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At least 19 records

Acid-catalyzed C–H reductive elimination from Au (III)

An unusual mode of C–H reductive elimination from a Au III complex catalyzed by acid is reported. The addition of triflic acid (HOTf) to [( tBu PCP)Au III –H]OTf (1-OTf, tBu PCP = 2,6-C 6 H 3 (CH 2 P t Bu 2 ) 2 promotes formal C–H reductive elimination. The Au I product [( tBu P(C–H)P)Au I ]OTf (2-OTf, tBu P(C–H)P = κ 2 (1,3-C 6 H 4 (CH 2 P t Bu 2 ) 2 )) was characterized by NMR spectroscopy and X-ray diffraction. It was shown that the reductive elimination of 1-OTf has a dependence on the identity of the acid catalyst which cannot be explained by acid strength. Mechanistic experiments are consistent with a concerted mechanism for C–H reductive elimination involving participation of basic moieties on the acid.

Ardon, Yotam [University of Pennsylvania, Philadel↗

Force-Modulated C–C Reductive Elimination from Nickel Bis(polyfluorophenyl) Complexes

We have analyzed the rate of C(sp 2 )–C(sp 2 ) reductive elimination from nickel(II) bis(2,4,6-trifluorophenyl) complex-es (P–P)Ni(2,4,6-C 6 H 2 F 3 ) 2 containing either MeOBiPhep (3a) or macrocyclic bisphosphine ligand (3b-3e) as a func-tion of force applied to the biaryl backbone of these ligands through intramolecular tension generated by a molecular force probe. Nickel complexes 3 were isolated in 22-60% yield from reaction of bisphosphine with the bis(tetrahydrofuranyl) complex (THF) 2 Ni(2,4,6-C 6 H 2 F 3 ) 2 followed by chromatography. Thermolysis of complexes 3 in C 6 D 6 at 68 °C leads to first-order decay through > 3 half-lives to form 2,2',4,4',6,6'-hexaflurorobiphenyl as the exclusive fluorine-containing product in ≥93% yield. Whereas compressive forces up to –65 pN have no significant effect on the rate of reductive elimination, extension forces increase the rate of reductive elimination by a factor of three over a ~230 pN range of restoring forces relative to the strain-free MeOBiphep complex. Furthermore, the rate response of reductive elimination from nickel(II) bis(trifluorophenyl) complexes as a function of extension force is similar to the previously reported 2.8-fold increase in the rate of reductive elimination from platinum diaryl complexes (P–P)Pt(4-C 6 H 4 NMe 2 ) 2 over the same range of forces

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Light-Promoted C(sp 3 )–C(sp 3 ) Reductive Elimination from Dialkyl NiII Complexes

Ni-catalyzed cross-coupling is a powerful strategy to forge C(sp 3 )–C(sp 3 ) bonds. Typically, to do so requires overcoming a challenging C–C bond-forming reductive elimination, often enabled by the intermediacy of highly oxidized Ni species or outer-sphere processes. While direct C(sp 3 )–C(sp 3 ) reductive elimination from the Ni II base oxidation state is normally thermally inaccessible, light-activation provides an avenue to affect such transformations. Here, we investigate the mechanism of light-induced C(sp 3 )–C(sp 3 ) bond formation from dialkyl bipyridine Ni II complexes through a variety of organometallic, spectroscopic, and computational studies. Wavelength-dependent quantum yields, ligand electronics–reactivity relationships, excited-state lifetimes, computed barriers, and product distributions from crossover studies support a photolysis/radical rebound mechanism. Furthermore, this reactivity paradigm complements existing strategies in the literature to promote reductive elimination from Ni II , such as the use of destabilizing, sterically hindered ligands and reduction of electron density at Ni through the binding of electron-deficient olefins. Hence, we envision that light-induced reductive elimination may enable the development of challenging C(sp 3 )–C(sp 3 ) couplings.

