2015年全国研究生数学建模竞赛F题综述

叙述了2015年全国研究生数学建模竞赛F题"旅游路线规划问题"的命题背景和目的,分析了本赛题的建模及求解思路,对评阅中发现的问题进行了综述,最后叙述了本赛题还需继续思考的问题.     

Calotropis procera mediated one pot green synthesis of Cupric oxide nanoparticles (CuO‐NPs) for adsorptive removal of Cr(VI) from aqueous solutions

The present study deals with the synthesis of CuO‐NPs via green route and investigated its application for removal of Cr(VI) from aqueous solutions. The experimental parameters were optimized through Box–Behnken Design (BBD) of response surface methodology for the optimum response. The adsorption equilibrium data was well fitted to Freundlich isotherm model and the kinetics was explained through pseudo‐second‐order kinetic model. The overall process was feasible, spontaneous and exothermic. Linear approach for analysing the isotherm as well as kinetic parameters was found more appropriate than the non‐linear approach. The adsorbent was successfully regenerated and reused up to five consecutive cycles without significant loss in removal capacity. The experimental results exhibited that CuO‐NPs can be a good alternative for Cr(VI) removal from aqueous solutions.     

General synthesis of metal sulfides nanocrystallines via a simple polyol route

In this report, a simple and easy polyol route for synthesizing many binary metal sulfides nanocrystallines is demonstrated. Powder X-ray electron diffraction and energy-dispersive X-ray spectrum are applied to investigate the crystallinity and composition of the nanoscale materials. The resulting particle size and morphology are examined by transmission electron microscopy, and the possible mechanism is also briefly discussed.     

Nanocrystalline CaTiO3 prepared by soft-chemical route

Nanocrystalline CaTiO₃ has been synthesized by using soft-chemical route. X-ray diffraction study indicates that as-prepared powders were amorphous in nature and formation of CaTiO₃ phase starts at about 773 K. Phase formation saturates at around 1023 K and it remains orthorhombic up to 1400 K. Microstructure analysis by the Rietveld method revealed that the CaTiO₃ crystal size varies from 22.9 to 49.3 nm, while the annealing temperature varies from 773 to 1023 K. The variation of DC resistivity with temperature in the range 400–560 K shows a polaronic behavior in this system.     

Mechanistic Insights into the Synthesis of [Rh(acac)(CO)(NHC)] (NHC=N-heterocyclic carbene) Complexes Using a Weak Base

A simple synthetic method to access a wide range of [Rh(acac)(CO)(NHC)] complexes is described. In situ infra-red monitoring provides insights into the mechanism of the reaction, including the identification of a key intermediate. An understanding of the reaction mechanism leads to the discovery of novel pathways to commonly used congeners.     

A facile, microwave-assisted synthesis of novel optically active polyamides derived from 5-(3-methyl-2-phthalimidylpentanoylamino)isophthalic acid and different diisocyanates

5-(3-Methyl-2-phthalimidylpentanoylamino)isophthalic acid as a novel aromatic diacid monomer was prepared in three steps. In the first step, phthalic anhydride was reacted with l-isoleucine in acetic acid solution, and the resulting imide acid was obtained in high yield. In the second step, treatment of this imide acid with excess thionyl chloride gave aliphatic acid chloride in good yield. In the last step, this acid chloride was reacted with 5-aminoisophthalic acid to provide novel bulky chiral aromatic diacid monomer. The direct polycondensation reactions of this diacid with several aromatic and aliphatic diisocyanates such as 4,4′-methylenebis(phenyl isocyanate), toluylene-2,4-diisocyanate, isophorone diisocyanate and hexamethylene diisocyanate were carried out under microwave irradiation. In order to compare this method with classical heating, the polymerization reactions were also performed under solution polycondensation conditions. The polymerization reactions occurred rapidly under microwave conditions and produced a series of novel optically active polyamides (PA)s containing pendent phthalimide group, with good yields and moderate inherent viscosities of 0.17-0.60 dL/g. Some of the new PAs showed good solubility and are readily soluble in organic solvents. The resulting macromolecules were characterized by FT-IR, specific rotation, and representative ones by ¹H NMR, elemental and thermogravimetric analyses (TGA).     

Aliphatic thermoplastic poly(ether urethane)s having long PEG sequences synthesized through a non-isocyanate route

A non-isocyanate route for synthesizing thermoplastic polyurethanes with excellent thermal and mechanical properties was described. Melt transurethane polycondensation of 1,6-bis(hydroxyethyloxy carbonyl amino)hexane with four poly(ethylene glycol)s(PEGs), i.e. PEG400, PEG600, PEG1000, or PEG1500, was conducted at different molar ratios. A series of thermoplastic poly(ether urethane)s(TPEUs) with long PEG sequences were prepared. The TPEUs were characterized via gel permeation chromatography, FTIR, 1H-NMR, differential scanning calorimetry, thermogravimetric analysis, wide-angle X-ray scattering, and tensile tests. The TPEUs exhibit Tg between 12.4 °C and-40.4 °C, Tm of up to 149.8 °C, and initial decomposition temperature over 239.4 °C. The tensile strength of the TPEUs reaches 38.39 MPa with a strain at break of 852.92%.     

含氟体系下高性能丝光沸石分子筛膜的制备及其性能

采用热涂-浸渍法在大孔α-Al2O3载体上形成薄且致密的晶种层,然后在不添加有机模板剂的含氟条件下二次水热生长法制备了高性能丝光沸石分子筛膜,考察了NaF含量、硅/铝比对丝光沸石分子筛膜形貌和性能的影响.将摩尔组成为6Na2O:1.2Al2O3:30SiO2:780H2O:1.5NaF条件下合成的丝光沸石分子筛膜用于渗透汽化分离91.5%乙醇/水体系,在渗透汽化温度70°C、真空度为400Pa条件下,分离因子和通量分别达到了6872和0.51kg/(m2·h);另外,在分离异丙醇/水、乙酸/水体系时,渗透侧水浓度达到了100%(在色谱检测极限范围内),该分离系数是目前报道的丝光沸石分子筛膜分离的最佳值,并在乙酸浓度为1mol/L的乙醇水溶液中表现出良好的耐酸性.该膜有望作为膜反应器在乙酸乙酯等酯类的生产中大大提高转化率.     

6/7Li NMR study of the Li1-zNi1+zO2 phases

A series of Li1-zNi1+zO2 materials have been synthesised by the coprecipitation route. An X-ray diffraction study was carried out on these materials using the Rietveld method to determine the departure from the ideal stoichiometry z, which ranges from 0 to 0.138. The actual Li/Ni ratio was also checked by chemical analyses using inductively coupled plasma (ICP) for each sample. The stoichiometric sample (z approximately 0) was obtained using a 15% Li excess. (6/7)Li NMR results from LiNiO2 (z approximately 0) show that the asymmetric shape of the NMR signal is due to anisotropy. Calculations give evidence that the paramagnetic dipolar interaction from the electron spins carried by Ni is anisotropic but does not completely explain the experimental anisotropy. (6)Li MAS NMR (magic angle spinning NMR) experiments and temperature standardisation NMR measurements unambiguously assign the isotropic position at +726 ppm. The static-echo NMR spectra of the non-stoichiometric Li1-zNi1+zO2 phases also exhibit an asymmetric shape whose width increases with the departure from the ideal stoichiometry z. (6/7)Li static and MAS NMR show that the 2zNi(2+) ions thus formed modify the dipolar interaction within the materials and also affect the Fermi contact interaction, since a distribution of Li environments is observed using (6)Li NMR for non-stoichiometric samples.