KEN) and distinguish it from the theoretical, experimentally nondetectable, and hence elusive “critical nucleus” of CNT. We define the KEN as the observed reaction order in a kinetically demonstrated nucleation step, specifically the reaction order, n, in the assembling monomeric precursor A, in a kinetically demonstrated nucleation step, [A]n. Noteworthy here is that the small, KEN will generally be below the detection limit or time resolution of most analytical methods, that is, even the KEN will generally be missed by most analytical methods.6 Those physical methods will, instead and in general, detect what we introduce and define herein as the first observable cluster (FOC), a concept we return to in the Results and Associated Discussion section. The KEN will, then, generally be detectable only by determining the kinetics of the phase change under study. These new concepts will tend to be especially applicable in systems that are not of the simpler nA → An type (e.g., not hydrocarbon droplet formation in the gas phase from low supersaturation conditions17), but rather where more complex chemistry is involved, such as the 2A + H2 → 2B system herein (vide inf ra). The 1997 Finke−Watzky Disproof Based Ockham’s Razor Obeying/Minimalistic Two-Step Mechanism: Slow, Continuous Nucleation Followed By Autocatalytic Surface Growth. In 1997, the Finke−Watzky (hereafter FW) two-step mechanism29,30 was the first to quantitatively fit sigmoidal nanoparticle formation data with a chemically precise mechanism and associated experimentally testable rate law. The FW two-step mechanism consists of two pseudo-elementary31 steps29 defined by their balanced reactions of: (i) slow, continuous nucleation, A → B (rate constant, k1obs) and (ii) autocatalytic surface growth, A + B → 2B (rate constant k2obs), where A equals the nanoparticle precursor (in the present case the precatalyst [A] = [(Bu 4 N) 5 Na 3 (1,5-COD)Ir I · P2W15Nb3O62]) and B is the growing nanoparticle, Ir(0)n. The disproof based, Ockham’s razor obeying, deliberately minimalistic FW two-step mechanistic model is supported by more than 700 kinetic experiments6 conducted mostly on the prototype transition-metal nanoparticle formation system in Scheme 1. As such, the Ir(0)n nanoparticle formation system in Scheme 1 is one of the best studied nucleation and growth systems available across nature.6,29 Those studies have yielded
Despite its widespread and continued use, CNT has proven unable to match experimental measurements of nucleation rate constants,13 often being off by even up to 106−10 in its predicted rate constants.14−16 CNT appears to be best suited for systems such as hydrocarbon associations in the gas phase,13,17 at high temperatures,6 or for latex particle associations18,19 in solutionwhat we will designate herein as weakly bonded (i.e., weakly associating) systems. Even then, nucleation is one of the few fields where predictions accurate within ±101−2 are considered “a major success”.20 Furthermore, the theoretical “critical nucleus” of CNT has arguably never been actually detected as one expects since it is by definition the least stable, highest energy species that, therefore, would be a fleeting transient between the starting material and the final, phase-changed product.6 Indeed, in 2001 Gasser and co-workers21 noted at the time that “No experiment has ever directly measured the size of the critical nucleus” prior to their confocal microscopy studies of the weakly associating poly-12-hydroxy-stearic acid-stabilized poly(methyl methacrylate) sphere aggregations; those larger, and preformed latex particles being used as a model of nucleation and growth, albeit one of preformed particles and not atomic or molecular precursors (and, therefore, really a study on the nucleation of aggregation). On reflection, it is remarkable that CNT continues to be so widely employed despite overwhelming, recurring, and repetitive evidence that CNT fails in especially more complex systems in nature.13−16,22 This statement applies especially to strongly associated (bonded) systems that are often not of the simple nA →An type such as the Ir nanoparticle