Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network

Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional base model parameterization of complex binary geological media. For inversion purposes, it has the attractive feature that random draws from an uncorrelated standard normal distribution yield model realizations with spatial characteristics that are in agreement with the training set. In comparison with the most commonly used parametric representations in probabilistic inversion, we find that our dimensionality reduction (DR) approach outperforms principle component analysis (PCA), optimization-PCA (OPCA) and discrete cosine transform (DCT) DR techniques for unconditional geostatistical simulation of a channelized prior model. For the considered examples, important compression ratios (200 - 500) are achieved. Given that the construction of our parameterization requires a training set of several tens of thousands of prior model realizations, our DR approach is more suited for probabilistic (or deterministic) inversion than for unconditional (or point-conditioned) geostatistical simulation. Probabilistic inversions of 2D steady-state and 3D transient hydraulic tomography data are used to demonstrate the DR-based inversion. For the 2D case study, the performance is superior compared to current state-of-the-art multiple-point statistics inversion by sequential geostatistical resampling (SGR). Inversion results for the 3D application are also encouraging

Regioselective Chain Shuttling Polymerization of Isoprene: An Approach To Access New Materials from Single Monomer

Chain shuttling polymerization (CSP) has exhibited unique privilege to combine monomer sequences of different properties into one macromolecular chain, which, however, is difficult to achieve because of low chain transfer efficiency and thus lead to poor architecture control over the resulting polymers. Herein, we reported that the pyridyl–methylene fluorenyl scandium complex <b>1</b> in combination with [Ph₃C]­[B­(C₆F₅)₄] and Al^<i>i</i>Bu₃ showed a high transfer efficiency (93.8%) in the presence of 10 equiv of Al^<i>i</i>Bu₃ toward the chain-transfer polymerization (CTP) of isoprene (IP) in high 1,4-selectivity (83%). Meanwhile, under the same conditions, the analogous lutetium precursor <b>3</b> based system was 3,4-regioselective and exhibited almost perfect chain transfer efficiency (96.5–100%) in a wide range of Al^<i>i</i>Bu₃-to-Lu ratios from 10:1 to 100:1, indicating that each Lu generated apparently 100 polyisoprene (PIP) macromolecules. Both CTPs performed fluently without compromising the selectivity and the activity and had comparable chain transfer rate constants. Based on this, 1,4- and 3,4-regioselective CSPs were realized by mixing <b>1</b> and <b>3</b> in various ratios to give a series of PIPs bearing different distribution of 1,4- and 3,4-PIP sequences and <i>T</i>_g values. This work provides a new strategy to access stereoregular and architecture controlled polymers from a single monomer

Regioselective Ring Opening Reactions of Pyridine N‑Oxide Analogues by Magnesium Hydride Complexes

The stoichiometric reactions of phosphinimino-amino (PIA)-supported magnesium hydride complex <b>1</b>, [L₁MgH]₂ (L₁ = (2,6-^<i>i</i>Pr₂-C₆H₃)­NC­(Me)­CHP­(Cy₂)­N­(2,6-Me₂-C₆H₃)), with pyridine <i>N</i>-oxide and 2-phenylpyridine <i>N</i>-oxide afforded 2,4-pentadiene-1-oximate complex <b>2</b> and 5-phenyl-2,4-pentadiene-1-oximate complex <b>3</b>, respectively. The reaction of <b>1</b> with 2-methylpyridine <i>N</i>-oxide showed a unique regioselectivity to produce 2,4-hexadiene-1-oximate <b>4a</b> in toluene and 3,5-hexadiene-2-oximate <b>4b</b> in THF, respectively. Treatment of β-diketiminato (BDI)-supported magnesium hydride complex <b>5</b>, [L₂MgH]₂ (L₂ = (2,6-^<i>i</i>Pr₂-C₆H₃)­NC­(Me)­CHC­(Me)­N­(2,6-^<i>i</i>Pr₂-C₆H₃)), with quinoline <i>N</i>-oxide gave 1,2-dihydroquinoline type product <b>6</b>, while treatment of complex <b>5</b> with 2-methylpyridine <i>N</i>-oxide either in toluene or THF afforded 1-methyl-2,4-pentadiene-1-oximate complex <b>7</b> as the only product. All these complexes were fully characterized by NMR spectroscopy and X-ray diffraction analyses, and mechanism researches were conducted to understand the ring-opening reaction of pyridine <i>N</i>-oxide