Alkyls↗

Electronic Rearrangement in Steps of Reductive Elimination of Polar Electrophiles Leads to Refinement of Redox Events

The oxidative addition/reductive elimination of polar molecules such as methyl iodide at late metal centers has a strongly supported $S_{N^2}$ mechanism for many key organometallic complexes, including important industrial catalysts. In the reductive elimination direction, it is proposed that a ligand initially dissociates, typically a halide, followed by subsequent nucleophilic attack at the ligand trans to the now vacant site. The prevailing view is the metal reduction occurs upon transferring the electrophile in the $S_{N^2}$ step. Herein, we report the use of an ensemble of computational techniques to characterize the electronic structure of the reactants and intermediates along this reductive elimination pathway. These calculations demonstrate, unexpectedly, that the initiating loss of an anionic ligand from the octahedral highly oxidized structure leads to an electronic rearrangement that shifts electron density from the apical ligand back toward the metal resulting in an inversion of the electron flow between the metal and apical ligand. The anisotropic shift in electron density to the metal disproportionately affects the apical position, which is best described as a Pt → Me dative bond. With this Pt → Me bonding description, our interpretation of the IUPAC oxidation state formalism would assign the intermediate as Pt ΙΙ . Although counterintuitive, the formal and functional reduction of the metal thus occurs upon halide dissociation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reductive Elimination From Tetra‐Alkyl Cuprates [Me n Cu(CF 3 ) 4− n ] − ( n =0–4): Beyond Simple Oxidation States

Abstract In recent years, the electronic structures of organocuprates in general and the complex [Cu(CF 3 ) 4 ] − in particular have attracted significant interest. A possible key indicator in this context is the reactivity of these species. Nonetheless, this aspect has received only limited attention. Here, we systematically study the series of tetra‐alkyl cuprates [Me n Cu(CF 3 ) 4− n ] − and their unimolecular reactivity in the gas phase, which includes concerted formal reductive eliminations as well as radical losses. Through computational studies, we characterize the electronic structures of the complexes and show how these are connected to their reactivity. We find that all [Me n Cu(CF 3 ) 4− n ] − ions feature inverted ligand fields and that the distinct reactivity patterns of the individual complexes arise from the interplay of different effects.

Zimmer, Bastian↗

Reconceptualizing the Ir III Role in Metallaphotoredox Catalysis: From Strong Photooxidant to Potent Energy Donor

Dual Ir III /L n Ni II metallaphotoredox catalyzed C(sp 3 )–C(sp 2 ) cross-coupling reactions are widely assumed to proceed by photoinduced single electron transfer steps due to the highly oxidizing Ir III * excited state (Ir III = [Ir(dF(CF 3 )ppy) 2 (dtbbpy)] + [PF 6 ] – ; dF(CF 3 )ppy = 2-(2,4-difluorophenyl)-5-(trifluoromethyl)pyridine; L n = dtbbpy = 4,4'-di-tert-butyl-2,2'-bipyridine). Using time-resolved absorption and emission spectroscopy, we reveal that energy transfer between Ir III * and various LnNi II precatalysts and intermediates with k q ≥ 10 8 M –1 s –1 also drives catalysis. Specifically, the excited states of L n Ni II dihalide precatalysts/organometallic intermediates accessible by energy transfer appear to drive bond homolysis, halogen radical elimination, and reductive elimination reactions that facilitate formation of cross-coupled products. Energy transfer dynamics consequently circumvent the need for photoinduced electron transfer, thereby extending substrate scopes to coupling partners that cannot be oxidized by Ir III *. Within a cross-electrophile coupling model reaction between 4-bromobenzotrifluoride and bromocyclohexane, energy transfer activates the L n Ni II precatalyst at early reaction times before nucleophilic reductants are present. In the absence of Ir III , direct excitation of L n Ni II (Br) 2 also activates the precatalyst to form a L n Ni II (Br)(Aryl) intermediate. To compare energy transfer and electron transfer kinetics, we determined rate constants for reductive quenching by Br – (k SET = 4.1 × 10 8 M –1 s –1 ) and for the subsequent electron transfer from reduced Ir III•– to L n Ni II (Br) 2 (k SET = 4.1 × 10 7 M –1 s –1 ) using Stern-Volmer analysis and pulse radiolysis, respectively. Energy transfer rate constants are competitive with the electron transfer rate constants and energy transfer is a parallel pathway within metallaphotoredox catalysis. Exploiting the energy transfer mechanism, we demonstrate highly selective cross-electrophile coupling between 4-chlorobenzotrifluoride and bromocyclohexane to form exclusively cross-coupled product. Here, with alkyl-trifluoroborate nucleophiles that do not reductively quench IrIII* emission, transmetalation with L n Ni II (Br/Cl)(Aryl) followed by energy transfer also drives excited state reductive elimination to form C(sp 3 )–C(sp 2 ) cross-coupled product. Similarly, energy transfer rather than Ni II oxidation drives C(sp 2 )–OR reductive elimination, despite the strongly oxidizing ability of Ir III *. In total, these reactions demonstrate energy transfer processes from Ir III * to L n Ni II in metallaphotoredox catalysis that can unlock alternative reactive pathways.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Crucial Role of Sb 2 F 10 in the Chemical Synthesis of F 2

