A Classic Azo–Dye Agglomeration System: Evidence for Slow

Article pubs.acs.org/JPCA

A Classic Azo−Dye Agglomeration System: Evidence for Slow, Continuous Nucleation, Autocatalytic Agglomerative Growth, Plus the Effects of Dust Removal by Microfiltration on the Kinetics 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: An important but virtually ignored 1978 paper by Reeves and co-workers, which examined a dye−OAc hydrolysis and then agglomeration system, is reanalyzed in light of current state of knowledge of nucleation and growth/ agglomeration phenomena. The Finke−Watzky two-step mechanism is used to account quantitatively for the kinetics data, in turn providing deconvolution of dye hydrolysis and nucleation of agglomerative growth, from the agglomerative growth step, including their separate rate constants. Significantly, the effects of microfiltration of the removable dust on the two steps and their rate constants are uncovered and quantitated for the first time, including the finding that the presence of dust accelerates both steps by ca. 10-fold or more. A postulated minimum mechanism able to account for all the observed results is provided. The results allow the excellently designed and executed, now nearly 40-years old, classic studies of Reeves and co-workers to be placed in its proper position in history, while at the same time providing six insights and conclusions detailed in the Discussion and Conclusions sections of the paper.

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INTRODUCTION

understanding of photographic dye stability and of absorption maxima that shifted due to dye agglomeration. The sigmoidal kinetics observed while monitoring the absorbance at 475 nm (A475), “the maximum absorbance of the dye product”14 (taken herein to mean the λmax of the aggregated, colloidal dye product), are reproduced in Figure 1. Several noteworthy points from this virtually ignored, greatly undercited, but actually classic (vide infra) study include: (i) filtering the reactant solution through a 0.2 μm Nucleopore microfiltration membrane slows the rate of colloidal product formation dramatically and changes the shape of the kinetic curve to linear (Figure 1, curves A vs B); and (ii) adding back/ “seeding” with unfiltered solution returns the faster, sigmoidal kinetics, Figure 1, curves F and G (where a solution from curve E was taken and added to F and G where the arrows indicate). Additionally, (iii) light scattering shows the formation of 0.35 μm colloidal, (dye)n, particles, the light scattering intensity curve paralleling the A475 curve (Figure 2, p. 3881 of the original work14). This latter result is significant, as it supports the assignment of the 475 nm absorbance to the agglomerated (dye)n particles.

Nucleation and growth are omnipresent across nature, occurring in all phase changes.1−6 Hence, the mechanisms underlying, and the factors affecting, nucleation, growth, and subsequent agglomeration phenomena are of broad, fundamental interest.7−11 In addition, although the effects of common dust on water vapor condensation have been known since 1875,12 the possible effects of dust on nucleation, growth, and agglomeration phenomena have been largely ignored since then outside of atmospheric chemistry, and hence are still illunderstood mechanistically, especially in terms of what step(s) can be influenced by dust. Quantitation of the effects of dust on individual mechanistic steps of particle formation outside of atmospheric chemistry has remained virtually unknown until recently.13 Reeves et al.’s 1978 Study of Azo−Dye Hydrolysis and Agglomeration. An important but overlooked and little cited paperonly two citations over nearly 30 years as of June 2017is that from Reeves and colleagues, then at Eastman Kodak company.14 Those authors were studying the hydrolysis of azo dyes, and then the agglomeration11 of the resultant alcohol form of the dye, to yield colloidal agglomerates of the hydrolyzed dyes, specifically those shown in Scheme 1. One can infer that their goals at the time likely included a better © XXXX American Chemical Society

