A modified finite element method for determining equilibrium capillary surfaces of liquids with specified volumes

This paper describes a modified finite element method (MFEM) for determining the static equilibrium shape of the capillary surface of a liquid with a prescribed volume constrained by rigid boundaries with arbitrary shapes. It is assumed that the liquid is in static equilibrium under the influence of surface tension, adhesion, and gravity forces. This problem can be solved by employing the conventional FEM; however, a major difficulty arises due to the presence of the volume (integral) constraint and usually requires the use of the Lagrange multiplier method, the sequential unconstrained minimization technique, or the augmented Lagrange multiplier method. With the MFEM, the space variables defining the equilibrium surfaces (or curves) are expanded in terms of parametric interpolation functions, which are designed such that the boundary conditions and the integral constraint equation are automatically satisfied during each iteration of a direct numerical search process. Hence, there is no need to include Lagrange multipliers and/or penalty factors and the problem can be treated more simply as one involving unconstrained optimization. This investigation indicates that the MFEM is more efficient and reliable than the other methods. Results are presented for several case study problems involving liquid solder drops. Copyright © 2000 John Wiley & Sons, Ltd.     

Kaliumtriamidostannat(II), K[Sn(NH2)3] – Synthese und Kristallstruktur

Potassium Triamidostannate(II), K[Sn(NH₂)₃] – Synthesis and Crystal Structure Rusty‐red crystals of K[Sn(NH₂)₃] were obtained by the reaction of SnBr₂ and KNH₂ in a 1 : 3 molar ratio in liquid ammonia at 233 K in the form of platelets. The structure was determined from single crystal X‐ray diffractometer data: Space group P3; Z = 2; a = 6.560(1) Å, c = 7.413(2) Å. The structure contains trigonal pyramidal complex anions [Sn(NH₂)₃]^– and potassium cations. These ions are arranged to one another following the motif of a strongly distorted hexagonal close packing of sequence A(Sn) B(Sn) A′(K) B′(K) …     

电聚合β-环糊精修饰电极的制备及其对铜离子的检测

采用循环伏安法(CV),由β-环糊精(β-CD)单体在玻碳电极(GCE)表面电聚合制得聚β-CD膜修饰电极(β-CD/GCE)。实验表明,β-CD/GCE对Cu2+具有明显的电催化作用,在pH=5.85的磷酸盐缓冲溶液(PBS)中,Cu2+浓度与其峰电流在4.01×10-4～1.05×10-7 mol·L-1范围内呈良好的线性关系,线性方程为:ip=-1.975c-1.336×10-4(i:A,c:mol·L-1),相关系数R=0.9981,检出限(S/N=3)为5.03×10-8mol·L-1。方法应用于实际样品测定,回收率在98.0%～103%之间。     

Effects of Permeation of Helium through the Walls of Fused Silica Capillary GC Columns

Hold-up times and peak widths have been measured in long fused silica GC capillary columns at high temperature with helium as the carrier gas. The results lead to the conclusion that the helium permeates through the column walls. The conventional Poiseuille theory of carrier gas flow has been extended to include this phenomenon. The resulting “loss modified Poiseuille” model, which uses literature values for the permeability of fused silica to helium, has been used to simulate the observed behavior. Good agreement between simulation and experiment validates the model. Simulations have been used to explore the effect of column permeability on hold-up times, peak widths, and velocity profiles over a broad range of column geometries.     

HUNTER: A conformational search program for acyclic to polycyclic molecules with special emphasis on stereochemistry

A new conformational search program, HUNTER, connected with the force fields MMP2 and MM3(92) is presented. The program accepts all types of molecules with most different substructures, considers stereochemical facts, and covers conformational space efficiently and completely. The most important facilities are an automated analysis of the stereochemistry including topographical facts, a separate perturbation of the acyclic and cyclic parts of the molecule using modified corner flapping, and an incremental rotation around single bonds with fixed flap and rotation angles, respectively; an exclusion of high energy structures by simulated annealing; the choice of the conformer lowest in energy, which is new as an initial structure for the next sampling run; and the use of a reduced set of dihedral angles to define a conformation. A specifically devised graphic interface, SERVANT, is used to feed in and control all informations necessary for a program run and to visualize the results. Most of the parameters are user-defined and thereby allow a flexible search, including a search for the most stable diastereomer. The efficiency of the different parameter sets was tested in calculation with cycloundecane ( 12 ), (Z)-oct-3-ene ( 13 ), and sipholenol-A monoacetate ( 14 ). The best performance regarding the number of different low-energy conformers was achieved with 60° ( 14 ) and 90° flaps ( 12 ), respectively, including substituent correction for the cyclic parts, and with 105° ( 14 ) and 120° rotations ( 13 ), respectively, for the acyclic parts. In comparison to the stochastic search routine implemented in MM3(92), HUNTER performed two ( 12 ) to six ( 14 ) times better. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1264–1281, 1997     