system herein with its relatively strong Ir−Ir and probably Ir−H−Ir bonds, vide inf ra. For such more complex systems there is no compelling evidence that CNT can predict, much less quantitatively account for even ex post facto, experimentally measured nucleation rate constants. The Distinction Between Strongly vs Weakly Bonding SystemsPlus the New Concept of a Kinetically Effective Nucleus. The inability to have a reversibly associating, nA →An type system up to the putative critical nucleus of CNT is expected to be especially pronounced in what we designate herein as strongly bonded (alternatively “strongly associating”) systems.6 Transition-metal nanoparticles, for example, formed from M0n nuclei (or very plausibly M−H species, vide inf ra)6 will generally have M−M (or M− H−M) bond energies of ≥25−30 kcal/mol23 (to ≥55−75 for M−H)24 and, therefore, are unlikely to exist as rapidly reversible systems associating up to the theoretical “critical nucleus” postulated by CNT. In the case of Ir, each Ir−Ir in a nucleus contributes a stabilizing enthalpy estimated to be at least ∼26 kcal/mol25 and each Ir−H an estimated 75 kcal/ mol.24 Especially if Ir−H−Ir or Ir−(H)2−Ir bonds form, then the resulting binuclear nucleus almost surely never reverses as CNT requires and assumes. The possible reversible formation of a less strong Ir−Ir is less clear, since Ir−Ir and Ir−L (and other M−M and M−L, M = transition metal) bonds are of roughly equal bond dissociation energies (BDEs).23 This in turn means that the presence of high concentrations of relatively strong binding, BDE ≥ 26 kcal/mol ligands, L, could in principle lead to reversible formation of a Irn (n ≥ 2) kinetic nucleus.26,27 These considerations again lead logically to the suggestion of M−H−M bonds in the rate-determining step of nucleation. In short, the above thermochemical analysis further supports our hypothesis that M−H−M may well be more generally involved in transition-metal nanoparticle nucleation
Scheme 1. Formation of Ir(0)∼300 From the [(1,5-COD)Ir· P2W15Nb3O62]8− Nanoparticle Precatalyst Under Hydrogen and in the Presence of 1 equiv of Proton Sponge to Scavenge the H+ Formed
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is used39,40 as well as evidence for bimolecular nucleation in H2SO4 droplet formation relevant to atmospheric chemistry.1,41,42 Looking a bit closer at the Rh nanocube formation study by XAFS, a discontinuous jump from zero to between one and two in the first-shell coordination of rhodium is observed during nucleation, implying Rh2 or Rh3 within experimental error.38 These XAFS results provide suggestive evidence consistent with an XAFS-average KEN of Rh2−3 within experimental error, although the needed definitive kinetic data unequivocally demonstrating bi- vs ter-molecular nucleation and thus the origins of the observed Rh2−3 and attempting to disprove higher-molecular nucleation hypotheses are currently unavailable. Note also that the author’s claim that “a Rh4 cluster acts as the critical nucleus species for the formation of the nanocubes” is arguably better interpreted as what we define herein as the FOC (vide inf ra). There is also suggestive, albeit not definitive, evidence for second-order [Pt]2 kinetics in PtIICl42− reduction by H2 to form Pt(0)n colloids in sodium citrate plus NaOH aqueous solutions.43 A side note of some interest here is that there is also increasing evidence for metastable M4 species as detectable (e.g., Pt4 by QXAFS),44 or isolable (e.g., Ir4H4(1,5-COD)4),45 or catalytically active (e.g., Rh4) species.46 The QXAFS direct observation of Pt4 is especially relevant to the present contribution since the FW two-step mechanism was employed in that literature study and provided an excellent fit to the initial nucleation and growth kinetics of the poly(N-vinylpyrrolidone)-stabilized Pt(0)n nanoparticles (formed from H2PtCl6 in EtOH under benzophenone or benzoin-sensitized irradiation). Such Pt4 and other M4 species could of course be readily formed from simple dimerization of two M2 kinetically effective nuclei to give M4 as the FOCs or perhaps by single metal (M) addition to an M3 KEN. Pt4 