Statistically Syndioselective Coordination (Co)polymerization of 4‑Methylthiostyrene

The homopolymerization of a polar monomer, 4-methylthiostyrene (MTS), was successfully achieved by a rare-earth metal based catalyst in the highest activity of 45.1 × 10⁴ g mol_Y^–1 h^–1 and the excellent syndioselectivity (<i>rrrr</i> > 99%). The polymerization was rather controllable that the resultant poly­(methyl­thiostyrene)­s (PMTS) had molecular weights comparable to the theoretic ones reaching up to 1.7 × 10⁵ while the molecular weight distributions were narrow (PDI = 1.3–1.9). Moreover, the copolymerization of this polar MTS with the nonpolar styrene (St) performed fluently under various MTS-to-St ratios in a quasi-living mode. The monomer reactivity ratios were <i>r</i>_MTS = 1.08 and <i>r</i>_St = 0.77, following the first Markov statistics, and was close to the ideal random copolymerization. Therefore, a series of unprecedented statistical random copolymers, P­(St-<i>r</i>-MTS)­s, where the compositions were strictly closed to the monomer fed ratios, had been accessed. Strikingly, both monomer sequences remained highly syndiotactic as their homopolymers regardless of the compositions, thus endowing P­(St-<i>r</i>-MTS)­s variable glass transition temperatures and melting points. The shortest number-averaged sequence length for these copolymers P­(St-<i>r</i>-MTS) crystallizing from the melts was <i>n̅</i>_St = 5.75 for PS sequences and <i>n̅</i>_MTS = 8.11 for PMTS

Highly <i>Cis</i>-1,4-Selective Living Polymerization of 3‑Methylenehepta-1,6-diene and Its Subsequent Thiol–Ene Reaction: An Efficient Approach to Functionalized Diene-Based Elastomer

Living polymerization of 3-methylenehepta-1,6-diene (MHD) catalyzed by bis­(phosphino)­carbazoleide-ligated yttrium alkyl complex afforded a new product bearing pendant terminal vinyl groups with high stereotacticity (<i>cis</i>-1,4-selectivity up to 98.5%), proved by the NMR (¹H, ¹³C, and 1D ROESY) spectroscopic analyses, which demonstrates overwhelmingly favorable chemoselectivity toward conjugated diene over α-olefin moieties. High <i>cis</i>-1,4 random copolymers of MHD and isoprene could also be obtained with pendant vinyl groups ranging from 10% to 90%. These vinyl groups in every chain unit can be cleanly and quantitatively converted into various functionalities via light-mediated thiol–ene reaction, resulting in homo- and copolymers of various functional butadiene derivatives, which display versatile thermal properties

NNN-Tridentate Pyrrolyl Rare-Earth Metal Complexes: Structure and Catalysis on Specific Selective Living Polymerization of Isoprene