Received: July 6, 2017 Revised: August 25, 2017

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Scheme 1. Azo−Dye Hydrolysis and Then Subsequent Agglomeration of the Alcohol Form of the Dye Studied by Reeves and Co-Workers14

lowering the so-called critical coagulation concentration15,16 and hence increasing the level of agglomeration, and resultant filterability, of the filterable agent, atmospheric dust according to the authors of the 1978 paper.14 The 1978 authors also (v) tried to fit the kinetics to an “E ⇌ [X] → P” mechanism but noted that the fit failed “even when the three rate constants (k1, k−1, k2) and the unknown absorption curve of X were allowed to vary as adjustable parameters”. That is, even with four adjustable rate constant parameters (plus a fifth adjustable parameter in the residual of the fit), the authors were unable to find a mechanism that fit the data, a limitation of the 1978 study that we will overcome as part of the present contribution (and with just two rate constants, plus the residual of the fit, vide infra). Importantly, because the authors had no idea of the particle formation mechanism back in 1978, the effects of filtration they documented and which they attribute to dust have remained unconnected, for over 39 years and until now (vide infra), to any particular kinetic step or steps in the net dye hydrolysis and subsequent agglomeration reaction, Scheme 1. This in turn explains why this previously hidden, but actually classic, 1978 paper has remained unrecognized, and not placed into its proper context in the extant literature, until now. Key, but often neglected, literature indicating the importance of dust in nucleation, growth, and agglomeration phenomena. P. J. Coulier and J. Aitken reported in the 1880s that airborne particles are a crucial component of vapor condensation processes.12,17−22 Turkevich’s pioneering 1951 paper on colloidal gold formation additionally notes that23 “In the absence of nuclei and in a dustfree atmosphere the growth medium undergoes no reduction of the auric ion for several hours.” Twelve years later Matijević and co-worker’s seminal 1963 paper on the formation of sulfur sols24 reports that the removal of dust by use of a 0.22 μm microfilter is necessary to achieve a reproducible synthesis of those Sn sols. However, in none of these seminal works was it possible at the time to elucidate the step or steps on which dust was having its effect(s). Unfortunately if not somewhat strangely, the role of dust in nucleation, growth, and agglomeration processes across nature seems to have then been largely forgotten over the next nearly 50 years in areas other than atmospheric chemistry. In 2013, an important, state-of-the-art crystallization kinetics study25 of isonicotinamide at supersaturating concentrations being heated, then cooled to induce crystallization, showed that the empirical “nucleation rate, J” (really the rate of formation of the firstobservable cluster monitored by a decrease in the intensity of transmitted light) drops 2.7-fold for solutions filtered through a 0.45 μm membrane filter. That 2.7-fold rate difference is attributed to room dust by the authors in that seminal study. Still, however, a rigorous chemical mechanism, complete with the necessary balanced chemical equations that define the (associated) differential equations used to fit the datathat is, a rigorous chemical mechanism so that the dust effects could be mechanistically understoodwas not reported.

Figure 1. Kinetics monitoring the A475 band for agglomeration of the hydrolyzed azo dye shown in Scheme 2 as reported by Reeves et al.14 Curve A is the normal, sigmoidal formation curve of the hydrolyzed, then aggregated dye starting from an unfiltered solution. B shows the greatly slowed rate starting from a solution that was filtered through a Nucleopore 0.2 μm microfiltration membrane. Curves C and D show “the effects of 10% added alcohol product on the initial rate of an unfiltered (curve C) and a filtered solution (curve D)”, quoting the authors.14 The alcohol product alone (i.e., without the HOAc coproduct) looks to have little effect on the kinetics. However, curves E, F, and G show, as the authors note,14 “the effects of seeding previously filtered solutions (curves F and G) with solution taken from an unfiltered solution (curve E)” and at different times in those separate experiments (F and G). The vertical arrows “indicate the time at which the seed solution was removed from E and added to F and G”.14 Clearly, the products/species in an unfiltered solution have a huge effect on the kinetics of filtered solutions, specifically, greatly accelerating the net dye hydrolysis and agglomeration reaction shown in Scheme 1. Reproduced with permission. Copyright 1978 American Chemical Society.

Also of considerable interest is (iv) that added electrolyte increased the author’s ability to filter out the rate-enhancing impurity, suggested to be room dust by the authors (vide infra). Although not discussed in the 1978 paper,14 the effect of added electrolyte is consistent with dust having a surface anionic charge as Derjaguin−Landau−Verway−Overbeek (ie., DLVO) theory predicts,15,16 the electrolyte then causing the well-known collapse of the thickness of the stabilizing multilayer,15,16 B

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determine which step or steps are influenced by dust, (c) to quantitate those effect(s); (d) to thereby learn what additional studies of dust effects in dye or other aggregation phenomenon merit future study; and (e) overall to place the important, previously overlooked, but actually classic paper by Reeves and co-workers in its proper place in the chemical literature.

