Fine Tunable,Redox Active Octapalladium Chains Supported by Linear Tetraphosphines,Leading to Dynamically 1D Self-Assembled Coordination Polymers

A series of the octapalladium chains supported by meso-Ph₂PCH₂P(Ph)CH₂P(Ph)CH₂PPh₂ (meso-dpmppm) ligands, [Pd₈(meso-dpmppm)₄(L)₂](BF₄)₄ (L=none ( 1 ), solvents: CH₃CN ( 2 a ), dmf ( 2 b ), dmso ( 2 c ), RN≡C: R=Xyl ( 3 a ), Mes ( 3 b ), Dip ( 3 c ), ^tBu ( 3 d ), Cy ( 3 e ), CH₃(CH₂)₇ ( 3 f ), CH₃(CH₂)₁₁ ( 3 g ), CH₃(CH₂)₁₇ ( 3 h )) and [Pd₈(meso-dpmppm)₄(X)₂](BF₄)₂ (X=Cl ( 4 a ), N₃ ( 4 b ), CN ( 4 c ), SCN ( 4 d )), were synthesized by using 2 a as a stable good precursor, and characterized by spectroscopic (IR, ¹H and ³¹P NMR, UV-vis-NIR, ESI-MS) measurements and X-ray crystallographic analyses (for 1 , 2 a , b , 3 a , b , e , f , 4 a – d ). On the basis of DFT calculations on the X-ray determined structure of 2 b ( [2b-Pd₈]⁴⁺ ) and the optimized models [Pd₈(meso-Ph₂PCH₂P(H)CH₂P(H)CH₂PH₂)₄(CH₃CN)₂]⁴⁺ ( [Pd₈Ph₈]⁴⁺ ) and [Pd₈(meso-H₂PCH₂P(H)CH₂P(H)CH₂PH₂)₄(CH₃CN)₂]⁴⁺ ( [Pd₈H₈]⁴⁺ ), with and without empirically calculating dispersion force stabilization energy (B3LYP-D3, B3LYP), the formation energy between the two Pd₄ fragments is assumed to involve mainly noncovalent interactions (ca. −70 kcal/mol) with four sets of interligand C−H/π interactions and Pd⋅⋅⋅Pd metallophilic one, while electron shared covalent interactions are almost canceled out within the Pd₈ chain. All the compounds isolated are stable in solution and exhibit characteristic absorption at ∼900 nm, which is assignable to a spin allowed HOMO to LUMO transition, and shows temperature dependent intensity change with variable absorption coefficients presumably due to coupling with some thermal vibrations. The structures and electronic states of the Pd₈ chains are found finely tunable by varying the terminal capping ligands. In particular, theoretical calculations elucidated that the HOMO-LUMO energy gap is systematically related to the central Pd−Pd distance (2.7319(6)–2.7575(6) Å) by two ways with neutral ligands L ( 1 , 2 , 3 ) and with anionic ligands X ( 4 ), which are reflected on the NIR absorption energy of 867–954 nm. The isocyanide terminated Pd₈ complexes ( 3 ) further reacted with excess of RNC (6 eq) to afford the Pd₄ complexes, [Pd₄(meso-dpmppm)₂(RNC)₂](BF₄)₂ ( 13 ), and the cyclic voltammograms of 2 a (L=CH₃CN), 3 , and 13 (R=Xyl, Mes, ^tBu, Cy) demonstrated wide range redox behaviors from 2{Pd₄}⁴⁺ to 2{Pd₄}⁰ through 2{Pd₄}²⁺↔{Pd₈}⁴⁺, {Pd₈}³⁺, and {Pd₈}²⁺ strings. The oxidized complexes, [Pd₄(meso-dpmppm)₂(RNC)₃](BF₄)₄ ( 16 ), were characterized by X-ray analyses, and the two-electron reduced chain of [Pd₈(meso-dpmppm)₄](BF₄)₂ ( 7 ) was analyzed by spectroscopic and electrochemical techniques and DFT calculations. Reactions of 2 a with 1 equiv. of aromatic linear bisisocyanide (BI) in CH₂Cl₂ deposited insoluble coordination polymers, {[Pd₈(meso-dpmppm)₄(BI)](BF₄)₄}_n ( 5 ), and interestingly, they were soluble in acetonitrile, ³¹P{¹H} and ¹H DOSY NMR spectra as well as SAXS curves suggesting that the coordination polymers may exist in acetonitrile as dynamically 1D self-assembled coordination polymers comprising ca. 50 units of the Pd₈ rod averaged within the timescale.     

非线性Black-Scholes模型下算术平均亚式期权定价问题

在非线性Black-Scholes模型下,研究了算术平均亚式期权定价问题.首先利用单参数摄动方法,将亚式期权适合的偏微分方程分解成一系列常系数抛物方程.其次通过计算这些常系数抛物型方程的解,给出了算术平均亚式期权的近似定价公式.最后分析了近似结论的误差估计,并通过数值算例验证了所得近似结论的合理性.     