The acid–base reactions of NNN-tridentate pyrrolyl ligands (HL¹: 2,5-bis­((pyrrolidin-1-yl)­methylene)-1<i>H</i>-pyrrole; HL²: 2,5-bis­((piperidino)­methylene)-1<i>H</i>-pyrrole) with rare-earth metal tris­(alkyl)­s, Ln­(CH₂SiMe₃)₃(THF)₂, afforded the corresponding bis­(alkyl) complexes L¹Ln­(CH₂SiMe₃)₂(THF)_<i>x</i> (Ln = Sc, <i>x</i> = 0 (<b>1a</b>); Ln = Y, <i>x</i> = 1 (<b>1b</b>); Ln = Lu, <i>x</i> = 1 (<b>1c</b>)), L²Sc­(CH₂SiMe₃)₂ (<b>2a</b>), and L²₂Ln₂(CH₂SiMe₃)₄ (Ln = Y (<b>2b</b>); Lu (<b>2c</b>)) in moderate to high yields. X-ray diffraction analysis revealed that the scandium complexes <b>1a</b> and <b>2a</b> are THF solvent-free monomers where the ligands coordinate to the Sc³⁺ ion in a κ¹:κ² mode, while the yttrium and lutetium complexes <b>1b</b> and <b>1c</b> have the same ligand coordination geometry to that of the scandium complex but are one-THF solvates; complex <b>2b</b>, however, is a dimer bridged by two anionic L² fragments that coordinate to the two yttrium ions in mixed η⁵:η⁵/κ¹:κ¹ coordination modes. Upon activation with an organoborate, all these complexes initiated the controlled polymerization of isoprene. In general, complexes <b>2a</b>–<b>c</b>, bearing ligand L², exhibited higher activity than the analogous complexes <b>1a</b>–<b>c</b>, attached to the L¹ ligand. Complex <b>2b</b>, in which the L² ligand adopts the mixed η⁵/κ¹ coordination mode, showed the highest activity and livingness mode toward the polymerization of isoprene with high <i>cis</i>-1,4-selectivity (94.1%), and both scandium complexes <b>1a</b> and <b>2a</b> exhibited high 3,4-selectivity (87%) irrespective of the ligand type; in contrast, the lutetium complexes initiated the atactic isoprene polymerization. The influences of thell ligand structural factors, the coordination solvent, and the central metal ion on the catalytic activity and selectivity are discussed

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Copolymerization of Ethylene with 1‑Hexene and 1‑Octene Catalyzed by Fluorenyl N‑Heterocyclic Carbene Ligated Rare-Earth Metal Precursors

Rare-earth metal bis­(alkyl) complexes (Flu–NHC)­Ln­(CH₂SiMe₃)₂ (Ln = Dy (<b>1</b>), Er (<b>2</b>), Sc (<b>3</b>)) attached by fluorenyl-modified N-heterocyclic carbene ligands ((Flu H–NHC–H)­Br) have been synthesized by treatment of (FluH–NHC–H)­Br with (trimethylsilylmethyl)lithium (LiCH₂SiMe₃) and rare-earth metal tris­(alkyl)­s (Ln­(CH₂SiMe₃)₃(THF)₂) via double-deprotonation reactions in moderate to high yields. Under mild conditions (40 °C and normal ethylene pressure), the scandium precursor <b>3</b>, upon activation of Al^<i>i</i>Bu₃ and [Ph₃C]­[B­(C₆F₅)₄], showed high activity (4120 kg mol_Sc^–1 h^–1 atm^–1) for the copolymerization of ethylene and 1-hexene with moderate 1-hexene insertion ratio (20.2%), although the analogous complexes <b>1</b> and <b>2</b> were inert. In addition, this system displayed excellent catalytic performances for the copolymerization of ethylene and a higher α-olefin 1-octene with an activity of up to 3640 kg mol_Sc^–1 h^–1 atm^–1. The content of 1-octene could be controlled swiftly from 2.1% to 38.7% by varying the 1-octene feed ratio. Thus the isolated P­(E-co-Oct) polymers varied from opaque crystalline solids with high melting points, e.g., <i>T</i>_m = 103.6 °C, to transparent elastomers. This represents the first rare-earth metal based homogeneous catalyst that can initiate the copolymerization of ethylene and 1-octene, the catalytic performances of which are comparable with those reported for the most active group 4 metallocene systems

Copolymerization of Ethylene with 1‑Hexene and 1‑Octene Catalyzed by Fluorenyl N‑Heterocyclic Carbene Ligated Rare-Earth Metal Precursors