Most recently in 2017, our own group examined the effects of microfiltration and dust removal, as well as the effects of the deliberate addition of dust, on the bimolecular nucleation26 (A + A → 2B, rate constant k1obs(bimol)) and autocatalytic surfacegrowth (A + B → 2B, rate constant k2obs(bimol)) kinetics and mechanism in the illustrative case of a prototype Ir(0)n nanoparticle formation system,13 A = an (1,5-COD)Ir+containing precatalyst reduced under H2 and B = Ir(0). Those studies included efforts to detect the dust by optical microscopy and dynamic light scattering. Previously unavailable, state-of-the-art insights from that study, quoting the Abstract from that paper, are:13 “(i) that the nucleation apparent rate ‘constant’ k1obs(bimol) is slowed by a factor from ∼5 to ∼7.6, depending on the precise experiment and its conditions, just by filtration of the precatalyst solution using a 0.20 μm filter and rinsing the glassware surface with 0.20 μm filtered propylene carbonate solvent; (ii) that simply employing a 0.20 μm filtration step narrows the size-distribution of the resulting Ir(0)n nanoparticles by a factor of 2.4 f rom ±19% to ±8%, a remarkable result; and (iii) that the narrower sizedistribution can be accounted for by the slowed nucleation rate constant, k1obs(bimol), yet unchanged autocatalytic growth rate constant, k2obs(bimol), that is, by the increased ratio of k2obs(bimol)/ k1obs(bimol) that further separates nucleation from growth in time for filtered, versus unfiltered, solutions.” Additionally, reported was the finding (iv) “that five lines of evidence indicate that the filterable component of the solution, which is having the nucleation rate-enhancing effect and size-dispersion broadening effect is dust.” It was during the construction of that publication,13 specifically during a careful review of the relevant literature, that we discovered the important Reeves et al. paper14 reexamined herein. The Focal Point of the Present Study. Can the Finke− Watzky (FW) two-step mechanism quantitatively account for the nucleation kinetic data of Reeves and co-workers? Does that classic 1978 study represent, then, an early, albeit overlooked, example of the role of dust in nucleation and agglomerative growth phenomena? What mechanistic step or steps are influenced by dust, and by how much, quantitatively? We suspected that the FW two-step (unimolecular nucleation,8 vide infra) mechanism would be the minimal mechanism able to account quantitatively for the sigmoidal kinetics data back in Figure 1 reported by Reeves et al. for the net dye hydrolysis and agglomeration reaction shown in Scheme 1.14 If so, that would be important, because it would be the historically first, albeit it was missed at the time, example of the connection of a deliberately minimalistic, disproof-based, and hence mechanistically rigorous mechanism of nucleation and growth to filtration effects attributed to dust14and only the second deconvolution of the effects of dust to individual mechanistic steps.13 That is, such a connection to the two-step mechanism of slow, continuous, formally unimolecular nucleation, A → B, then autocatalytic growth, A + B → 2B (A = dye−OAc, with the precise identity and composition of B to be determined) would, then and in turn, connect those implied dust effects to nucleation, or autocatalytic agglomerative growth, or possibly both (depending on the results seen from the curve fits, vide infra). Hence, a reanalysis of the Reeves et al. classic system and its kinetics data is examined in what follows (a) to provide further evidence for or against the role of dust in nucleation and autocatalytic agglomerative growth phenomena, (b) to

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EXPERIMENTAL SECTION Kinetics Data. Scanned plots of the data in Figure 1 from the 1978 paper14 were digitized using the Java program Plot Digitizer Version 2.6.8. Kinetics Analysis. The kinetics data were fit to the following, minimal two-step mechanism consisting of slow, continuous nucleation (rate constant k1; eq 1) and autocatalytic surface growth (rate constant k2; eq 2), that sums to eq 3 and is known in the literature as the FW two-step, original unimolecular nucleation mechanism,8 eqs 1−3, which follow. The chemical identities of A and B will be revealed as part of the research results that follow. Note that we know from our past work that the more complex bimolecular nucleation mechanism would likely also work if the unimolecular nucleation mechanism fits the data,26 but we will follow Ockham’s razor in what follows and stick to the simplest possible mechanism able to account for the data. k1

