Mesogenic and optical properties of α,α′‐bis(4‐alkoxyphenylethynyl)oligothiophenes

Liquid crystalline α,α′‐bis(4‐alkoxyphenylethynyl)oligothiophenes (bi‐ and ter‐thiophene) have been synthesized and their mesogenic behaviour and optical properties investigated. They all exhibited a nematic mesophase, and compounds with long alkoxy chains also showed lamellar phases. Increasing the number of thiophene units increased both the transition temperatures and the mesophase ranges. As for their optical properties, incorporating more thiophene units results in red‐shifted absorption and emission spectra, slightly enhanced quantum efficiency, and a larger Stoke's shift. Most importantly, in terms of the absorption and emission maxima, the incorporation of one 4‐alkoxyphenylethynyl moiety was found to be equivalent to adding one thiophene ring.     

Effect of spacer length on mesomorphic behaviours of chiral liquid crystal compounds containing (-)-menthyl

ABSTRACT

A homologous series of new chiral liquid crystal compounds, MnBEB (n = 4–10), was prepared by covalently linking a chiral (–)-menthyl with biphenyl-benzoate via a dicarboxylic spacer of varying length and parity. A combination of analysis methods, such as FT-IR, ¹H NMR spectra, differential scanning calorimetry (DSC), polarised optical microscopy (POM) and X-ray diffraction was carried out to systematically investigate their phase structures and phase transition behaviours. The length and parity of the flexible spacers has a profound influence on the T_m and T_c and a modest odd-even effect is observed for the chiral liquid crystal compounds MnBEB. Only compound M4BEB developed an N* phase with selectively reflection on heating and a blue phase on cooling process. In addition, increasing the length of the flexible spacers tends to narrow the temperature range of the N* phase and widen the smectic phase, moreover, the pitch becomes longer with the spacer increases.     

Strategic measures in optimal control problems for stochastic sequences

Controlled discrete–time stochastic processes axe studied using the convex–analytic approach. Some new properties of strategic measures spaces are established, particular Markov models are considered. The meaningful example is presented.     

Nuclear Structure and Electromagnetic Transitions Investigation in Er Isotopes within Framework of Interacting Boson Model

Interacting Boson Model-2(IBM-2)is used to determine the Hamiltonian for Er nuclei.Fit values of parameters are used to construct the Hamiltonian,energy levels and electromagnetic transitions(B(E2),B(M1))multipole mixing ratios(δ(E2/M1))for some even-even Er nuclei and monopole transition probability are estimated.New ideas are used for counting bosons number at N=64 and results are compared with previous works.     

The polynomial reconstruction problem: The first 50 years

The problem of reconstructing the characteristic polynomial of a graph of order at least 3 from the collection of characteristic polynomials of its vertex-deleted subgraphs was posed by Cvetkovi? in 1973 as a spectral counter part to the well-known Ulam's reconstruction conjecture. Over the last 50 years, this problem has received notable attention, many positive results have been obtained, but in the general case the problem is still unresolved. In particular, no counter example is found in literature. In this expository paper we survey classical and some more recent results concerning the polynomial reconstruction problem, discuss some related problems, variations and generalizations.     

Synergistic Effect of Boron Nitride and Carbon Domains in Boron Carbide Nitride Nanotube Supported Single-Atom Catalysts for Efficient Nitrogen Fixation

Developing the low-cost and efficient single-atom catalysts (SACs) for nitrogen reduction reaction (NRR) is of great importance while remains as a great challenge. The catalytic activity, selectivity and durability are all fundamentally related to the elaborate coordination environment of SACs. Using first-principles calculations, we investigated the SACs with single transition metal (TM) atom supported on defective boron carbide nitride nanotubes (BCNTs) as NRR electrocatalysts. Our results suggest that boron-vacancy defects on BCNTs can strongly immobilize TM atoms with large enough binding energy and high thermal/structural stability. Importantly, the synergistic effect of boron nitride (BN) and carbon domains comes up with the modifications of the charge polarization of single-TM-atom active site and the electronic properties of material, which has been proven to be the essential key to promote N₂ adsorption, activation, and reduction. Specifically, six SACs (namely V, Mn, Fe, Mo, Ru, and W atoms embedded into defective BCNTs) can be used as promising candidates for NRR electrocatalysts as their NRR activity is higher than the state-of-the art Ru(0001) catalyst. In particular, single Mo atom supported on defective BCNTs with large tube diameter possesses the highest NRR activity while suppressing the competitive hydrogen evolution reaction, with a low limiting potential of −0.62 V via associative distal path. This work suggests new opportunities for driving NH₃ production by carbon-based single-atom electrocatalysts under ambient conditions.     

再谈Minc-Sathre不等式的上下界

用调和平均值、均值不等式之间的关系及对数平均不等式,对Minc-Sathre不等式的上下界进行改进,使结论更精确.     

Synthesis and Characterization of Hydrophilic Trityl Radical TFO for Biomedical and Biophysical Applications

Tetrathiatriarylmethyl (TAM, trityl) radicals have found wide applications as spin probes/labels for EPR spectroscopy and imaging, and as polarizing agents for dynamic nuclear polarization. The high hydrophilicity of TAM radicals is essential for their biomedical applications. However, the synthesis of hydrophilic TAM radicals (e.g., OX063) is extremely challenging and has only been reported in the patent literature, to date. Herein, an efficient synthesis of a highly water-soluble TAM radical bis(8-carboxyl-2,2,6,6-tetramethylbenzo[1,2-d:4,5-d′]bis([1,3]dithiol-4-yl)-mono-(8-carboxyl-2,2,6,6-tetrakis(2-hydroxyethyl)benzo[1,2-d:4,5-d′]bis([1,3]dithiol-4-yl)methyl (TFO), which contains four additional hydroxylethyl groups, relative to the Finland trityl radical CT-03, is reported. Similar to OX063, TFO exhibits excellent properties, including high water solubility in phosphate buffer, low log P, low pK_a, long relaxation times, and negligible binding with bovine serum albumin. On the other hand, TFO has a sharper EPR line and higher O₂ sensitivity than those of OX063. Therefore, in combination with its facile synthesis, TFO should find wide applications in magnetic resonance related fields and this synthetic approach would shed new light on the synthesis of other hydrophilic TAM radicals.     

Classroom note: Using the binomial series to prove the arithmetic mean–geometric mean inequality

In 1968, Leon Gerber compared (1 + x) ^a to its kth partial sum as a binomial series. His result is stated and, as an application of this result, a proof of the arithmetic mean–geometric mean inequality is presented.     

Salt effect on molecular orientation at air/liquid methanol interface

The salt effects on molecular orientation at air/liquid methanol interface were investigated by the polarization-dependent sum frequency generation vibrational spectroscopy(SFG-VS). We clarified that the average tilting angle of the methyl group to be u = 308 58 at the air/pure methanol surface assuming a d-function orientational distribution. Upon the addition of 3 mol/L Na I, the methyl group tilts further away from the surface normal with a new u = 418 38. This orientational change does not explain the enhancement of the SFG-VS intensities when adding Na I, implying the number density of the methanol molecules with a net polar ordering in the surface region also changed with the Na I concentrations. These spectroscopic findings shed new light on the salt effects on the surfaces structures of the polar organic solutions. It was also shown that the accurate determination of the bulk refractive indices and Raman depolarization ratios for different salt concentrations is crucial to quantitatively interpret the SFG-VS data.