was designated by those authors as the “nucleus” in their work,44 but the published evidence44 does not allow one to distinguish between the observed M4 simply being the FOCs rather than the more fleeting KEN. Even more relevant to the present study is the rapid reaction of the isolated, crystallographically and XAFS characterized, coordinatively unsaturated subnanometer cluster45 Ir4H4(1,5-COD)4 under H2 to yield Ir(0)n. Given that this system rapidly grows without an induction period to give a highly catalytically active system,45 it provides strong evidence that the KEN is n ≤ 4 in at least such Ir systems such as the one studied herein (vide inf ra). Also exceedingly interesting and tantalizing is the observation of key Td symmetry, M4 building blocks in achieving dense packing in growing systems such as quasicrystals.47,48 Any M4 system can be formed at least formally by a dimerization of dimers, (M2)2, although it remains to be determined what the nucleation rate-determining step and the implied KEN are in these intriguing processes. A bottom line, then, post-examining the extant nucleation and growth literature across nature is that definitive kinetic evidence for even the reaction order of the rate-determining step of nucleation is lacking. Further lacking is the mechanistic insight necessary to uncover the true molecularity of nucleation. This gap in our knowledge of nucleation across nature exists despite the anticipated much broader implications and fundamental importance of establishing the true KEN in at least a few prototype systems. A crucial conceptual point to raise at this juncture is the important distinction between the more readily determined reaction order in a precursor or precatalyst A, [A]n, vs the true
nine valuable mechanistic and synthetic insights summarized in a footnote for the interested reader.32 The limitations of the FW two-step mechanism are also discussed elsewhere for the interested reader, limitations that derive, ultimately, from the minimalistic and thus too simple nature of the kinetic model and the average rate constants, average size, and other average nanoparticle properties that result from the deliberately minimalistic, Ockham’s razor obeying, kinetic model.33 However, of considerable significance is that the two steps of the FW two-step model define and describe precisely and chemically the respective steps of the slow, continuous nucleation and autocatalytic growth, even if primarily phenomenologically and even if via composite, pseudoelementary31 steps that oversimplify the true, underlying, multistep nucleation and growth process. The significance of such balanced chemical equations, and thus mechanistically well-defined, precise kinetic and mechanistic descriptors for the overall phase change, is hard to overstate. In their absence, confusion and convolution of concepts and words result, for example, seen in purely physical chemical or engineering models, as documented and discussed elsewhere.34,35 The implied corollary here is that, ultimately, model building of dynamic chemical systems in science proceeds rationally best from, and therefore needs to rest upon, a foundation of initially minimalistic, disproof-based, mechanistic models. Emerging Evidence that Nucleation May Often Be Bimolecular or Possibly Termolecular in More Complex Systems and the Alternative Hypotheses of Tetra- or Higher-Molecularity Nucleation. The simplest, first hypotheses that could describe the KEN include: unimolecular, bimolecular, termolecular (i.e., trimolecular, 3A → 3B (= (B)3)) or conceivably tetra- (4A → 4B (= (B)4)) or even higher-order formulations of the nucleation rate-determining step. Note here again that since true, concerted termolecular reactions are seen primarily for only gas-phase reactions;12 hence what is meant by the above net stoichiometric equations is that reversible, prior associative equilibria would somehow be involved and lead to the net pseudo-elementary steps shown above with their implied, for example, net third or fourth orders in the primary reactant, A. Within these possibilities and for the case of nucleation of Ir(0)n