(1)

A→B k2

A + B → 2B

(2)

net 2A → 2B

(3)

fast

B ⎯→ ⎯

1 (B)n n

(4)

Under the mechanistic assumption that the formation of B is slow, that is, that agglomeration to the detected Bn (λmax = 475 according to the 1978 paper14) via step (4) is relatively fast under the reaction conditions, the differential and integrated forms of the corresponding rate law are provided in eqs 5 and 6, respectively, as first derived in a prior publication.8 −

d[A] d[B] = = k1obs[A]t + k 2obs[A]t [B]t dt dt

⎛ ⎞ k1 + k 2[A]0 ⎟⎟ [B]t = [A]0 ⎜⎜1 − k 2[A]0 + k1·e(k1+ k 2[A]0 )t ⎠ ⎝

(5)

(6)

We use the integrated rate eq 7 derived by substituting (A475)t for [B]t, and (A475)∞ for [A]o in the Supporting Information to fit the data in terms of absorbance at 475 nm, A475. Note that the curve fit yields k2′ (and not k2). They are related to each other as follows and as derived in the Supporting Information: k2 = C1k2′ or C1 = constant = nbε475, where ε475 is the molar extinction coefficient at 475 nm, and b is the path length for the light. Derivation details are available in the Supporting Information. ⎛ ⎞ k1 + k 2′(A475)∞ ⎟⎟ (A475)t = (A475)∞ ⎜⎜1 − k 2′(A475)∞ + k1e(k1+ k 2 ′ (A 475)∞)t ⎠ ⎝ (7)

Data Analysis. This was accomplished by nonlinear leastsquares curve-fitting of the kinetics data to eq 7 using Origin 8.5, all as detailed in our prior papers.8−11 C

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detailed mechanism, vide infra. Note that the A + B → 2B equation is the kinetic def inition of autocatalysis; note also that one cannot simplify this equation by “dividing out a B from both sides of the equation” to yield “A → B” because the (sigmoidal; autocatalytic) kinetics depend on both of the concentrations of [A]1 and [B]1, the (pseudoelementary, vide infra) step A + B → 2B behaving in that sense as if it were truly elementary. The added implication of the good curve fit to eq 6, corresponding to the two-step mechanism in eqs 1 and 2, is that the assumption of a relatively fast agglomeration step to Bn, eq (4) vide infra, is also supported. Note that the second, as-shown termolecular step in Scheme 2 is, therefore, almost surely a composite of greater than or equal to two steps that also include the H2O reactant and ROH product in addition to the formally autocatalytic A + B → 2B components. Put another way, the second equation in Scheme 2 is an excellent example of a so-called pseudo-elementary step that behaves elementary, in effectively exhibiting the kinetics of an elementary autocatalytic step (and for the purposes of curvefitting), but really is a composite of two or more elementary steps. The reader interested in learning more about pseudoelementary steps, and their importance in the kinetic and mechanistic analysis of complex reactions, is directed to the relevant literature.8,30−32 The important conclusion here is that the sigmoidal dye hydrolysis, then resultant dye−OH agglomeration, kinetics data in the Reeve’s et al. classic paper can now be quantitatively accounted for using a simple, widely applied two-step mechanism, including thereby uncovering evidence that HOAc plus dye−OH are components of the autocatalytic agent, B. 2. Obtaining the Hydrolysis Rate Constant for the Slow, Parallel, Background Reaction in the Microfiltered Solution in Figure 1B.14 Next an estimate is needed of the rate constant for the slower dye hydrolysis in the filtered solution, that is, the background rate constants k1obs,background and k2obs,background, where the rate-accelerating effect had been removed of the filterable dust. This was done by fitting the slower, only slightly nonlinear (slightly upwardly curving) kinetics in Figure 1 curve B to the integrated eq 7, that is, under the assumption that the mechanism has not changed dramatically due to filtering the solution, even if the rate constants obviously must have changed to give the barely sigmoidal, nearly linear-appearing kinetics seen in Figure 1, curve B.14 The needed fit was accomplished via the FW twostep mechanism (as detailed in the Experimental section), and the result is shown in Figure 3. The results from the two fits of kinetics data for the hydrolysis and agglomeration of dye with dust (Figure 2, from fitting the sigmoidal curve in Figure 1A) versus with the filterable dust removed (Figure 3, from fitting Figure 1B), are, respectively, and quite intriguingly: k1obs = (5.1 ± 0.5) × 10−3 h−1 and k′2obs = (4.7 ± 0.5) × 10−2 absorbance−1 h−1 versus k1obs,background = (5.5 ± 0.3) × 10−4 h−1 and k′2obs,background = (2.2 ± 0.8) × 10−3 absorbance−1 h−1. The ratio of the hydrolysis/ nucleation k1 steps for the dust-assisted versus dust-removed first step is k1obs/k1obs,background = (5.1 × 10−3)/(5.5 × 10−4) = 9.3, nearly an order of magnitude acceleration of the f irst step due to dust. The ratio of the second autocatalytic (agglomeration, vide infra) step also shows a large effect due to the removal of dust, k′2obs/k′2obs,background = (4.7 × 10−2)/(2.2 × 10−3) = 21, over an order of magnitude acceleration in the second step due to the presence of dust. This is the first time that the effects of dust

