23 research outputs found
Palladium(0) Nanoparticle Formation, Stabilization, and Mechanistic Studies: Pd(acac)<sub>2</sub> as a Preferred Precursor, [Bu<sub>4</sub>N]<sub>2</sub>HPO<sub>4</sub> Stabilizer, plus the Stoichiometry, Kinetics, and Minimal, Four-Step Mechanism of the Palladium Nanoparticle Formation and Subsequent Agglomeration Reactions
PalladiumĀ(0)
nanoparticles continue to be important in the field
of catalysis. However, and despite the many prior reports of Pd(0)<sub>n</sub> nanoparticles, missing is a study that reports the kinetically
controlled formation of Pd(0)<sub>n</sub> nanoparticles with the simple
stabilizer [Bu<sub>4</sub>N]<sub>2</sub>HPO<sub>4</sub> in an established,
balanced formation reaction where the kinetics and mechanism of the
nanoparticle-formation reaction are also provided. It is just such
studies that are the focus of the present work. Specifically, the
present studies reveal that PdĀ(acac)<sub>2</sub>, in the presence
of 1 equiv of [Bu<sub>4</sub>N]<sub>2</sub>HPO<sub>4</sub> as stabilizer
in propylene carbonate, serves as a preferred precatalyst for the
kinetically controlled nucleation following reduction under 40 Ā±
1 psig initial H<sub>2</sub> pressure at 22.0 Ā± 0.1 Ā°C to
yield 7 Ā± 2 nm palladium(0) nanoparticles. Studies of the balanced
stoichiometry of the Pd(0)<sub>n</sub> nanoparticle-formation reaction
shows that 1.0 PdĀ(acac)<sub>2</sub> consumes 1.0 equiv of H<sub>2</sub> and produces 1.0 equiv of Pd(0)<sub>n</sub> while also releasing
2.0 Ā± 0.2 equiv of acetylacetone. The inexpensive, readily available
HPO<sub>4</sub><sup>2ā</sup> also proved to be as effective
a Pd(0)<sub>n</sub> nanoparticle stabilizer as the more anionic, sterically
larger, āGold Standardā stabilizer P<sub>2</sub>W<sub>15</sub>Nb<sub>3</sub>O<sub>62</sub><sup>9ā</sup>. The kinetics
and associated minimal mechanism of formation of the [Bu<sub>4</sub>N]<sub>2</sub>HPO<sub>4</sub>-stabilized Pd(0)<sub>n</sub> nanoparticles
are also provided, arguably the most novel part of the present studies,
specifically the four-step mechanism of nucleation (A ā B,
rate constant <i>k</i><sub>1</sub>), autocatalytic surface
growth (A + B ā 2B, rate constant <i>k</i><sub>2</sub>), bimolecular agglomeration (B + B ā C, rate constant <i>k</i><sub>3</sub>), and secondary autocatalytic surface growth
(A + C ā 1.5C, rate constant <i>k</i><sub>4</sub>), where A is PdĀ(acac)<sub>2</sub>, B represents the growing, smaller
Pd(0)<sub>n</sub> nanoparticles, and C represents the larger, most
catalytically active Pd(0)<sub>n</sub> nanoparticles. Additional details
on the mechanism and catalytic properties of the resultant Pd(0)<sub>n</sub>Ā·HPO<sub>4</sub><sup>2ā</sup> nanoparticles are
provided in this work
A Classic AzoāDye Agglomeration System: Evidence for Slow, Continuous Nucleation, Autocatalytic Agglomerative Growth, Plus the Effects of Dust Removal by Microfiltration on the Kinetics
An important but
virtually ignored 1978 paper by Reeves and co-workers,
which examined a dyeāOAc hydrolysis and then agglomeration
system, is reanalyzed in light of current state of knowledge of nucleation
and growth/agglomeration phenomena. The FinkeāWatzky 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 <i>microfiltration of the removable dust</i> on the two steps and
their rate constants are uncovered and quantitated for the first time,
including the finding that the <i>presence of dust accelerates <u>both</u> steps by ca. 10-fold or more</i>. 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