nanoparticles as studied herein, the greatest “energetic/ physical discontinuity” would seem to occur when the first 2 A (i.e., herein the first two Ir) or perhaps the first three A form the first one or two A−A bonds (herein the first one or two Ir− H−Ir or Ir−Ir bonds). That is, rate-limiting bimolecular nucleation step, A + A → 2B, to an implied KEN of 2, makes intuitive sense in the case of relatively strongly bonding A−A such as transition-metal nanoparticle formation (as opposed to relatively weak bonding of, say, nucleation of hydrocarbon aggregation in the gas phase and where improved CNT models can reproduce nucleation rate constants to within a ∼101−2 error).17 Not unexpectedly, therefore, hints suggestive of bimolecular or possibly termolecular nucleation are beginning to appear in the literature of phase changes across nature. Four cases of note are kinetic evidence in 1989 for approximately bimolecular to termolecular (n obsd ∼ 2.2) nucleation in Gelatin R1 renaturation,36 the detection of Ag2 in the formation of Ag(0)n nanoparticles,37 a 2012 XAFS study of the formation of rhodium nanocubes suggesting Rh∼2−3 species (vide inf ra),38 protein aggregative nucleation and growth where a nucleus of 2 C
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molecularity of the rate-determining step of the underlying, more intimate nucleation mechanism. These will generally be the same only in the case where A is the assembling monomer, nA → An. In the present case, where A = the precatalyst (Bu4N)5Na3(1,5-COD)IrI·P2W15Nb3O62, we can, for example, write more intimate mechanisms that will exhibit apparent nucleation kinetics second-order in A, [A]2, but via mechanisms termolecular in Ir at the rate-determining step of nucleation; so that apparent second-order kinetics would actually correspond to a termolecular reaction in [Ir] and, therefore, a KEN of 3. Nevertheless, the first job at hand is to measure precise enough nucleation kinetics, a considerable challenge in its own right, to determine the net reaction order in the precatalyst A, in the present case, A = (Bu4N)5Na3(1,5-COD)IrI·P2W15Nb3O62 for the prototype case of Ir(0)n nanoparticle formation. In a subsequent study in progress we will return to the even more challenging task of distinguishing unequivocally bi- from termolecular nucleation, that is, distinguishing a KEN of 2 vs a KEN of 3. The Prototype [(1,5-COD)Ir·P2W15Nb3O62]8− Precatalyst and Resultant Ir(0) n Nanoparticle Formation Systems Plus the FW Two-Step Mechanism and Kinetics Exploited Herein. We employ herein our well-established (Bu4N)5Na3(1,5-COD)Ir·P2W15Nb3O62 precursor and nanoparticle catalyst formation, the system where the FW two-step mechanism of slow continuous nucleation and autocatalytic surface growth was discovered and developed.29 When placed in acetone or propylene carbonate under ∼40 psig hydrogen, the polyoxometalate supported, (1,5-COD)Ir+ containing precatalyst [(1,5-COD)Ir·P2W15Nb3O62]8− is reduced to form near-monodisperse (i.e., by definition ≤ ± 15% size distribution)49 Ir(0)∼300 nanoparticles stabilized by the P2W15Nb3O629− polyoxometalate, Scheme 1. The Ir(0)∼300 nanoparticles form a very active cyclohexene hydrogenation catalyst which, in turn, serves as a welldeveloped reporter reaction29 in which the slow steps of nucleation and growth can be followed and their signal amplified, by using cyclohexene:Ir ratios ≫1. The development of the Ir(0)n catalyst is, then, followed by the uptake of hydrogen involved in the net cyclohexene plus H2 to cyclohexane, catalytic reporter reaction,29 Scheme 2. Impor-
Figure 1. Representative sigmoidal kinetics for the (Bu4N)5Na3(1,5COD)Ir·P2W15Nb3O62 catalyst precursor in propylene carbonate under an initial 40 psig H2 and coupled to the cyclohexene reporter reaction (Scheme 2). Also shown is the subsequent curve-fit to the FW two-step mechanism over the parts of the kinetic curve where the conditions necessary for the validity of the pseudo-elementary-step reporter reaction kinetic method are satisified.29 The arrow shows qualitatively where the first observable catalytically effective cluster, N*, can be detected.