RESULTS 1. A Quantitative Fit of Reeves’ and Coworkers Sigmoidal Kinetics Data to the FW Two-Step Unimolecular Nucleation Mechanism. Figure 2 shows that we

Figure 2. Quantitative analysis of Reeves et al.’s kinetics data by the first-order two-step FW mechanism in eq 7. The Reeves et al.’s kinetics data were digitized from Figure 1 of their paper, sigmoidal curve A.14 As shown above, those blue points and associated curves are well fit (red line) by the FW two-step mechanism yielding k1obs = (5.1 ± 0.5) × 10−3 h−1 and k′2obs = (4.7 ± 0.5) × 10−2 absorbance−1 h−1 with R2 = 0.993 and curve-fit residual = 4.01 × 10−4.

were able to quantitatively f it the kinetic curves f rom Reeves et al. by just two rate constants and the residual (R) value using the FW two-step mechanism back in eqs 1 and 2. Since one starts with the unhydrolyzed dye ester, the implication is that A is the monomeric, unhydrolyzed dye ester, dye−OAc. Reflection on the products of that first, A → B reaction, Scheme 2, along with Scheme 2. Balanced Reactions That Show What A Is, and What One Componenta of B Is, in the FW Two-Step Mechanism Fit of Reeves and Co-Worker’s Kinetics Data

a

dye−OH and dust will be the other components, vide infra.

literature precedent leads to an assignment for B and insight into why the reaction is autocatalytic: B must include HOAc, a precedented ester hydrolysis autocatalysis reagent27−29 that is both a reactant and product, A + B → 2B, Scheme 2. Since HOAc and dye−OH are always formed in a 1:1 ratio, B can be taken to include HOAc + dye−OH, as this will also make most mechanistic sense when it comes time to propose a more D

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autocatalytic agglomerative growth step of a nonatmospheric, solution-based, particle-formation system. 3. A Postulated Minimum Mechanism. A postulated minimum mechanism, consistent with the kinetics and products data and the good curve fits to the sigmoidal kinetics as well as the accounting of the slow, background reaction post filtration, is shown in Scheme 3. It consists of parallel paths of slow, dye− OAc hydrolysis (one unassisted, the other dust-catalyzed) followed by an autocatalytic step, and then fast dye aggregation, steps 1−6 in Scheme 3, which add up to the observed dye hydrolysis and agglomeration reaction, step 7. Since the HOAc/dye−OH ratio is always 1:1, the autocatalytic agent B can be taken to contain both of them, (HOAc + dye−OH). Moreover, to account for the kinetic effects of filtration of the removable dust, B is best represented presently as containing that dust B = (HOAc + dye−OH)·dust.