Nanoparticle Nucleation Is Termolecular in Metal and Involves Hydrogen: Evidence for a Kinetically Effective Nucleus of Three {Ir<sub>3</sub>H<sub>2<i>x</i></sub>Ā·P<sub>2</sub>W<sub>15</sub>Nb<sub>3</sub>O<sub>62</sub>}<sup>6ā</sup> in Ir(0)<sub><i>n</i></sub> Nanoparticle Formation From [(1,5-COD)Ir<sup>I</sup>Ā·P<sub>2</sub>W<sub>15</sub>Nb<sub>3</sub>O<sub>62</sub>]<sup>8ā</sup> Plus Dihydrogen
The nucleation process yielding Ir(0)<sub>ā¼300</sub> nanoparticles
from (Bu<sub>4</sub>N)<sub>5</sub>Na<sub>3</sub>[(1,5-COD)ĀIrĀ·P<sub>2</sub>W<sub>15</sub>Nb<sub>3</sub>O<sub>62</sub>] (abbreviated hereafter
as (COD)ĀIrĀ·POM<sup>8ā</sup>, where POM<sup>9ā</sup> = the polyoxometalate, P<sub>2</sub>W<sub>15</sub>Nb<sub>3</sub>O<sub>62</sub><sup>9ā</sup>) under H<sub>2</sub> 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 transition-metal nanoparticle
formation system (J. Am. Chem. Soc. 2014, 136, 17601ā17615) revealed
that nucleation in this system is an apparent second-order in the
precatalyst, <b>A</b> = (COD)ĀIrĀ·POM<sup>8ā</sup>, not the higher order implied by classic nucleation theory and its <i>n</i><b>A</b> ā <b>A</b><sub><i>n</i></sub>, ācritical nucleusā, <b>A</b><sub><i>n</i></sub> concept. Herein, the three most reasonable more
intimate mechanisms of nucleation are tested: bimolecular nucleation,
termolecular nucleation, and a mechanism termed āalternative
termolecular nucleationā in which 2Ā(COD)ĀIr<sup>+</sup> and
1Ā(COD)ĀIrĀ·POM<sup>8ā</sup> 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, Ir<sub>3</sub>. All higher molecularity nucleation mechanisms were also
ruled out. Further insights into the KEN and its more detailed composition
involving hydrogen, {Ir<sub>3</sub>H<sub>2<i>x</i></sub>POM}<sup>6ā</sup>, are also obtained from the established
role of H<sub>2</sub> in the Ir(0)<sub>ā¼300</sub> formation
balanced reaction stoichiometry, from the pĀ(H<sub>2</sub>) dependence
of the kinetics, and from a D<sub>2</sub>/H<sub>2</sub> kinetic isotope
effect of 1.2(Ā±0.3). Eight insights and conclusions are presented.
A section covering caveats in the current work, and thus needed future
studies, is also included
Kinetic Evidence for Bimolecular Nucleation in Supported-Transition-Metal-Nanoparticle Catalyst Formation in Contact with Solution: The Prototype Ir(1,5-COD)Cl/Ī³-Al<sub>2</sub>O<sub>3</sub> to Ir(0)<sub>ā¼900</sub>/Ī³-Al<sub>2</sub>O<sub>3</sub> System
Kinetic and mechanistic studies of the formation of supported-nanoparticle
catalysts in contact with solution hold promise of driving the next
generation syntheses of size, shape, and compositionally controlled
catalysts. Recently, we studied the kinetics and mechanism of formation
of a prototype Ir(0)<sub>ā¼900</sub>/Ī³-Al<sub>2</sub>O<sub>3</sub> supported-nanoparticle catalyst from IrĀ(1,5-COD)ĀCl/Ī³-Al<sub>2</sub>O<sub>3</sub> in contact with solution (Mondloch, J.E.; Finke,
R.G. <i>J. Am. Chem. Soc.</i> <b>2011</b>, <i>133</i>, 7744). Key kinetic evidence was extracted from Ī³-Al<sub>2</sub>O<sub>3</sub>- and acetone-dependent kinetic curves in the
form of rate constants for nucleation (A ā B, rate constant <i>k</i><sub>1obs</sub>) and autocatalyic surface growth (A + B
ā 2B, rate constant <i>k</i><sub>2obs</sub>), where
A is nominally the IrĀ(1,5-COD)ĀCl/Ī³-Al<sub>2</sub>O<sub>3</sub> and B the growing, supported Ir(0)<sub><i>n</i></sub>/Ī³-Al<sub>2</sub>O<sub>3</sub> nanoparticle. The resultant data provided evidence
for a mechanism consisting of four main steps: IrĀ(1,5-COD)ĀClĀ(solvent)
dissociation from the Ī³-Al<sub>2</sub>O<sub>3</sub> support,
then IrĀ(1,5-COD)ĀClĀ(solvent) solution-based nucleation, fast nanoparticle
capture by the Ī³-Al<sub>2</sub>O<sub>3</sub> and then subsequent