the integrated, analytic rate equation corresponding to the FW two-step mechanistic model, Scheme 2, using nonlinear-leastsquares fitting, resulting in the desired nucleation rate constant k1obs (as well as k2obs) and associated fitting error estimates. Indicated qualitatively by the arrow shown in Figure 1, the end of the induction period is where hydrogenation catalysis is first detectable by our catalytic reporter reaction monitoring methodology.29 That point designates the FOC by the catalytic reporter reaction monitoring method, what we previously called the catalytically effective cluster, N*.50 Addition of Bimolecular Nucleation to the FW TwoStep Mechanism: The Bimolecular-FW Two-Step Mechanism. In what follows, we formulate a bimolecular nucleation version of the FW two-step kinetic model. In doing so, we are treating the fundamental, conceptual simplest case where A is the assembling monomer and where bimolecular nucleation is an elementary step. Put another way, we will measure an apparent molecularity and apparent KEN size, n, as well as apparent bimolecular k1obs(bimol) rate constants in what follows, all under the assumption that A = (Bu4N)5Na3(1,5-COD)Ir· P2W15Nb3O62 is the assembling monomer. Once we get to the experimental results, we will be careful to refer to what the experimental data actually provide, the observed reaction order in the precatalyst. Connecting that observed reaction order to the true molecularity of the nucleation step, and hence to the true size, n, of the KEN, can be done unequivocally only when the more complete, underlying mechanism is known with some certainty. We have realized for some time now that true bi- or termolecular (or conceivably higher molecularity) nucleation could easily be kinetically hidden in the historical FW twostep kinetic model. This latter point follows since the concentration of the precursor, [A], is effectively constant to a precision of ≥99.95% (i.e., [A]t ≅ [A]0) during the induction period and associated primary nucleation. Equation 1 shows the differential rate equation for the nucleation first step of the historical, unimolecular formulation for the FW two-step mechanism shown back in Scheme 2:
Scheme 2. FW Two-Step Mechanism and Its Coupling to the Cyclohexene Reporter Reaction
tantly, controls checking the reporter reaction have been performed many times by following the cyclooctane evolution (Scheme 1) directly by GLC and by verifying the zero-order dependence on the [cyclohexene] required to ensure that the reporter reaction is fast and not rate determining and, therefore, working properly29 (Scheme 2, vide infra). The H2-loss kinetic data are then converted for convenience to their corresponding cyclohexene-loss curve, Figure 1, via the established 1:1 H2 to cyclohexene stoichiometry.29 The characteristic sigmoidal kinetic curve in Figure 1 is then fit to D
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d[A] = k1obs[A] dt
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drybox), CH2Cl2 (HPLC grade stored in a drybox), acetone (Burdick & Jackson 99.5%) was passed through indicating moisture and O2 scavenging traps (Trigon Technologies) before use in hydrogenations. Deuterated NMR solvents (CD3CN, CD3NO2, and CD2Cl2) were obtained from Cambridge Isotope Laboratories in 1 g sealed glass ampules and were transferred into a drybox before use in NMR tubes sealed with rubber stoppers. D2O was obtained from Sigma-Aldrich. All aqueous solutions were prepared using 18 MΩ deionized water from a nanopure filtration system.
(1)
However, a higher reaction order, n, nucleation mechanism would have the kinetics shown in eq 2:
−
d[A] = nk1obs(n)[A]n dt
(2)
A bimolecular, n = 2, nucleation step with the rate constant k1obs(bimol), hereafter the bimolecular-FW two-step mechanism, is expected to show the kinetics given in eq 3, which includes the proper statistical factor of 2 that results from the 2A → 2B (= B2) stoichiometry: −
d[A] = 2k1obs(bimol)[A]2 dt
