Tail behavior of supremum of a random walk when Cramér’s condition fails

We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and O-subexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.     

Molecular structure and properties of click hydrogels with controlled dangling end defect

In this study, controlled amount of dangling ends is introduced to the two series of poly(ethylene glycol)‐based hydrogel networks with three and four crosslinking functionality by using click chemistry. The structure of the gels with regulated defect percentage is confirmed by comparing the results of low‐field NMR characterization and Monte Carlo simulation. The mechanical properties of these gels were characterized by tensile stress–strain behaviors of the gels, and the results are analyzed by Gent model and Mooney–Rivlin model. The shear modulus of the swollen gels is found to be dependent on the functionality of the network, and decreases with the defect percentage. Furthermore, the value of shear modulus well obeys the Phantom model for all the gels with varied percentage of the defects. The maximum extension ratio, obtained from the fitting of Gent model, is also found to be dependent on the functionality of the network, and does not change with the defect percentage, except at very high defect percentage. The value of the maximum extension ratio is between that predicted from Phantom model and the Affine model. This indicates that at the large deformation, the fluctuation of the crosslinking points is suppressed for some extend but still exists. Polymer volume fractions at various defect percentages obtained from prediction of Flory–Rehner model are found to be in well agreement with the swelling experiment. All these results indicate that click chemistry is a powerful method to regulate the network structure and mechanical properties of the gels. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1227–1236     

新型蒽类聚方酸菁的合成及其性能

以蒽为起始原料,经溴代反应和Witting-Horner反应制得单体9,10-双[2-(1-辛基-1H-吡咯-2-基)乙烯基]蒽(3);3与芳酸缩聚合成了一个新型的蒽类聚方酸菁(4),其结构和性能经UV-Vis,1HNMR,13CNMR,IR,XRD,SEM和TG表征。4在氯仿中的λmax位于700nm;4为非晶态结构;4的初始分解温度为297.1℃。     

Synthesis and UCST‐type phase behavior of polypeptide with alkyl side‐chains in alcohol or ethanol/water solvent mixtures

A series of thermoresponsive polypeptides bearing 1‐butyl, 1‐hexyl, or 1‐dodecyl side‐chains (i.e., 6a ‐ 6c ) were synthesized by copper‐mediated 1,3‐dipolar cycloaddition with high grafting efficiency (>95%) between side‐chain “clickable” polypeptide, namely poly(γ‐4‐(propargoxycarbonyl)benzyl‐_L‐glutamate) ( 5 ) and 1‐azidoalkanes. 5 with different degree of polymerization (DP = 48–86) were prepared from triethylamine initiated ring‐opening polymerization of γ‐4‐(propargoxycarbonyl)benzyl‐_L‐glutamic acid based N‐carboxyanhydride ( 4 ). ¹H NMR, FTIR, and GPC results revealed the successful preparation of the resulting polypeptides. 6a ‐ 6c showed reversible UCST‐type phase behaviors in methanol, ethanol, and ethanol/water solvent mixtures depending on the polymer main‐chain length, alkyl side‐chain length, weight percentage of ethanol (f_w) in the binary solvent, and so forth. FTIR analysis revealed the presence of the van der Waals interaction between the alkyl pendants of polypeptides and alkyl groups of alcoholic solvents. Variable‐temperature UV‐vis spectroscopy revealed that the UCST‐type phase transition temperature (T_pt) increased as polymer main‐chain length or concentration increased. In ethanol/water solvent mixtures, polypeptide with short alkyl pendant (i.e., 1‐butyl group) and short main‐chain length (DP = 41) showed the widest f_w range and T_pts in the range of 61.0–71.1 °C. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 3425–3435     

A Terbium Metal–Organic Framework for Highly Selective and Sensitive Luminescence Sensing of Hg2+ Ions in Aqueous Solution

A series of isomorphic lanthanide metal–organic frameworks (MOFs) Ln(TATAB)?(DMF)₄(H₂O)(MeOH)_0.5 (LnTATAB, Ln=Eu, Tb, Sm, Dy, Gd; H₃TATAB=4,4′,4′′‐s‐triazine‐1,3,5‐triyltri‐p‐aminobenzoic acid) have been solvothermally synthesized and structurally characterized. Among these MOFs, TbTATAB exhibits good water stability and a high fluorescence quantum yield. Because mercury ions (Hg²⁺) have a high affinity to nitrogen atoms, and the space between multiple nitrogen atoms from triazine and imino groups is suitable for interacting with Hg²⁺ ions, TbTATAB shows highly selective and sensitive detection of Hg²⁺ in aqueous solution with a detection limit of 4.4 nm . Furthermore, it was successfully applied to detect Hg²⁺ ions in natural water samples.     