The purely chemical synthesis of fluorine is a spectacular reaction which for more than a century had been believed to be impossible. In 1986, it was finally experimentally achieved, but since then this important reaction has not been further studied and its detailed mechanism had been a mystery. The known thermal stability of MnF 4 casts serious doubts on the originally proposed hypothesis that MnF 4 is thermodynamically unstable and decomposes spontaneously to a lower manganese fluoride and F 2 . This apparent discrepancy has now been resolved experimentally and by electronic structure calculations. It is shown that the reductive elimination of F 2 requires a large excess of SbF 5 and occurs in the last reaction step when in the intermediate [SbF 6 ][MnF 2 ][Sb 2 F 11 ] the addition of one more SbF 5 molecule to the [SbF 6 ] - anion generates a second tridentate [Sb 2 F 11 ] - anion. The two tridentate [Sb 2 F 11 ] - anions then provide six fluorine bridges to the Mn atom thereby facilitating the reductive elimination of the two fluorine ligands as F 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Olefin Coupling Catalyzed by (Pybox)Os Complexes via Osmacyclopentane Intermediates: Comparison with Isoelectronic (Phebox)Ir

(Pybox)Os is found to catalyze alkene hydrovinylation, effecting the dimerization of ethylene, tail-to-tail coupling of propene and 1-butene, and cross-coupling of ethylene with higher α-olefins. This reactivity contrasts with the previously reported dehydrogenative coupling of ethylene to give butadiene catalyzed by the isoelectronic fragment (Phebox)Ir. The reaction mechanism was investigated through computational and experimental means. Both the Os- and Ir-catalyzed reactions proceed through a [2 + 2 + 1] cyclization of the corresponding bis-olefin complex to yield an experimentally observed metallacyclopentane intermediate. In both cases, the metallacyclopentane undergoes β- H elimination, via a dechelated κ 2 -pincer-ligated intermediate, to yield a σ−π-but-3-enyl hydride complex or derivative. Both the greater reactivity and the distinct chemoselectivity of the Os system relative to the Ir system are attributable to C−H reductive elimination by the σ−π-but-3-enyl hydride having a barrier for Os much lower than that for Ir. This lower barrier to C−H elimination for Os is unexpected given that the thermodynamic driving force for elimination is much less for Os than for Ir. Computational studies of model complexes were conducted, comparing (Pybox)Os(L)(CH 3 )(H) with the isoelectronic (Phebox)Ir(L)(CH 3 )(H). The results indicate that the more facile kinetics with Os relative to Ir may be general for C−H elimination from six-coordinate d 6 complexes of the two metals, as well as for the microscopic reverse, i.e., C−H addition to the corresponding four-coordinate d 8 species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mechanism of Ni-Catalyzed Photochemical Halogen Atom-Mediated C(sp 3 )–H Arylation