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INSTRUMENTATION All pH measurements were made with a pH electrode standardized with two buffers (pH of 4.00, 7.00, or 10.01, bracketing the desired range). NMR spectra were obtained in 5.0 mm o.d. NMR tubes with the respective deuterated solvent prepared in a drybox and capped with rubber airtight stoppers. 31 P, 1H, and 13C NMR spectra were recorded on Varian Inova 300 or 400 MHz spectrometer at 21 °C. 31P NMRs were externally referenced to 85% H3PO4. Air- and moisturesensitive reactions were routinely preformed in a Vacuum Atmospheres drybox kept below 2 ppm of O2 and constantly monitored by a Vacuum Atmospheres O2 sensor, and air sensitive compounds were stored double bottled in the drybox. (1,5-COD)Ir(CH3CN)2BF4 Synthesis. This precursor was synthesized by the literature methods,56 except BF4− was substituted for PF6− as described elsewhere.57 The identity and purity of the product were established by 1H NMR in CD2Cl2 and 13C NMR in CD3NO2 in comparison to the published spectra.56 K6[α-P2W18O62] Synthesis. This parent Wells−Dawson polyoxometalate was synthesized by Nadjo’s method,58 but as detailed by Graham,59 via that faster, higher yield, better atom economy and higher purity synthesis now available.60 Purity of the product is 99.9% by 31P NMR in D2O in comparison to the published spectrum.59 Na12[α-P2W15O56] Synthesis. The synthesis of this lacunary polyoxometalate precursor was carried out by our new, improved methodology61 for obtaining the highest known purity Na12[α-P2W15O56]. A detailed procedure is provided therein,61 one that must be followed to the letter to obtain the highest purity product. Briefly, a preparation by Droege et al.62 was used except that the clay-like product was fully suspended during each of the five washing steps, including two added washes using deionized water that helped ensure all residual WO42− is removed at a slight, twothirds of the data. They report a “nucleus size”, n* = 11−50, but note that what they are actually monitoring is the first-observable cluster, as defined herein, via their light-transmission threshold value, yielding solid product that is formed predominantly as a result of dust-initiated, heterogeneous nucleation. (b) Kulkarni, S. A.; Kadam, S. S.; Meekes, H.; Stankiewicz, A. I.; ter Horst, J. H. Cryst. Growth Des. 2013, 13, 2435−2440. (69) Li, Z.; Zhong, J.; Levin, D. A.; Garrison, B. J. J. Chem. Phys. 2009, 130, 174309. (70) 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. (71) Goldstein, R. F.; Stryer, L. Biophys. J. 1986, 50, 583−599 Stryer makes a comment on p. 593 based on his results and earlier results of others regarding nucleation, a comment that strikes a cord in light of our current second-order nucleation studies, “...the pre-equilibrium assumption is highly suspect···”. “Why was this not discovered earlier?”. (72) (a) A recent reference in this regard is the paper by Kumar, et al.72b which adds population balance (PB) modeling to the FW twostep mechanism to try to account for the relatively narrow, ≤ ±15% nanoparticle size distributions typically seen when the FW two-step mechanism fits the nanoparticle formation kinetic data. However and unfortunately, that paper: (i) only examines one limited data set digitized from our original literature (i.e., so that the high precision of the original data is lost for the subsequent curve-fitting); (ii) does not know, and therefore fails to consider, the true intimate mechanism of nucleationa major weakness since nucleation is the step(s) that the study is trying to understand; (iii) fails to consider a range of known mechanisms that could explain the data; (iv) fails to consider a stochastic approach to the size distribution problem; (v) then adds, in an ad hoc and thus nonmechanistic way, what ultimately is a solubilitybased “burst” nucleation in their “PBM-4s” model in place of the now known, second-order, continuous nucleation; and (vi) fails to present and discuss in the main text any of the assumptions and approximations in the PB modeling and how they might influence the paper’s conclusions. Hence, (vii) the primary conclusion in this PB modeling paper, that nucleation must somehow be “delayed”, cannot