nanoparticle growth between Ir(0)<sub><i>n</i></sub>/Ī³-Al<sub>2</sub>O<sub>3</sub> and IrĀ(1,5-COD)ĀClĀ(solvent) in solution. While
the <i>k</i><sub>2obs</sub> vs [Ī³-Al<sub>2</sub>O<sub>3</sub>]<sub>sus</sub> and [acetone] autocatalytic surface growth
rate constants were nicely accounted for by the proposed mechanism,
the <i>k</i><sub>1obs</sub> nucleation rate constants were
only āroughlyā accounted for by the previously proposed <i>unimolecular</i> solution-based nucleation mechanism. Hence,
in the present work we have reexamined that Ī³-Al<sub>2</sub>O<sub>3</sub>- and acetone-dependent nucleation data in light of
the hypothesis that nucleation is actually <i>bimolecular</i>. Extracting bimolecular, <i>k</i><sub>1obs(bimol)</sub>, rate constants by curve-fitting yields qualitative (i.e., visual
inspection) as well as quantitative (i.e., increased <i>R</i><sup>2</sup> values) <i>evidence consistent with and strongly
supportive of solution-based bimolecular nucleation</i> (A +
A ā 2B, rate constant <i>k</i><sub>1obs(bimol)</sub>) for the IrĀ(1,5-COD)ĀCl/Ī³-Al<sub>2</sub>O<sub>3</sub> to Ir(0)<sub>ā¼900</sub>/Ī³-Al<sub>2</sub>O<sub>3</sub> system in contact
with acetone. The extracted <i>k</i><sub>1obs(bimol)</sub> vs [Ī³-Al<sub>2</sub>O<sub>3</sub>]<sub>sus</sub> and [acetone]
data in turn rule out the solution-based unimolecular mechanism (as
well as a hypothetical termolecular nucleation mechanism). This study
is significant in that (i) it is the first evidence for bimolecular
nucleation in transition-metal nanoparticle formation in any system,
be it ligand- or support-stabilized nanoparticle formation in solution
or on solid-supports in gasāsolid systems, and since (ii) it
shows that mechanism-based nanoparticle size control, previously demonstrated
to depend on <i>k</i><sub>1obs</sub>, is hereby shown to
actually depend on 2<i>k</i><sub>1obs(bimol)</sub>[A]<sup>1</sup>. Furthermore, the results presented are of broad significance
since (iii) they are part of a growing literature suggesting that
simple, bimolecular nucleation may well be closer to the rule, rather
than the exception, in a range of systems across nature, and since
the results herein (iv) disprove, for at least the present system,
the higher nuclearity nucleation kinetics suggested by nucleation
theory and its often discussed critical nucleus concept. The results
also (v) argue for the new concept of a ākinetically effective
nucleusā, in this case binuclear M<sub>2</sub> (M = metal)
Sensitization of Nanocrystalline Metal Oxides with a Phosphonate-Functionalized Perylene Diimide for Photoelectrochemical Water Oxidation with a CoO<sub><i>x</i></sub> Catalyst
A planar
organic thin film composed of a perylene diimide dye (N,Nā²-bisĀ(phosphonomethyl)-3,4,9,10-perylenediimide,
PMPDI) with photoelectrochemically deposited cobalt oxide (CoO<sub><i>x</i></sub>) catalyst was previously shown to photoelectrochemically
oxidize water (DOI: 10.1021/am405598w). Herein, the same PMPDI dye
is studied for the sensitization of different nanostructured metal
oxide (nano-MO<sub><i>x</i></sub>) films in a dye-sensitized
photoelectrochemical cell architecture. Dye adsorption kinetics and
saturation decreases in the order TiO<sub>2</sub> > SnO<sub>2</sub> ā« WO<sub>3</sub>. Despite highest initial dye loading on
TiO<sub>2</sub> films, photocurrent with hydroquinone (H<sub>2</sub>Q) sacrificial reductant in pH 7 aqueous solution is much higher
on SnO<sub>2</sub> films, likely due to a higher driving force for
charge injection into the more positive conduction band energy of
SnO<sub>2</sub>. Dyeing conditions and SnO<sub>2</sub> film thickness