Within the context of Ni photoredox catalysis, halogen atom photoelimination from Ni has emerged as a fruitful strategy for enabling hydrogen atom transfer (HAT)-mediated C(sp 3 )–H functionalization. Despite the numerous synthetic transformations invoking this paradigm, a unified mechanistic hypothesis that is consistent with experimental findings on the catalytic systems and accounts for halogen radical formation and facile C(sp 2 )–C(sp 3 ) bond formation remains elusive. We employ kinetic analysis, organometallic synthesis, and computational investigations to decipher the mechanism of a prototypical Ni-catalyzed photochemical C(sp 3 )–H arylation reaction. Our findings revise the previous mechanistic proposals, first by examining the relevance of SET and EnT processes from Ni intermediates relevant to the HAT-based arylation reaction. Our investigation highlights the ability for blue light to promote efficient Ni–C(sp 2 ) bond homolysis from cationic Ni III and C(sp 2 )–C(sp 3 ) reductive elimination from bipyridine Ni II complexes. However interesting, the rates and selectivities of these processes do not account for the productive catalytic pathway. Instead, our studies support a mechanism that involves halogen atom evolution from in situ generated Ni II dihalide intermediates, radical capture by a Ni II (aryl)(halide) resting state, and key C–C bond formation from Ni III . Oxidative addition to Ni I , as opposed to Ni 0 , and rapid Ni III /Ni I comproportionation play key roles in this process. Furthermore, the findings presented herein offer fundamental insight into the reactivity of Ni in the broader context of catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

How thermal fluctuations influence the function of the FeMo cofactor in nitrogenase enzymes

The catalytic mechanism of N 2 fixation by nitrogenase remains unresolved in how the strong N≡N bond is activated and why the reductive elimination of H 2 is required. Here, we use density functional theory and physiologically relevant thermal simulations to elucidate the mechanism of the complete nitrogenase catalytic cycle. Over the accumulation of four reducing equivalents, we find that protons and electrons transfer to the FeMo cofactor to weaken and break its bridge Fe–S bond, leading to temporary H 2 S formation that exposes the Fe sites to weakly bind N 2 . Remarkably, we find that subsequent H 2 formation is responsible for chemical activation to an N=N double bond accompanied by a low barrier for H 2 release. We emphasize that finite temperature effects smooth out mechanistic differences between DFT functionals observed at 0 K, thus leading to a consistent understanding as to why H formation is an obligatory step in N 2 adsorption and activation.

DFT↗

Cyclometalated Platinum Compounds from Competing C–H/C–X Bond Activation Pathways

X−C^N^N (X = Br, Cl) ligands were reacted with [Pt 2 Me 4 (μ- SMe 2 ) 2 ], 1, resulting in a six-coordinate cyclometalated platinum(IV) compound containing an anionic C^N^N ligand when X = Br and both a platinum(IV) and a platinum(II) product when X = Cl. The platinum(II) species was formed by C−H activation, followed by reductive elimination of methane. The platinum compounds were characterized by multinuclear NMR spectroscopy and single-crystal X-ray diffraction (SCXRD). Photophysical properties were explored by using UV/vis, emission, and transient absorption (TA) spectroscopies. DFT and TDDFT calculations were performed to examine the competition between C−H activation and C−X oxidative addition and compared to experimental results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Remotely Bonded Bridging Dioxygen Ligands Enhance Hydrogen Transfer in a Silica-Supported Tetrairidium Cluster Catalyst

A longstanding challenge in catalysis by noble metals has been to understand the origin of enhancements of rates of hydrogen transfer that result from bonding of oxygen near metal sites. We investigated structurally well-defined catalysts consisting of supported tetrairidium carbonyl clusters with single-atom (apical iridium) catalytic sites for ethylene hydrogenation. Reaction of the clusters with ethylene and H 2 followed by O 2 led to the onset of catalytic activity as a terminal CO ligand at each apical Ir atom was removed and bridging dioxygen ligands replaced CO ligands at neighboring (basal-plane) sites. The presence of the dioxygen ligands caused a 6-fold increase in the catalytic reaction rate, which is explained by the electron-withdrawing capability induced by the bridging dioxygen ligands, consistent with the inference that reductive elimination is rate determining. Electronic structure calculations demonstrate an additional role of the dioxygen ligands, changing the mechanism of hydrogen transfer from that involving equatorial hydride ligands to that involving bridging hydride ligands. This mechanism is made evident by an inverse kinetic isotope effect observed in ethylene hydrogenation reactions with H 2 and, alternatively, with D 2 on the cluster incorporating the dioxygen ligands, and is a consequence of quasi-equilibrated hydrogen transfer in this catalyst. The same mechanism accounts for rate enhancements induced by the bridging dioxygen ligands for the catalytic reaction of H 2 with D 2 to give HD. Here, we posit that the mechanism involving bridging hydride ligands facilitated by oxygen ligands remote from the catalytic site may have some generality in catalysis by oxide-supported noble metals.