Figure 3. Quantitative analysis of Reeves et al.’s background (filtered solution) kinetics data, digitized from Figure 1, curve B, of their paper14 (also curve B in Figure 1 herein), by the first-order two-step FW mechanism in eq 7. As shown above, this slight curve is well-fit by the FW two-step mechanism yielding k1obs,background = (5.5 ± 0.3) × 10−4 h−1 and k′2obs,background = (2.2 ± 0.8) × 10−3 absorbance−1 h−1 with R2 = 0.997 and curve-fit residual = 3.01 × 10−6.

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DISCUSSION The fit of the Reeves and co-workers’ kinetics data by the FW two-step mechanism, quantitatively accounting for it for the first time, is significant in at least six ways: (i) first, it shows once more the broader generality of the FW two-step

have been deconvoluted and shown to occur in both the first, nucleation/hydrolysis step and then also in the subsequent

Scheme 3. Postulated Minimum Mechanism Consistent with and Supported by the Observed Sigmoidal Kinetics, The Effects on the Kinetics of Microfiltration through a Nucleopore 0.2 μm Membrane, and the Observed Products of the Overall Dye Hydrolysis and Agglomeration Reaction

E

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The Journal of Physical Chemistry A mechanism,8 a mechanism that has been used to fit a broad range of nucleation and growth kinetics data in the literature ranging from Ir(0)n, Rh(0)n, Pt(0)n and many other metal nanoparticle catalyst formation,7,33−39 metal film formation,40 protein agglomeration in all the major neurological diseases,41−43 crystallization data fit by the Avrami equation,11,44 contaminant uptake data by water-improvement resins,45 and recently organic dye hydrolysis and agglomeration 46,47 including the present example, to mention a few among other examples across nature.43 Second, (ii) the results allow the deconvolution of the rate constants for dye hydrolysis/ nucleation of agglomerative growth, k1obs, from the rate constant for autocatalytic agglomerative growth, k2obs; and (iii) the effects of microfiltration of the thereby removable dust have been demonstrated as well as quantitated, effects ca. 10fold or more on both of the steps of the two-step FW mechanism, the first such demonstration of dust effects on both nucleation as well as on autocatalytic growth/agglomeration. Additionally, (iv) a minimum mechanism, Scheme 2, was written consistent with the kinetic and product data, and (v) that data also allow a kinetically effective nucleus (KEN)26 for this system to be inferred, namely, {(Azo-dye)m·dust}, where m = 1 is the result from the present work, but m ≈ 2−3 is also possible if not expected based on recent work.26,48 Noteworthy here is that this proposed KEN of {(Azo-dye)m·dust} has little to do with the putative “Critical Nucleus” of much higher nuclearity, n, (dye)n (n ≫ 2) predicted by at least Classical (homogeneous) Nucleation Theory49a theory that has no provision for “dust” as part of at least its original development, although later versions do add additional parameters to attempt to account for heterogeneous nucleation.50 Sixth, of historical interest is that (vi) the well-designed experiments and resultant excellent kinetics data by Reeves and co-workers in their 1978 study can now be identified as a classic study of dye−OAc hydrolysis and then agglomeration. Indeed, the prior authors14 were close to discovering the 1997 FW two-step mechanism,8 but nearly 20 years earlier, and if they had, then they would have also connected the two-step mechanism to the effects of filterable dust in 1978. If that connection had happened before it was discovered in 2017,13 then it would have had a large impact on the subsequent literature given the broad applicability of the FW two-step mechanism since 1997.7−9,11,33−47

effects of omnipresent room dust. Those resultant insights are state-of-the-art even though the original results were reported ca. 40 years ago and even in light of other, highly recommended25,46 recent contributions to the field of selfassembled π-conjugated, dye or other molecules.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b06648. Derivation of the kinetic equations employed (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Saim Ö zkar: 0000-0002-6302-1429 Richard G. Finke: 0000-0002-3668-7903 Present Address

Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, United States. Funding

This work was supported at Colorado State Univ. by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, via DOE Grant No. SE-FG40203ER15453. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The support of this work by the aforementioned DOE grant, and help critiquing and proofreading early versions of the manuscript by members of the Finke research group, are gratefully acknowledged.