were subsequently optimized to achieve light-harvesting efficiency
>99% at the Ī»<sub>max</sub> of the dye, and absorbed photon-to-current
efficiency of 13% with H<sub>2</sub>Q, a 2-fold improvement over the
previous thin-film architecture. A CoO<sub><i>x</i></sub> water-oxidation catalyst was photoelectrochemically deposited, allowing
for photoelectrochemical water oxidation with a faradaic efficiency
of 31 Ā± 7%, thus demonstrating the second example of a water-oxidizing,
dye-sensitized photoelectrolysis cell composed entirely of earth-abundant
materials. However, deposition of CoO<sub><i>x</i></sub> always results in lower photocurrent due to enhanced recombination
between catalyst and photoinjected electrons in SnO<sub>2</sub>, as
confirmed by open-circuit photovoltage measurements. Possible future
studies to enhance photoanode performance are discussed, including
alternative catalyst deposition strategies or structural derivatization
of the perylene dye
Electrochemical Water Oxidation Catalysis Beginning with Co(II) Polyoxometalates: The Case of the Precatalyst Co<sub>4</sub>V<sub>2</sub>W<sub>18</sub>O<sub>68</sub><sup>10ā</sup>
The question is addressed
of whether the cobalt polyoxometalate
(Co-POM) precatalyst Co<sub>4</sub>V<sub>2</sub>W<sub>18</sub>O<sub>68</sub><sup>10ā</sup> (hereafter <b>Co</b><sub><b>4</b></sub><b>V</b><sub><b>2</b></sub><b>W</b><sub><b>18</b></sub>) is a stable, homogeneous water oxidation
catalyst under electrochemically driven conditions and in 0.1 M pH
5.8 and 8.0 NaPi buffer as well as pH 9.0 sodium borate (NaB) buffer.
This question is of considerable interest since <b>Co</b><sub><b>4</b></sub><b>V</b><sub><b>2</b></sub><b>W</b><sub><b>18</b></sub> has been reported to be highly
stable and a 200-fold faster water oxidation catalyst than its P congener
Co<sub>4</sub>P<sub>2</sub>W<sub>18</sub>O<sub>68</sub><sup>10ā</sup> (hereafter <b>Co</b><sub><b>4</b></sub><b>V</b><sub><b>2</b></sub><b>W</b><sub><b>18</b></sub>), for reasons that were not specified. The nature of the true water
oxidation catalyst with <b>Co</b><sub><b>4</b></sub><b>V</b><sub><b>2</b></sub><b>W</b><sub><b>18</b></sub> as the starting material is of further fundamental interest
because a recent report reveals that the <sup>51</sup>V NMR peak at
ca. ā507 ppm assigned by others to <b>Co</b><sub><b>4</b></sub><b>V</b><sub><b>2</b></sub><b>W</b><sub><b>18</b></sub> and used to argue for its solution stability
is, instead, correctly assigned to the highly stable <i>cis</i>-V<sub>2</sub>W<sub>4</sub>O<sub>19</sub><sup>4ā</sup>, in
turn raising the question of the true stability of <b>Co</b><sub><b>4</b></sub><b>V</b><sub><b>2</b></sub><b>W</b><sub><b>18</b></sub> under water oxidation catalysis
conditions. A battery of physical methods is used to address the questions
of the stability and true water oxidation catalyst with <b>Co</b><sub><b>4</b></sub><b>V</b><sub><b>2</b></sub><b>W</b><sub><b>18</b></sub> as the precatalyst: <sup>31</sup>P line-broadening detection of CoĀ(II) present in solution from leaching
or as a counterion impurity; a check of those CoĀ(II) concentration
results by the second method of cathodic stripping; the O<sub>2</sub> yield (and, hence, Faradaic efficiency) of electrocatalytic water
oxidation; electrochemical, SEM, EDX, and XPS characterization of
CoO<sub><i>x</i></sub> films produced on the electrode;
and multiple controls and other experiments designed to test alternative
hypotheses that might explain the observed results. The collective
evidence provides a compelling case that CoĀ(II) derived from <b>Co</b><sub><b>4</b></sub><b>V</b><sub><b>2</b></sub><b>W</b><sub><b>18</b></sub> forms a CoO<sub><i>x</i></sub> film on the electrode which, in turn, carries all