02 PETROLEUM↗

Mechanistic Insights into the Origins of Selectivity in a Cu-Catalyzed C–H Amidation Reaction

The catalytic transformation of C-H to C-N bonds offers rapid access to fine chemicals and high-performance materials, but achieving high selectivity from undirected aminations of unactivated C(sp 3 )-H bonds remains an outstanding challenge. Here, we report the origins of the reactivity and selectivity of a Cu-catalyzed C-H amidation of simple alkanes. Using a combination of experimental and computational mechanistic studies and energy decomposition techniques, we uncover a switch in mechanism from inner-sphere to outer-sphere coupling between alkyl radicals and the active Cu(II) catalyst with increasing substitution of the alkyl radical. The combination of computational predictions and detailed experimental validation shows that simultaneous minimization of both Cu-C covalency and alkyl radical size increases the rate of reductive elimination and that both strongly electron-donating and electron-withdrawing substituents on the catalyst accelerate the selectivity-determining C-N bond formation process as a result of a change in mechanism. These findings offer design principles for the development of improved catalyst scaffolds for radical C-H functionalization reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Sulfite Is Not Required for N 2 Reduction Catalyzed by Mo-Nitrogenase

Mo-nitrogenase catalyzes the reduction of dinitrogen (N 2 ) to two ammonia (NH 3 ) at the active-site FeMo-cofactor. Substrate activation requires the accumulation of three or four electrons and protons as two Fe-bound hydrides and is coupled to obligatory H 2 release through reductive hydride elimination. Subsequent delivery of four or five additional electrons and protons to the bound N 2 yields two NH 3 molecules. Increasing evidence suggests that at least one belt sulfide within FeMo-cofactor is dynamically involved in the catalytic cycle. A recent report further proposed that sulfite (SO 3 2− ) is required for N 2 reduction, with sulfite binding required for NH 3 release and a subsequent six-electron reduction of the bound sulfite to regenerate the resting cofactor. To test this proposal, we conducted turnover studies of Mo-nitrogenase under sulfite-free conditions using a reduced viologen as reductant and protein preparations devoid of dithionite or sulfite. Under these conditions, nitrogenase effectively catalyzed both N 2 reduction and proton reduction, exhibiting steady-state turnover under N 2 for 6 min, with a turnover number exceeding 150, approaching that observed with dithionite as reductant. The same H 2 -formed/N 2 -reduced ratio was observed whether dithionite or the viologen species was used as reductant. Further, EPR spectroscopic analyses showed that the FeMo-cofactor returned to its resting state after multiple catalytic cycles in the absence of sulfite. Finally, physiological bypass of sulfite formation does not affect the capacity for diazotrophic growth of the model nitrogen-fixing organism Azotobacter vinelandii . Finally, these results demonstrate that sulfite is not required for Mo-nitrogenase-catalyzed N 2 reduction either in vitro or in vivo .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Rerouting reductant flux via protein tethering enhances biohydrogen production in Thermococcus kodakarensis