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REFERENCES

(1) Kashchiev, D. Nucleation: Basic Theory with Applications; Butterworth-Heinemann: Oxford, U.K., 2000. (2) Zhang, T. H.; Liu, X. Y. Nucleation: What Happens at the Initial Stage? Angew. Chem., Int. Ed. 2009, 48, 1308−1312. (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. The Role of Sulfuric Acid in Atmospheric Nucleation. Science 2010, 327, 1243−1246. (4) Chen, S.; Ferrone, F. A.; Wetzel, R. Huntington’s Disease Age-ofOnset Linked to Polyglutamine Aggregation Nucleation. Proc. Natl. Acad. Sci. U. S. A. 2002, 99, 11884−11889. (5) Dauer, W.; Przedborski, S. Parkinson’s Disease: Mechanisms and Models. Neuron 2003, 39, 889−909. (6) Thanh, N. T. K.; Maclean, N.; Mahiddine, S. Mechanisms of Nucleation and Growth of Nanoparticles in Solution. Chem. Rev. 2014, 114, 7610−7630. (7) Finney, E. E.; Finke, R. G. Nanocluster Nucleation and Growth Kinetic and Mechanistic Studies: A Review Emphasizing TransitionMetal Nanoclusters. J. Colloid Interface Sci. 2008, 317, 351−374 and references cited therein.. (8) Watzky, M. A.; Finke, R. G. Transition Metal Nanocluster Formation Kinetic and Mechanistic Studies. A New Mechanism When Hydrogen Is the Reductant: Slow, Continuous Nucleation and Fast Autocatalytic Surface Growth. J. Am. Chem. Soc. 1997, 119, 10382− 10400.

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CONCLUSIONS In summary, a 1978 paper by Reeves and co-workers, of the dye−OAc hydrolysis and agglomeration system back in Scheme 1, has been reanalyzed in light of current state of knowledge of nucleation and growth/agglomeration phenomena. The FW two-step mechanism has been shown to account quantitatively for the kinetics data, in turn providing deconvolution of dye hydrolysis and nucleation of agglomerative growth, from the agglomerative growth step, including their separate rate constants. Significantly, the effects of microfiltration of the removable dust on the two steps and their rate constants have been uncovered and quantitated for the first time, including the finding that the presence of dust accelerates both steps by ca. 10fold or more. A postulated minimum mechanism able to account for all the observed results was provided. The results allow the excellently designed and executed, now nearly 40 years old studies of Reeves and co-workers to be identified as a classic contribution, one that, with the analysis provided in the present contribution, provides insights into dye agglomeration and the F

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DOI: 10.1021/acs.jpca.7b06648 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A (47) Avinash, M. B.; Sandeepa, K. V.; Govindaraju, T. Emergent Behaviors in Kinetically Controlled Dynamic Self-Assembly of Synthetic Molecular Systems. ACS Omega 2016, 1, 378−387. (48) Ö zkar, S.; Finke, R. G. 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 [(1,5-COD)IrI·P2W15Nb3O62]8− Plus Dihydrogen. J. Am. Chem. Soc. 2017, 139, 5444−5457. (49) Volmer, M.; Weber, A. Keimbildung in Ubersattigten Gebilden. Z. Phys. Chem. 1926, 119U, 277−301 Nucleation in supersaturated systems.. (50) Wheeler, M. J.; Bertram, A. K. Deposition Nucleation on Mineral Dust Particles: A Case Against Classical Nucleation Theory with the Assumption of a Single Contact Angle. Atmos. Chem. Phys. 2012, 12, 1189−1201 In this study the authors tried to account for the effects of ice formation that, experimentally, proved to be a strong function of the dust surface area made available for nucleation. Classical Nucleation Theory (CNT) was not able to account for the data, nor was CNT modified by the assumption of a single contact angle (the “single α-model” therein), able to account for the authors’ data. However, the use of a distribution of contact angles was able to account for the strong effect of added kaolinite or illite mineral dusts on the formation of ice crystals observed by optical microscopy (so, again, really the First Observable Clusters26, and not necessarily the desired Kinetically Effective Nucleus). The author’s main conclusion was stated as part of their paper’s title, “...A Case Against Classical Nucleation Theory With the Assumption of a Single Contact Angle”..

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DOI: 10.1021/acs.jpca.7b06648 J. Phys. Chem. A XXXX, XXX, XXX−XXX