the observed, electrochemically driven water-oxidation catalysis current
within experimental error. A list of seven main findings is provided
as a summary
Nucleation is Second Order: An Apparent Kinetically Effective Nucleus of Two for Ir(0)<sub><i>n</i></sub> Nanoparticle Formation from [(1,5-COD)Ir<sup>I</sup>Ā·P<sub>2</sub>W<sub>15</sub>Nb<sub>3</sub>O<sub>62</sub>]<sup>8ā</sup> Plus Hydrogen
Nucleation initiates phase changes
across nature. A fundamentally
important, presently unanswered question is if nucleation begins as
classical nucleation theory (CNT) postulates, with <i>n</i> equivalents of monomer A forming a ācritical nucleusā,
A<i><sub>n</sub></i>, 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] = [(Bu<sub>4</sub>N)<sub>5</sub>Na<sub>3</sub>(1,5-COD)ĀIr<sup>I</sup>Ā·P<sub>2</sub>W<sub>15</sub>Nb<sub>3</sub>O<sub>62</sub>], forming soluble/dispersible, B = Ir(0)<sub>ā¼300</sub> nanoparticles stabilized by the P<sub>2</sub>W<sub>15</sub>Nb<sub>3</sub>O<sub>62</sub><sup>9ā</sup> polyoxoanion. The resulting
sigmoidal kinetic curves are analyzed using the 1997 FinkeāWatzky
(hereafter FW) two-step mechanism of (i) slow continuous nucleation
(A ā B, rate constant <i>k</i><sub>1obs</sub>), then
(ii) fast autocatalytic surface growth (A + B ā 2B, rate constant <i>k</i><sub>2obs</sub>). Relatively precise homogeneous nucleation
rate constants, <i>k</i><sub>1obs</sub>, examined as a function
of the amount of precatalyst, A, reveal that <i>k</i><sub>1obs</sub> has an added dependence on the concentration of the precursor, <i>k</i><sub>1obs</sub> = <i>k</i><sub>1obs(bimolecular)</sub>[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 ā 2B (rate constant, <i>k</i><sub>1obs(bimol)</sub>). The results are significant and of broad interest as an experimental
disproof of the applicability of the ācritical nucleusā
of CNT to nanocluster formation systems such as the Ir(0)<sub><i>n</i></sub> 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
Water Oxidation Catalysis Beginning with 2.5 Ī¼M [Co<sub>4</sub>(H<sub>2</sub>O)<sub>2</sub>(PW<sub>9</sub>O<sub>34</sub>)<sub>2</sub>]<sup>10ā</sup>: Investigation of the True Electrochemically Driven Catalyst at ā„600 mV Overpotential at a Glassy Carbon Electrode
Evidence for the true water oxidation
catalyst (WOC) when beginning with the cobalt polyoxometalate [Co<sub>4</sub>(H<sub>2</sub>O)<sub>2</sub>(PW<sub>9</sub>O<sub>34</sub>)<sub>2</sub>]<sup>10ā</sup> (Co<sub>4</sub>āPOM) is investigated
at deliberately chosen low polyoxometalate concentrations (2.5 Ī¼M)
and high electrochemical potentials (ā„1.3 V vs Ag/AgCl) in
pH 5.8 and 8.0 sodium phosphate electrolyte at a glassy carbon working
electrodeīøconditions which ostensibly favor Co<sub>4</sub>āPOM
catalysis if present. Multiple experiments argue against the dominant
catalyst being CoO<sub><i>x</i></sub> formed exclusively
from Co<sup>2+</sup> dissociated from the parent POM. Measurement
of [Co<sup>2+</sup>] in the Co<sub>4</sub>āPOM solution and
catalytic controls with the corresponding amount of CoĀ(NO<sub>3</sub>)<sub>2</sub> cannot account for the O<sub>2</sub> generated from
2.5 Ī¼M [Co<sub>4</sub>(H<sub>2</sub>O)<sub>2</sub>(PW<sub>9</sub>O<sub>34</sub>)<sub>2</sub>]<sup>10ā</sup> solutions. This
result contrasts with our prior investigation of Co<sub>4</sub>āPOM
under higher concentration and lower potential conditions (i.e., 500
Ī¼M [Co<sub>4</sub>(H<sub>2</sub>O)<sub>2</sub>(PW<sub>9</sub>O<sub>34</sub>)<sub>2</sub>]<sup>10ā</sup>, 1.1 V vs Ag/AgCl,
as described in Stracke, J. J.; Finke, R. G. <i>J. Am. Chem.