Microbes that generate copious amounts of hydrogen (H 2 ) via dark fermentation are a promising means to evolve and improve renewable biofuels. Many anaerobic hyperthermophilic archaea, such as the fast-growing, genetically tractable, heterotroph Thermococcus kodakarensis, produce generous quantities of H2 and provide an idealized platform to further optimize naturally high levels of biohydrogen reduction. Precise genetic manipulations and modifications to growth conditions have already resulted in substantial increases to H2 output but additional improvements are desired. An unexamined and potentially valuable route towards increased H 2 production is to tether select electron donor and acceptor proteins together to reroute and maximize the flow of electrons towards H 2 production. Such strategies have shown promise in Bacteria and Eukarya but have not yet been investigated in thermophilic Archaea. Here, we generate and evaluate twelve novel T. kodakarensis strains wherein a proteinaceous electron carrier (a ferredoxin, Fd) is physically tethered to the membrane-bound-hydrogenase (MBH), the sole H 2 producing enzyme, to direct electron flux towards biohydrogen generation. Growth assessments and H 2 output measurements demonstrate that strains encoding protein-fusions evolve up to ~ 40% more H2 per cell than the host strain. Eliminating H 2 consumption and alternative routes of electron sinks in concert with protein tethering further increased H2 output per cell for a maximum increase of ~ 66% over the host strain. Our results demonstrate that rerouting electron flux via protein tethering coupled with the elimination of reductant sinks is a promising means towards improved biohydrogen production in T. kodakarensis. KEY POINTS: Protein tethering between redox proteins can reroute electron flux in vivo. Enforced protein proximity results in ~ 40% increases in H2 production per cell. Protein-tethering provides a generalizable framework to redirect redox metabolism.

59 BASIC BIOLOGICAL SCIENCES↗

Probabilistic flux limiters

The stable numerical integration of shocks in compressible flow simulations relies on the reduction or elimination of Gibbs phenomena (unstable, spurious oscillations). A popular method to virtually eliminate Gibbs oscillations caused by numerical discretization in under-resolved simulations is to use a flux limiter. A wide range of flux limiters have been studied in the literature, with recent interest in their optimization via machine learning methods trained on high-resolution datasets. The common use of flux limiters in numerical codes as plug-and-play blackbox components makes them key targets for design improvement. Even for deterministic dynamical models, numerical uncertainty is introduced via coarse-graining required by insufficient computational power to solve all scales of motion. Conventional flux limiters are deterministic and lack the capacity to address uncertainties, both aleatoric (inherent randomness) and epistemic (modeling uncertainty due to limited knowledge), which arise in coarse-grained numerical simulations. Here, we introduce a conceptually distinct type of flux limiter that is designed to handle the effects of randomness in the model and uncertainty in model parameters. Unlike traditional single-function flux limiters, these new probabilistic flux limiters incorporate multiple flux limiting functions, each applied with a learned probability drawn from high-resolution data to mitigate the effects of uncertainty in numerical simulations. This approach departs from traditional single-function limiters by explicitly modeling and incorporating uncertainty into the shock capturing process. Using the example of Burgers' equation as a testbed, we show that a machine learned, probabilistic flux limiter may be used in a shock capturing code to more accurately capture shock profiles. In particular, we show that our probabilistic flux limiter outperforms standard limiters and can be successively improved upon (up to a point) by expanding the set of probabilistically chosen flux limiting functions.

97 MATHEMATICS AND COMPUTING↗

Boundary Corrections for Kernel Approximation to Differential Operators

The kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same computational cost as an explicit finite difference scheme but can exhibit order reduction at boundaries. In previous work on periodic domains, order reduction was addressed, yielding high-order accuracy. The issue addressed in this work is the elimination of order reduction of the kernel-based approach for a more general set of boundary conditions. Further, we consider the case of both first and second order operators. To demonstrate the theory, we provide not only the mathematical proofs but also experimental results by applying various boundary conditions to different types of equations. The results agree with the theory, demonstrating a systematic path to high order for kernel-based methods on bounded domains.

97 MATHEMATICS AND COMPUTING↗

Iron Oxide Reduction Rate Affects Iron Product Morphology

Magnetite concentrates from different parts of the Mesabi Range, exhibiting varying tendencies to encapsulate, were reduced using thermogravimetric analysis (TGA) and a high-temperature confocal scanning laser microscope (CSLM). Gas-phase mass-transfer conditions were intentionally varied by employing two reactors with different geometries: the TGA produced significantly slower reduction, whereas the CSLM setup yielded reduction rates up to 20 times faster under mass-transfer-controlled conditions. A preliminary mechanism is proposed to explain the transition from a porous iron product to a dense encapsulating layer. Encapsulation is interpreted as the outcome of competition between pore creation, driven by the reduction rate, and pore elimination, driven by surface diffusion. When pore formation is insufficient to counteract pore coarsening, a dense iron layer develops and restricts further reduction.

encapsulation↗