Unravelling Structural Mysteries of Simple Organozinc Alkoxides

Simple RZnOR’ alkoxides are among the first known organozinc compounds, and widespread interest in their multifaced chemistry has been driven by their fundamental significance and potential applications including various catalytic reactions. Nevertheless, their chemistry in solution and in the solid state remains both relatively poorly understood and a subject of constant debate. Herein, the synthesis and structural characterization of long-sought structural forms, a roof-like trimer [(tBuZn)₃(μ-OC(H)Ph₂)₂(μ₃-OC(H)Ph₂)] and a ladder-type tetramer [(PhZn)₄(μ-OC(H)Ph₂)₂(μ₃-OC(H)Ph₂)₂], incorporating diphenylmethanolate as a model alkoxide ligand, are reported. Both novel aggregates are robust in the solid state and resistant towards mechanical force. By using ¹H NMR and diffusion-order spectroscopy, it is demonstrated that new RZnOR’ alkoxides are kinetically labile in solution and readily undergo ligand scrambling, such as in the case of Schlenk equilibrium. The elucidated key structural issues, which have remained undiscovered for decades, significantly advance the chemistry of RZnOR’ alkoxides and should support the rational design of zinc alkoxide-based applications.     

On subgame perfect equilibria in quantum Stackelberg duopoly with incomplete information

The Li–Du–Massar quantum duopoly model is one of the generally accepted quantum game schemes. It has applications in a wide range of duopoly problems. Our purpose is to study Stackelberg's duopoly with incomplete information in the quantum domain. The result of Lo and Kiang has shown that the correlation of players' quantities caused by the quantum entanglement enhances the first-mover advantage in the game. Our work demonstrates that there is no first-mover advantage if the players' actions are maximally correlated. Furthermore, we proved that the second mover gains a higher equilibrium payoff than the first one.     

The structure factor for liquid lead

Abstract

The structure factor for liquid lead at the temperatures 613 K, 643 K, 863 K and 1163 K are measured by neutron diffraction. Extensive comparisons to earlier measurements are made as well as comparisons to different hard-core models.     

Hybrid projection method for generalized mixed equilibrium problem and fixed point problem of infinite family of asymptotically quasi-?-nonexpansive mappings in Banach spaces

In this paper, we consider a hybrid projection method for finding a common element in the set of fixed points of a infinite family of asymptotically quasi-?-nonexpansive mappings and in the set of solutions of a generalized mixed equilibrium problem. Some strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. The results presented in the paper improve and extend some recent results.     

Correlation functions from a unified variational principle: Trial Lie groups

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces the original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie–Poisson structure. At second order, the variational expression for two-time correlation functions separates–as does its exact counterpart–the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical Gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero- and high-temperature limits, static and dynamic stability of small deviations.     

Phosphorinane and Enol Rings in One Molecule. Evidence for Reciprocal Stabilization of Half-Chair Conformations

Abstract.

The X-ray crystal structure of 2-(2′,4′-dioxo-3′-pentyl)-5,5-dimethyl-2-oxo-1,3,2-dioxaphosphorinane (2) reveals significant half-chair distortion of the axially oriented cisenol ring. The molecule also undergoes in-plane deformations. R(O...O) = 2.410 Å in the enol moiety indicates a very strong hydrogen bonding. The enol content, δ_OH and thermodynamic parameters for the axial-equatorial conformational and keto-enol equilibriums were obtained from ¹H, ³¹P NMR and IR measurements in comparison with the planar 4,6-dimethyl isomer (1) containing equatorially oriented enol ring. The X-ray single crystal structure of 5,5-dimethyl-2-(methoxycarbonyl-3′-oxo-2′-butyl)-2-oxo-1,3,2-dioxaphosphorinane (3) reveals the unusual half-chair conformation of the dioxaphosphorinane cycle disposed a trans-enol ring substituent. ¹H, ³¹P NMR and IR solution data support the same structure displays a strong conformational preference while the minor forms are chair conformers with an axial or equatorial cis-enol ring.     