Soc.</i> <b>2011</b>, <i>133</i>, 14872) and <i>highlights the importance of</i> <i>reaction</i> <i>conditions in governing the identity of the true, active WOC.</i> Although electrochemical studies are consistent with Co<sub>4</sub>āPOM being oxidized at the glassy carbon electrode, it is
not yet possible to distinguish a Co<sub>4</sub>āPOM catalyst
from a CoO<sub><i>x</i></sub> catalyst formed via decomposition
of Co<sub>4</sub>āPOM. Controls with authentic CoO<sub><i>x</i></sub> indicate conversion of only 3.4% or 8.3% (at pH
8.0 and 5.8) of Co<sub>4</sub>āPOM into a CoO<sub><i>x</i></sub> catalyst could account for the O<sub>2</sub>-generating activity,
and HPLC quantification of the Co<sub>4</sub>āPOM stability
shows the postreaction Co<sub>4</sub>āPOM concentration decreases
by 2.7 Ā± 7.6% and 9.4 Ā± 5.1% at pH 8.0 and 5.8. Additionally,
the [Co<sup>2+</sup>] in a 2.5 Ī¼M Co<sub>4</sub>āPOM
solution increases by 0.55 Ī¼M during 3 min of electrolysisīøfurther
evidence of the <i>Co</i><sub><i>4</i></sub><i>-POM instability under oxidizing conditions</i>. Overall, this
study demonstrates the challenges of identifying the true WOC when
examining micromolar amounts of a partially stable material and when <i>nanomolar</i> heterogeneous metal-oxide will account for the
observed O<sub>2</sub>-generating activity
Catalyst Sintering Kinetics Data: Is There a Minimal Chemical Mechanism Underlying Kinetics Previously Fit by Empirical Power-Law Expressionsīøand if So, What Are Its Implications?
Catalyst
sintering is an undesired, but general, and hence practically
important catalyst deactivation process. Understanding sintering kinetics
and, then, the associated mechanism(s) is an important goal, one crucial
to being better able to limit and otherwise control catalyst sintering
rationally. However, and despite the availability of atomic-based
sintering models, the kinetics of sintering of practical catalysts
are to this day most often accounted for by curve-fitting with <i>empirical</i> power laws. Such empirical kinetics treatments
are, unfortunately, devoid of rigorous mechanistic insight because
they lack the balanced chemical equations that are required to define
the rate constants and to also define the proper concepts and associated
words that, in turn, are crucial for being able to describe correctly
the sintering process physically. Hence, addressed herein is the key,
previously unanswered question: is there a disproof-based, Ockhamās
razor-obeying, hence mechanistically rigorous, minimal chemical mechanism
that can be used to curve-fit sintering kinetics data previously accounted
for by empirical power law expressions? If so, then what are its implications?
The results provided demonstrate that literature catalyst sintering
data, previously fit using empirical power laws, can instead be quantitatively
accounted for by a simple, deliberately minimalistic, two-step kinetic
model consisting of bimolecular nucleation of agglomeration, B + B
ā C (rate constant <i>k</i><sub>3</sub>), followed
by autocatalytic agglomeration, B + C ā 1.5C (rate constant <i>k</i><sub>4</sub>), in which B is the average starting nanoparticle,
and C is the average larger, agglomerated nanoparticle. The results
and findings compellingly demonstrate that the two-step mechanism
can account for a variety of sintering kinetics data previously fit
only by empirical power laws. Evidence is presented that the kinetic
model appears to correspond to what has been called Particle Migration