(40) Meisl, G.; Yang, X.; Hellstrand, E.; Frohm, B.; Kirkegaard, J. B.; Cohen, S. I. A.; Dobson, C. M.; Linse, S.; Knowles, T. P. J. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 9384−9389. (41) (a) Zhang, R. Science 2010, 328, 1366−1367. See the interesting discussion thereindiscussion highly relevant to the concepts proposed herein of a KEN and first-observable clusterof the most recent nucleation studies by more sensitive methods that suggest a “critical nucleus” for H2SO4 droplet nucleation of 2 (what we call herein a 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 apparently missed the true (kinetically effective) nucleus and are, instead, what we define herein the first-observable cluster(s). (b) Sipilä, M.; Berndt, T.; Petäjä, T.; Brus, D.; Vanhanen, J.; Stratmann, F.; Patokoski, J.; Mauldin, R. L., III; Hyvärinen, A.-P.; Lihavainen, H.; Kulmala, M. Science 2010, 327, 1243−1246. (42) Atmospheric nucleation is obviously complex, as the following paper detailing the large effects of NH3 on atmospheric H2SO4 nucleation demonstrate: 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. (43) Henglein, A.; Giersig, M. J. Phys. Chem. B 2000, 104, 6767− 6772. (44) Harada, M.; Kamigaito, Y. Langmuir 2012, 28, 2415−2428. (45) Yih, K.-H.; Hamdemir, I. K.; Mondloch, J. E.; Bayram, E.; Ö zkar, S.; Vasic, R.; Frenkel, A. I.; Anderson, O. P.; Finke, R. G. Inorg. Chem. 2012, 51, 3186−3193. See also the list therein of other known M4 clusters. (46) Bayram, E.; Linehan, J. C.; Fulton, J. L.; Roberts, J. A. S.; Szymczak, N. K.; Smurthwaite, T. D.; Ö zkar, S.; Balasubramanian, M.; Finke, R. G. J. Am. Chem. Soc. 2011, 133, 18889−18902. (47) Duff, D. G.; Curtis, A. C.; Edwards, P. P.; Jefferson, D. A.; Johnson, B. F. G.; Logan, D. E. J. C. S. Chem. Comm. 1987, 1264− 1266. (48) (a) Amir, H.-A.; Engel, M.; Keys, A. S.; Zheng, X.; Petschek, R. G.; Palffy-Muhoray, P.; Glotzer, S. C. Nature 2009, 462, 773−777. (b) Chen, E. R.; Engel, M.; Glotzer, S. C. Condensed Matter 2010, 1− 26. (49) Finke, R. G. In Metal Nanoparticles: Synthesis, Characterization and Applications; Feldheim, D. L.; Foss Jr., C. A., Eds.; Marcel Dekker, Inc.: New York, 2002, Chapter 2, pp 17−54. (50) Watzky, M. A.; Finney, E. E.; Finke, R. G. J. Am. Chem. Soc. 2008, 130, 11959−11969. (51) Mondloch, J. E.; Finke, R. G. ACS Catal. 2012, 2, 298−305. (52) Mondloch, J. E.; Finke, R. G. J. Am. Chem. Soc. 2011, 133, 7744−7756. (53) Besson, C.; Finney, E. E.; Finke, R. G. J. Am. Chem. Soc. 2005, 127, 8179. (54) Ö zkar, S.; Finke, R. G. J. Am. Chem. Soc. 2002, 124, 5796−5810. (55) Ir(0)∼300 nanoparticles formed at 1.2 mM standard conditions. Nanoparticle size increases at higher concentration of catalyst precursor and range from ∼1.8(±0.2) nm to 3.4(±0.5) nm for smples in this study. (56) Day, V. W.; Klemperer, W. G.; Main, D. J. Inorg. Chem. 1990, 29, 2345−2355. (57) Weiner, H.; Aiken, J. D.; Finke, R. G. Inorg. Chem. 1996, 35, 7905−7913. N
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be trusted at present. Required is more careful scrutiny and testing via PB modeling once we have finished elucidating and report the more intimate mechanism of nucleation underlying the FW two-step model, that correct chemical mechanism being the presently missing, but required input, for reliable PB modeling. (b) Perala, S. R. K.; Kumar, S. Langmuir 2014, 30, 12703−12711. (73) We are working on just such a needed, critical reanalysis of LaMer’s mechanism and its evidence, including literature that claims to use and support LaMer’s mechanism. We will report on that effort in due course. (74) Turkevich, J.; Stevenson, P. C.; Hillier, J. Discuss. Faraday Soc. 1951, 11, 55. (75) Perala, S. R. K.; Kumar, S. Langmuir 2013, 29, 9863−9873. This paper assumes CNT for modeling nucleation, assumes a mechanism, assumes (somewhat randomly, and almost surely incorrectly) a nucleus of Au10, and then uses a population balance model that has 10 parameters to purportedly rule out the burst nucleation mechanism of LaMer. The paper then claims to support what is worded and implied to be novel as a “continuous nucleation growth passivation based mechanism”, but the paper does not offer any compelling evidence for “continuous nucleation” since that step is basically input as an assumption in their (assumed) mechanism. In addition, since continuous nucleation was first reported by Watzky 16 years earlier,50 one should ignore these author’s ill-advised, implied claim of novelty for their proposed “continuous nucleation”.
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