A comparison of polymerization characteristics and mechanisms of ε-caprolactone and trimethylene-carbonate with rare earth halides

Characteristics and mechanisms of the ring opening-polymerizations of ε-caprolactone (CL) and trimethylene carbonate (TMC) with rare earth halides have been compared for the first time. It has been found that rare earth halides show high catalytic activities for the polymerization of TMC, but very low activities for that of CL polymerization. The copolymerization of CL and TMC can proceed only in the presence of high contents of TMC in the comonomer feed. The copolymerization rate decreases rapidly with increasing molar fraction of CL in the feed. The mechanism study by IR, ¹H-, ¹³C-, and ³¹P-NMR spectra shows that the first step reaction of the polymerization of TMC or CL with rare earth halide is the complexation of monomer to the rare earth ion. The strong coordination of TMC to rare earth ion induces the ring-cleavage of TMC and generation of the cationic species, which initiate the polymerization of TMC via a cationic process. However, the polymerization of CL with rare earth halide is an “activated-hydrolysis” process, in which rare earth catalyst does not initiate the polymerization but serves as an activator of CL. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 1339–1352, 1997     

Alkali-Activated Hybrid Cements Based on Fly Ash and Construction and Demolition Wastes Using Sodium Sulfate and Sodium Carbonate

This article demonstrates the possibility of producing alkali-activated hybrid cements based on fly ash (FA), and construction and demolition wastes (concrete waste, COW; ceramic waste, CEW; and masonry waste, MAW) using sodium sulfate (Na₂SO₄) (2–6%) and sodium carbonate (Na₂CO₃) (5–10%) as activators. From a mixture of COW, CEW, and MAW in equal proportions (33.33%), a new precursor called CDW was generated. The precursors were mixed with ordinary Portland cement (OPC) (10–30%). Curing of the materials was performed at room temperature (25 °C). The hybrid cements activated with Na₂SO₄ reached compressive strengths of up to 31 MPa at 28 days of curing, and the hybrid cements activated with Na₂CO₃ yielded compressive strengths of up to 22 MPa. Based on their mechanical performance, the optimal mixtures were selected: FA/30OPC-4%Na₂SO₄, CDW/30OPC-4%Na₂SO₄, FA/30OPC-10%Na₂CO₃, and CDW/30OPC-10%Na₂CO₃. At prolonged ages (180 days), these mixtures reached compressive strength values similar to those reported for pastes based on 100% OPC. A notable advantage is the reduction of the heat of the reaction, which can be reduced by up to 10 times relative to that reported for the hydration of Portland cement. These results show the feasibility of manufacturing alkaline-activated hybrid cements using alternative activators with a lower environmental impact.     

修正的Bakhvalov-Shishkin网格上奇异摄动问题的一致收敛性

研究具有两个边界层的奇异摄动两点边界值问题，为了提高其数值解的精度，构造了修正的Bakhvalov—Shishkin网格及相应的离散差分格式，并且利用Green函数证明了该差分格式具有O(N^-2)，一致于撮动参数ε的收敛阶，从而本质上改进了在Shishkin网格上得到的结果，即相应的差分格式具有关于ε一致的收敛阶O(N^-2 ln^2 N)，其中N为网格结点数．最后用数值例子说明该方法的可行性．     

Template Assembly of Polyiodide Networks at Complexed Metal Cations: Synthesis and Structures of [Pd2Cl2([18]aneN2S4)]1.5I5(I3)2 and [K([15]aneO5)2]I9

The cations [Pd ₂ Cl ₂ L] ²⁺ and [KL ₂ ^{′ +} (L = [18]aneN₂S₄, L′ =[15]aneO₅) have been used as templates for the synthesis of unique three-dimensional polyiodide networks. The metal cations in [Pd₂Cl₂L]_1.5I₅(I₃)₂ are linked into infinite chains by pairwise hydrogen bonding; the resulting cationic polymers run through channels formed by the extended polyiodide network. [KL₂^′]I₉ shows a three-dimensional network of puckered cubic cages of I₉⁻ ions whose cavities are occupied by the metal cations (section from the structure shown on the right).     

The First Six-Membered “True” Heterocycle – Hydrogen-Bond-Assisted Ladder Formation in a KOCNPS Ring System

A ladder of alternating K₂S₂ and K₂O₂ rings exists in K[Ph₂P(S)NC(O)Ph]⋅MeOH, the first six-membered “true” heterocycle, in the solid state (see picture). A simple P–N bond-forming reaction between benzamide and Ph₂PCl gives the precursor Ph₂P(S)NHC(O)Ph, from which the potassium salt can be generated by reaction with KOtBu.