and Coalescence (PMC) in the prior literature. Ten conclusions and
hypotheses, as well as four caveats, are listed in the Conclusion
section, along with suggestions for further research
Water Oxidation Catalysis Beginning with Co<sub>4</sub>(H<sub>2</sub>O)<sub>2</sub>(PW<sub>9</sub>O<sub>34</sub>)<sub>2</sub><sup>10ā</sup> When Driven by the Chemical Oxidant Ruthenium(III)tris(2,2ā²-bipyridine): Stoichiometry, Kinetic, and Mechanistic Studies en Route to Identifying the True Catalyst
Stoichiometry and kinetics are reported
for catalytic water oxidation
to O<sub>2</sub> beginning with the cobalt polyoxometalate Co<sub>4</sub>(H<sub>2</sub>O)<sub>2</sub>(PW<sub>9</sub>O<sub>34</sub>)<sub>2</sub><sup>10ā</sup> (Co<sub>4</sub>POM) and the chemical
oxidant rutheniumĀ(III)ĀtrisĀ(2,2ā²-bipyridine) (RuĀ(III)Ā(bpy)<sub>3</sub><sup>3+</sup>). This specific water oxidation system was first
reported in a 2010 <i>Science</i> paper (Yin et al. <i>Science</i> <b>2010</b>, <i>328</i>, 342). Under
standard conditions employed herein of 1.0 Ī¼M Co<sub>4</sub>POM, 500 Ī¼M RuĀ(III)Ā(bpy)<sub>3</sub><sup>3+</sup>, 100 Ī¼M
RuĀ(II)Ā(bpy)<sub>3</sub><sup>2+</sup>, pH 7.2, and 0.03 M sodium phosphate
buffer, the highest O<sub>2</sub> yields of 22% observed herein are
seen when RuĀ(II)Ā(bpy)<sub>3</sub><sup>2+</sup> is added prior to the
RuĀ(III)Ā(bpy)<sub>3</sub><sup>3+</sup> oxidant; hence, those conditions
are employed in the present study. Measurement of the initial O<sub>2</sub> evolution and RuĀ(III)Ā(bpy)<sub>3</sub><sup>3+</sup> reduction
rates while varying the initial pH, [RuĀ(III)Ā(bpy)<sub>3</sub><sup>3+</sup>], [RuĀ(II)Ā(bpy)<sub>3</sub><sup>2+</sup>], and [Co<sub>4</sub>POM] indicate that the reaction follows the empirical rate law: ādĀ[RuĀ(III)Ā(bpy)<sub>3</sub><sup>3+</sup>]/d<i>t</i> = (<i>k</i><sub>1</sub> + <i>k</i><sub>2</sub>)Ā[Co<sub>4</sub>POM]<sub>soluble</sub>[RuĀ(III)Ā(bpy)<sub>3</sub><sup>3+</sup>]/[H<sup>+</sup>], where the rate constants <i>k</i><sub>1</sub> ā¼
0.0014 s<sup>ā1</sup> and <i>k</i><sub>2</sub> ā¼
0.0044 s<sup>ā1</sup> correspond to the water oxidation and
ligand oxidation reactions, and for O<sub>2</sub> evolution, dĀ[O<sub>2</sub>]/d<i>t</i> = (<i>k</i><sub>1</sub>/4)Ā[Co<sub>4</sub>POM]<sub>soluble</sub>[RuĀ(III)Ā(bpy)<sub>3</sub><sup>3+</sup>]/[H<sup>+</sup>]. Overall, at least seven important insights result
from the present studies: (i) Parallel WOC and RuĀ(III)Ā(bpy)<sub>3</sub><sup>3+</sup> self-oxidation reactions well documented in the prior
literature limit the desired WOC and selectivity to O<sub>2</sub> in
the present system to ā¤28%. (ii) The formation of a precipitate
from ā¼2 RuĀ(II)Ā(bpy)<sub>3</sub><sup>2+</sup>/3 Co<sub>4</sub>(H<sub>2</sub>O)<sub>2</sub>(PW<sub>9</sub>O<sub>34</sub>)<sub>2</sub><sup>10ā</sup> with a <i>K</i><sub>sp</sub> = (8
Ā± 7) Ć 10<sup>ā25</sup> (M<sup>5</sup>) greatly complicates
the reaction and interpretation of the observed kinetics, but (iii)
the best O<sub>2</sub> yields are still when RuĀ(II)Ā(bpy)<sub>3</sub><sup>2+</sup> is preadded. (iv) CoO<sub><i>x</i></sub> is
2ā11 times more active than Co<sub>4</sub>POM under the reaction
conditions, but (v) Co<sub>4</sub>POM is still the dominant WOC under
the Co<sub>4</sub>POM/RuĀ(III)Ā(bpy)<sub>3</sub><sup>3+</sup> and other
reaction conditions employed. The present studies also (vi) confirm
that the specific conditions matter greatly in determining the true
WOC and (vii) allow one to begin to construct a plausible WOC mechanism
for the Co<sub>4</sub>POM/RuĀ(III)Ā(bpy)<sub>3</sub><sup>3+</sup> system