Electrical conductivity,impedance, and percolation behavior of carbon nanofiber and carbon nanotube containing gellan gum hydrogels

The electrical impedance behavior of gellan gum (GG), GG–carbon nanotube, and GG–carbon nanofiber hydrogel composites is reported. It is demonstrated that the impedance behavior of these gels can be modeled using a Warburg element in series with a resistor. Sonolysis (required to disperse the carbon fillers) does not affect GG hydrogel electrical conductivity (1.2 ± 0.1 mS/cm), but has a detrimental effect on the gel's mechanical characteristics. It was found that the electrical conductivity (evaluated using impedance analysis) increases with increasing volume fraction of the carbon fillers and decreasing water content. For example, carbon nanotube containing hydrogels exhibited a six‐ to sevenfold increase in electrical conductivity (to 7 ± 2 mS/cm) at water content of 82%. It is demonstrated that at water content of 95 ± 2% the electrical behavior of multiwalled nanotube containing hydrogels transitions (percolates) from transport dominated by ions (owing to GG) to transport dominated by electrons (owing to the carbon nanotube network). © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 864–871     

Side chain impacts on pH‐ and thermo‐responsiveness of tertiary amine functionalized polypeptides

The systemic investigation of the structural impacts of side chains on the pH‐ and thermo‐responsiveness of tertiary amine functionalized poly(l ‐glutamate)s (TA‐PGs) was carried out. The TA‐PGs polymers were effectively synthesized by Cu(I)‐catalyzed azide‐alkyne cycloaddition click reaction of azido tertiary amines with poly(γ‐propargyl‐l ‐glutamate) (PPLG). Turbimetric measurements were performed to characterize the pH‐ and temperature‐induced phase transition of TA‐PGs in aqueous solution, which suggested a structural dependence of the properties on the N‐substituted groups and the “linkers” between 1,2,3‐triazole ring and the tertiary amine groups in the side chains. In detail, the pH responsive properties of TA‐PGs were basically determined by the hydrophobicity of the N‐substituted groups in the side chains and the pH transition point (pH_t) decreased as the increasing hydrophobicity of the N‐substituted groups, while the temperature‐responsiveness of TA‐PGs were affected by either the N‐substituted groups or the “linkers.” TA‐PGs with a moderate N‐substituted amine group (e.g., DEA, PR, and PD) or a branched “linker” (e.g., iso‐propylene and 2‐methylpropylene group) were more likely to express the LCST‐type phase transition tuned by pH variation. These structure–property relationships revealed in this study would help to develop the applications of TA‐PGs in smart drug delivery systems. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 671–679     

新型含氮配体多核铜配合物的合成、晶体结构及其性能研究

以1,10-邻菲罗啉(phen)为配体,采用溶剂蒸发法在水中分别合成了羟基桥连和氯离子桥连的两个新型的含氮配体多核铜离子配合物[Cu4(phen)4(H2O)2(OH)4·(NO3)4·2H2O(1)和Cu2(phen)2Cl4(2)],其结构经元素分析和X-射线单晶衍射表征。1属三斜晶系,空间群P-1,晶胞参数a=10.143 0(9),b=11.900 1(11),c=12.629 9(13),α=111.060(2)°,β=91.070 0(10)°,γ=110.920(2)°,Z=1,V=1 309.8(2)3,F(000)=692。2属单斜晶系,空间群Cc,晶胞参数a=9.860 9(8),b=17.852 9(13),c=13.412 3(15),β=106.583(11)°,Z=4,V=2 263.0(4)3,F(000)=1 256。用荧光光谱和热分析分别研究了1和2的荧光性质和热稳定性,结果表明:在310 nm激发波长激发下,与phen相比,1和2的荧光发射峰分别发生红移和蓝移,λem分别位于451 nm和374 nm。1和2的初始分解温度分别为298℃和300℃。     

UV Emission of Gd3+ in the Presence of Cu2+: Towards Luminescence Quenching through Quantum Cutting?

The first investigation into the ultraviolet (UV) photoluminescence of gadolinium(III) in the presence of copper(II) is reported. A melt‐quenched barium phosphate glass was used as a model matrix. The optical spectroscopy assessment shows that with increasing CuO concentration the Cu²⁺ absorption band grows steadily, whereas the UV emission from Gd³⁺ ions is progressively quenched. The data, thus, suggests the existence of a Gd³⁺→Cu²⁺ energy‐transfer process ocurring through quantum cutting. A downconversion/cross‐relaxation pathway proceeding through a virtual state in Gd³⁺ is proposed. These findings suggest gadolinium(III) could potentially be used in the optical sensing of copper(II).