Synthesis and Characterization of Hydrophilic Trityl Radical TFO for Biomedical and Biophysical Applications

Tetrathiatriarylmethyl (TAM, trityl) radicals have found wide applications as spin probes/labels for EPR spectroscopy and imaging, and as polarizing agents for dynamic nuclear polarization. The high hydrophilicity of TAM radicals is essential for their biomedical applications. However, the synthesis of hydrophilic TAM radicals (e.g., OX063) is extremely challenging and has only been reported in the patent literature, to date. Herein, an efficient synthesis of a highly water-soluble TAM radical bis(8-carboxyl-2,2,6,6-tetramethylbenzo[1,2-d:4,5-d′]bis([1,3]dithiol-4-yl)-mono-(8-carboxyl-2,2,6,6-tetrakis(2-hydroxyethyl)benzo[1,2-d:4,5-d′]bis([1,3]dithiol-4-yl)methyl (TFO), which contains four additional hydroxylethyl groups, relative to the Finland trityl radical CT-03, is reported. Similar to OX063, TFO exhibits excellent properties, including high water solubility in phosphate buffer, low log P, low pK_a, long relaxation times, and negligible binding with bovine serum albumin. On the other hand, TFO has a sharper EPR line and higher O₂ sensitivity than those of OX063. Therefore, in combination with its facile synthesis, TFO should find wide applications in magnetic resonance related fields and this synthetic approach would shed new light on the synthesis of other hydrophilic TAM radicals.     

Multipod structures of lamellae‐forming diblock copolymers in three‐dimensional confinement spaces: Experimental observation and computer simulation

The three‐dimensional (3D) confinement effect on the microphase‐separated structure of a diblock copolymer was investigated both experimentally and computationally. Block copolymer nanoparticles were prepared by adding a poor solvent into a block copolymer solution and subsequently evaporating the good solvent. The 3D structures of the nanoparticles were quantitatively determined with transmission electron microtomography (TEMT). TEMT observations revealed that various complex structures, including tennis‐ball, mushroom‐like, and multipod structures, were formed in the 3D confinement. Detailed structural analysis, showed that one block of the diblock copolymer slightly prefers to segregate into the particle surface compared with the other block. The observed structures were further elaborated using cell dynamics computer simulation. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1702–1709     

A BGK‐penalization‐based asymptotic‐preserving scheme for the multispecies Boltzmann equation

An asymptotic‐preserving (AP) scheme is efficient in solving multiscale problems where kinetic and hydrodynamic regimes coexist. In this article, we extend the BGK‐penalization‐based AP scheme, originally introduced by Filbet and Jin for the single species Boltzmann equation (Filbet and Jin, J Comput Phys 229 (2010) 7625–7648), to its multispecies counterpart. For the multispecies Boltzmann equation, the new difficulties arise due to: (1) the breaking down of the conservation laws for each species and (2) different convergence rates to equilibria for different species in disparate masses systems. To resolve these issues, we find a suitable penalty function—the local Maxwellian that is based on the mean velocity and mean temperature and justify various asymptotic properties of this method. This AP scheme does not contain any nonlinear nonlocal implicit solver, yet it can capture the fluid dynamic limit with time step and mesh size independent of the Knudsen number. Numerical examples demonstrate the correct asymptotic‐behavior of the scheme. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013     

Dynamic modeling of the morphology of latex particles with in situ formation of graft copolymer

Modification of the polymer–polymer interfacial tension is a way to tailor‐make particle morphology of waterborne polymer–polymer hybrids. This allows achieving a broader spectrum of application properties and maximizing the synergy of the positive properties of both polymers, avoiding their drawbacks. In situ formation of graft copolymer during polymerization is an efficient way to modify the polymer–polymer interfacial tension. Currently, no dynamic model is available for polymer–polymer hybrids in which a graft copolymer is generated during polymerization. In this article, a novel model based on stochastic dynamics is developed for predicting the dynamics of the development of particle morphology for composite waterborne systems in which a graft copolymer is produced in situ during the process. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Classroom note: The area under x α by geometry

By stretching the area under the curve x ^α it is shown to be of the form x ^{α + 1} p(α). Geometry is then used to prove p(α) = 1/(α + 1).     

Preliminary communication Liquid crystalline cardanyl β-D-glucopyranosides

Two novel aryl glycosides were synthesized, which varied in the extent of unsaturation in the lipophilic part, from plant/crop-based renewable resource materials. Their liquid crystalline properties were characterized by optical polarizing microscopy, differential scanning calorimetry and X-ray diffraction. All the mesophases are identified as lamellar in structure.     

Modelling day‐ahead electricity prices

A production‐based approach is introduced to take into account different attitudes and liabilities of market participants to discuss the equilibrium day‐ahead prices on electricity. Conditions ensuring the existence of the equilibrium are given and price distribution is considered. A discussion of reasons for high price volatility is given.