Study on Dyeing Properties of Functional Acrylic Fiber

Anti‐mite acrylic fiber is a new type of functional fiber which incorporates a small amount of anti‐mite agent. Basic dye can be used in the dyeing of the functional acrylic fiber. Compared with the dyeing properties of conventional fibers, the dyeing properties of the functional acrylic fiber have new characteristics such as different dyeing temperature, time, amount of leveling agent and pH level due to the rough surface and larger size of micro‐channels in the functional fiber structure that helps basic dye molecules to diffuse into the fiber.     

Synthesis and Characterization of New Chelating Resin: Adsorption Study of Copper(II) and Chromium (III) Ions

Acrylamide based monomer, 5-methyl-2-thiozyl methacrylamide (MTMAAm) was synthesized by the reaction of 2-Amino-5-methyl thiazole with methacryloyl chloride in the presence of triethylamine(NR₃) at 0–5°C. The monomer MTMAAm was characterized by FT-IR and ¹H-and ¹³C-NMR spectral studies. A new chelating resin, poly(5-methyl-2-thiozyl methacrylamide-co-2-acrylamido-2-methyl-1-propanesulfonic acid-co-divinylbenzene) [MTMAAm/AMPS/DVB] was synthesized. This resin was characterized by FT-IR. In order to determine the adsorption behavior of chelating resin, the adsorption isotherm of Cr(III) and Cu(II) were studied. It was found that the adsorption isotherm of the ions fitted with Langmuir-type isotherms. From the Langmuir equation, the adsorption capacity of chelating resin for Cr(III) and Cu(II) was found to be 7.77 mg g^{? 1} and 4.27 mg g^{? 1}, respectively. Binding equilibrium constant was calculated to be 0.155 L mg^{? 1} and 0.106 L mg^{? 1} for Cu(II) and Cr(III), respectively.     

Spectroscopic Analysis of Two Distinct Equilibrium States for the Exchange Reaction of Sodium Cholate and Oligo‐DNA on Single‐Walled Carbon Nanotubes

Understanding the quantitative analysis of the transition adsorption structures of molecules on single‐walled carbon nanotubes (SWNTs) is of importance from the point of view of both fundamental science and applications of nanotubes. Absorption spectroscopy reveals that two different equilibrium states are existent for the exchange reaction of sodium cholate (SC) and oligo‐DNA (single‐stranded 20‐mer cytosine) on SWNTs. This is derived from the transitions of the adsorption structures of different chirality‐types of SWNTs and SC/DNA at certain SC concentrations below the critical micelle concentration of SC.     

Thermodynamic modeling for clathrate hydrates of ozone

We report a theoretical study to predict the phase-equilibrium properties of ozone-containing clathrate hydrates based on the statistical thermodynamics model developed by van der Waals and Platteeuw. The Patel–Teja–Valderrama equation of state is employed for an accurate estimation of the properties of gas phase ozone. We determined the three parameters of the Kihara intermolecular potential for ozone as a = 6.815 · 10⁻² nm, σ = 2.9909 · 10⁻¹ nm, and ε · k_B⁻¹ = 184.00 K. An infinite set of ε–σ parameters for ozone were determined, reproducing the experimental phase equilibrium pressure–temperature data of the (O₃ + O₂ + CO₂) clathrate hydrate. A unique parameter pair was chosen based on the experimental ozone storage capacity data for the (O₃ + O₂ + CCl₄) hydrate that we reported previously. The prediction with the developed model showed good agreement with the experimental phase equilibrium data within ±2% of the average deviation of the pressure. The Kihara parameters of ozone showed slightly better suitability for the structure-I hydrate than CO₂, which was used as a help guest. Our model suggests the possibility of increasing the ozone storage capacity of clathrate hydrates (∼7% on a mass basis) from the previously reported experimental capacity (∼1%).