Rare-earth metal bis­(alkyl) complexes (Flu–NHC)­Ln­(CH₂SiMe₃)₂ (Ln = Dy (<b>1</b>), Er (<b>2</b>), Sc (<b>3</b>)) attached by fluorenyl-modified N-heterocyclic carbene ligands ((Flu H–NHC–H)­Br) have been synthesized by treatment of (FluH–NHC–H)­Br with (trimethylsilylmethyl)lithium (LiCH₂SiMe₃) and rare-earth metal tris­(alkyl)­s (Ln­(CH₂SiMe₃)₃(THF)₂) via double-deprotonation reactions in moderate to high yields. Under mild conditions (40 °C and normal ethylene pressure), the scandium precursor <b>3</b>, upon activation of Al^<i>i</i>Bu₃ and [Ph₃C]­[B­(C₆F₅)₄], showed high activity (4120 kg mol_Sc^–1 h^–1 atm^–1) for the copolymerization of ethylene and 1-hexene with moderate 1-hexene insertion ratio (20.2%), although the analogous complexes <b>1</b> and <b>2</b> were inert. In addition, this system displayed excellent catalytic performances for the copolymerization of ethylene and a higher α-olefin 1-octene with an activity of up to 3640 kg mol_Sc^–1 h^–1 atm^–1. The content of 1-octene could be controlled swiftly from 2.1% to 38.7% by varying the 1-octene feed ratio. Thus the isolated P­(E-co-Oct) polymers varied from opaque crystalline solids with high melting points, e.g., <i>T</i>_m = 103.6 °C, to transparent elastomers. This represents the first rare-earth metal based homogeneous catalyst that can initiate the copolymerization of ethylene and 1-octene, the catalytic performances of which are comparable with those reported for the most active group 4 metallocene systems

Binuclear Rare-Earth-Metal Alkyl Complexes Ligated by Phenylene-Bridged β‑Diketiminate Ligands: Synthesis, Characterization, and Catalysis toward Isoprene Polymerization

Deprotonation of <i>m</i>-phenylene-bridged bis­(β-diketiminate) ligands (PBDI^<i>i</i>Pr-H₂ = [2,6-^<i>i</i>Pr₂C₆H₃NHC­(Me)­C­(H)­C­(Me)­N]₂-(<i>m</i>-phenylene); PBDI^Et-H₂ = [2,6-Et₂C₆H₃NHC­(Me)­C­(H)­C­(Me)­N]₂-(<i>m</i>-phenylene); PBDI^Me-H₂ = [2,6-Me₂C₆H₃NHC­(Me)­C­(H)­C­(Me)­N]₂-(<i>m</i>-phenylene)) by rare-earth-metal tris­(alkyls) Ln­(CH₂SiMe₃)₃(THF)₂ (Ln = Y, Lu, Sc) gave a series of rare-earth-metal bis­(alkyl) complexes: PBDI^<i>i</i>Pr-[Y­(CH₂SiMe₃)₂]₂(THF)₂ (<b>1</b>), PBDI^Et-[Ln­(CH₂SiMe₃)₂]₂(THF)_<i>n</i> (<b>2a</b>, Ln = Y, <i>n</i> = 2; <b>2b</b>, Ln = Lu, <i>n</i> = 2; <b>2c</b>, Ln = Sc, <i>n</i> = 1), and PBDI^Me-[Y­(CH₂SiMe₃)₂]₂(THF)₂ (<b>3</b>). All these complexes were fully characterized by NMR spectroscopy, X-ray diffraction, and elemental analyses, adopting binuclear structures with the two rare-earth-metal ions taking <i>trans</i> positions versus the phenyl ring. Complexes <b>1</b>, <b>2a</b>,<b>b</b>, and <b>3</b> coordinate two solvated THF molecules, while the scandium complex <b>2c</b> incorporates only one THF molecule, owing to the steric crowding. Upon activation with 2 equiv of organoborate, the yttrium systems showed higher catalytic activity toward isoprene polymerization in comparison to those based on lutetium, and the scandium system was less active. Addition of aluminum alkyls to the above binary systems accelerated dramatically the polymerization rate irrespective of the central metal type through scavenging impurities in the systems and abstracting the solvated THF molecules in the precursors. The resultant polyisoprene had higher 3,4-regularity (20% vs 5%) as well as higher molecular weights in comparison with the mononuclear systems, which might be attributed to the steric bulky effect of the binuclear systems