The Stefan problem of evaporation of a volatile component from a binary liquid mixture

The study is concerned with the Stefan problem of evaporation of a volatile component from its solution with a virtually non-volatile material. The analysis provides an analytical solution to the problem based on mass-transfer fundamentals. Results yield the evaporation rate, interfacial mole fractions, concentration profiles in the gas and liquid phases, and the location of the evaporation front. The analysis can be used to provide the binary liquid diffusion coefficient of the volatile component based on experimental data for the liquid–gas interface position as a function of time. The requirements for such a measurement are discussed in terms of the volatility of the evaporating component and its initial concentration in the liquid mixture. Fig. 1 Gas–liquid interface movement in a partially filled tube

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杂化化合物(C7H11N2)2[CdCl4]·0.5H2O的晶体结构、光谱表征和光学性质

开发了标题化合物（C₇H₁₁N₂）₂[CdCl₄]·0.5H₂O （C₇H₁₁N₂=4-（二甲基氨基）吡啶鎓）的制备程序,并得到良好的收率和纯度。Cd（Ⅱ）离子在略微扭曲的四面体环境中与4个氯离子配位。晶体排列显示出层状结构,有机层和无机层交替排列,平行于（001）平面,位于x=n+1/2（n∈Z）。在晶体中,有机层和无机层通过C—H…Cl、C—H…O、N—H…Cl和N—H…O氢键相互作用连接。Hirshfeld表面分析和结构的指纹图表明分子堆积受氢键和π堆积的控制。UV-Vis漫反射光谱使我们能够用Tauc外推法确定具有半导体特性的3.596 eV的直接带隙。观察到的在562 nm处具有最大值的光致发光带归属于4-（二甲基氨基）吡啶鎓阳离子中的激发π-π^*态。     

Synthesis of [MnCl<Subscript>3</Subscript>(H<Subscript>2</Subscript>O)<Subscript>2</Subscript>(Hatz)]·H<Subscript>2</Subscript>O and investigation of its structure via X-ray diffraction,spectroscopic measurements and DFT calculations

The 3-amino-1,2,4-triazole (atz)-based manganese complex was prepared and characterized through single-crystal X-ray diffraction, IR, EPR, and UV–visible spectroscopy. In the crystal structure, individual complex are interconnected through N(O)–H…Cl hydrogen bonds into 1D undulating chains running parallel to the [110] direction of the unit cell. Chains further grow into 2D supramolecular layers by way of the lattice water molecules of coordination and the chloride anions (O–H…Cl). Layers pack along the b-axis of the unit cell mediated by O–H…Cl(N) and N–H…O(Cl) hydrogen bonds forming a 3D supramolecular architecture. The theoretical calculations were also performed to optimize the structure of the complexes in the gas phase to confirm the structures proposed by X-ray crystallography. In addition, IR and UV–visible spectra of complex were calculated and compared with the corresponding experimental spectra to complete the experimental structural identification. The three-dimensional Hirshfeld surface (3D-HS) and their relative two-dimensional fingerprint plots (2D-FP) reveal that the structure is dominated by H…Cl/Cl…H (50.5%), H…O/O…H (11.3%) and N…O/O…N (10.2%) contacts.     

Stereoselective synthesis of functionalized vinyl ethers from allyl bromides activated by triethylamine

An efficient coupling reaction of allyl bromides with various alcohols as nucleophiles activated by triethylamine, leading to functionalized vinyl ethers in good yields and with full stereoselectivity.     

A generalization of Fan��s matching theorem

We introduce a generalized coercivity type condition for setvalued maps defined on topological spaces endowed with a generalized convex structure and we extend Fan’s matching theorem.     

Remote control of extended depth of field focusing

We propose a novel system allowing remote control of the location of the extended focal depth region. This system may find applications in situations where controllable optical access to an enclosure is needed and it is desirable to minimize the movement of the focusing lens. Our scheme uses three axicons, two external ones generating a ring and an internal one producing the focal region. We present a proof of concept of this system, consisting of measurements of the longitudinal and transverse intensity distributions, for a reference configuration and one with a displaced position of the extended depth of field focus.     

Kinetics of the reactions of OH radicals with some oxygenated volatile organic compounds under simulated atmospheric conditions

Some relative rate experiments have been carried out at room temperature and at atmospheric pressure. This concerns the OH-oxidation of some oxygenated volatile organic compounds including methanol (k₁), ethanol (k₂), MTBE (k₃), ethyl acetate (k₄), n-propyl acetate (k₅), isopropyl acetate (k₆), n-butyl acetate (k₇), isobutyl acetate (k₈), and t-butyl acetate (k₉). The experiments were performed in a Teflon-film bag smog chamber. The rate constants obtained are (in cm³ molecule⁻¹ s⁻¹): k₁=(0.90±0.08)×10⁻¹²; k₂=(3.88±0.11)×10⁻¹²; k₃=(2.98±0.06)×10⁻¹²; k₄=(1.73±0.20)×10⁻¹²; k₅=(3.56±0.15)×10⁻¹²; k₆=(3.97±0.18)×10⁻¹²; k₇=(5.78±0.15)×10⁻¹²; k₈=(6.77±0.30)×10⁻¹²; and k₉=(0.56±0.11)×10⁻¹². The agreement between the obtained rate constants and some previously published data has allowed for most of the studied compounds to point out a coherent group of values and to suggest recommended values. Atmospheric implications are also discussed. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet 30: 839–847, 1998     

A Leray-Schauder type theorem for approximable maps: a simple proof

We present a simple and direct proof for a Leray-Schauder type alternative for a large class of condensing or compact set-valued maps containing convex as well as nonconvex maps.

     

Crystal structure of 1-cyclohexylpiperazine-1,4-diium dichromate(VI)

Single crystals of 1-cyclohexylpiperazine-1,4-diium dichromate(VI), (C₁₀H₂₂N₂)[Cr₂O₇], were obtained by slow evaporation at room temperature from an aqueous solution of potassium dichromate, hydrochloric acid and 1-cyclohexylpiperazine. (C₁₀H₂₂N₂)[Cr₂O₇] is triclinic (P\(\bar 1\)) with a = 10.351(2) Å, b = 12.766(3) Å, c = 6.111(1) Å, α = 91.50(2)°, β = 104.26(3)°, γ = 94.91(2)°, V = 778.8(3) ų, and Z = 2. The structure determination performed from single crystal X-ray diffraction data leads to R₁/wR₂ reliability factors of 0.032/0.078. The asymmetric unit of the title salt C₁₀H₂₂N₂²⁺·Cr₂O₇^2?, consists of one 1-cyclohexylpiperazine-1,4-diium dication and one dichromate dianion. These entities are linked together by N–H···O hydrogen bonds to form {(C₁₀H₂₂N₂)[Cr₂O₇]}_n infinite chains lying parallel to the (100) plane and running along the c axis. The intermolecular N–H···O hydrogen bonds link these chains into a two-dimensional network structure consolidated through C–H···O weak interactions.