Dependence of the methylene selectivity on the composition of hydro-organic eluents for reversed-phase liquid chromatographic systems with alkyl bonded phases

Summary A theoretical treatment is presented which considers differences between the composition of the mobile phase and solvents that are incorporated into the bonded phase via preferential sorption. Equations are derived and used to analyze retention data for various homologs chromatographed under reversed-phase conditions using alkyl bonded phases and combinations of water-methanol, water-acetonitrile and watertetrahydrofuran as mobile phases. In the case of water-methanol the surface phase and bulk mobile phase compositions are similar. However, significant differences in composition between the two phases are observed when binary combinations of water-acetonitrile and water-tetrahydrofuran are used as the cluents.     

一个简单的能呈现二分岔现象的双分子反应模型

二分岔现象(pitchfork bifurcation)是非平衡非线性动力系统中最典型和最简单的分岔现象.1972年Schlogl提出了如下一个化学反应模型: A+2x?3X,X?B (1)假定组份A和B的浓度可由外界控制为恒定,在某些条件下该模型可呈现出二分岔现象.自那以后,Schlogl模型已成为人们研究非平衡相变时最广泛采用的理论模型,该模型对推动非平衡非线性现象的研究起了十分重要的作用.但从物理-化学的角度来看,该模型存在着如下一些问题:首先该模型涉及一个三分子自催化反应步骤,这种反应步骤在现实反应系统     

Preparation of pyrenebutyric acid-modified magnesia-zirconia stationary phases using phosphonate as spacers and their application to the separation of fullerenes

A novel method was proposed for the preparation of pyrenebutyric acid-modified magnesia-zirconia stationary phases. Pyrenebutyric acid was grafted to magnesia-zirconia composites with different pore sizes via the sodium salt of cis-(3-methyloxiranyl)phosphonic acid (fosfomycin) as spacers. Aminated fosfomycin was first absorbed onto the surface of magnesia-zirconia composites during the preliminary step to provide amino and hydroxy reactive sites. And then the pyrenebutyric acid was covalently attached to the amine or hydroxyl groups via amide or ester bonds. The resulting stationary phases were characterized by elemental analysis, diffused reflectance FT-IR, nitrogen adsorption analysis and ¹³C solid state NMR spectra. The HPLC separation of fullerenes on the new stationary phases with different pore sizes was also investigated. The chromatographic performance showed a dependence on the pore size of the magnesia-zirconia matrix. Little retention of fullerenes was observed on the stationary phase with pore sizes about 4.5 nm. However, on the modified magnesia-zirconia with pore sizes about 10 nm, selectivity factors (α) for C₇₀/C₆₀ separation were determined to be 1.76, 2.29, 2.41, 3.10, with carbon disulfide, chlorobenzene, xylene and toluene as mobile phases, respectively. And the high solubility of fullerenes in these solvents dramatically increased the overall potential with regard to preparative fullerene purification. Among the reported stationary phases with pyrene ligands, the pyrenebutyric acid-modified magnesia-zirconia (PYB-F-(ZrO₂-MgO)) with larger pore sizes exhibited the best selectivity for fullerenes. The thermodynamic and kinetic behavior of fullerenes was also examined.     

Selectivity optimization for the capillary gas chromatographic analysis of bacterial cellular fatty acids

Summary The importance of selectivity in the capillary gas chromatographic analysis of the cellular fatty acids of micro-organisms is underestimated. The analysis on apolar silicone phases can lead to erratic elucidation of the fatty acid structure. Qualitative errors have been detected in commercially available standards on which computer matching identification techniques are based. Using highly polar capillary columns of the cyanopropyl silicone type, the errors could be elucidated. The exact identification of the hydrolysis products of bacteria is a must for chemotaxonomic studies applying chromatographic techniques. The fatty acid methyl ester profiles can also contain other chemical components which are very important taxonomic markers. Fatty aldehydes, for example, are main components in someClostridium species. Fractionation techniques are described for selective enrichment of fatty aldehydes and hydroxy fatty acids.Dedicated to Prof. Dr. A Liberti on the occasion of his 70th birthday     

Selectivity of long chain stationary phases in reversed phase liquid chromatography

A series of commercial monomeric and polymeric C(18), C(27), and C(30) stationary phases were compared with immobilized poly(ethylene-co-acrylic acid) stationary phases synthesized in-house. The columns were characterized on the basis of methylene selectivity, silanol activity, metal activity, pore size, shape selectivity, and the ability to separate tocopherol isomers and carotenoid isomers. Monomeric and polymeric C(30) phases were shown to yield excellent separations of the tocopherol isomers while the polymeric C(30) and polyethylene phases were more appropriate to the separation of carotenoids.     

Superoxes,high temperature universal phases in (GC)2

Most of the common classes of organic compounds chromatograph normally on Superoxes. There is no tailing or adverse effect from excessively different activity different activity coefficients. Superoxes are therefore universal phases for gas chromatography. This is also expressed by a wide useful temperature range from ～50° to ～300°. High MW Superox-4 has a MAOT about 20° higher than the lower MW Superox-0.1. Several applications illustrating the versatility of Superox phases in (GC)² are presented.     

Data loci in algebraic optimization

We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.     

曲率流的参数化有限元逼近

许多物理现象可以在数学上描述为受曲率驱动的自由界面运动,例如薄膜和泡沫的演变、晶体生长,等等.这些薄膜和界面的运动常依赖于其表面曲率,从而可以用相应的曲率流来描述,其相关自由界面问题的数值计算和误差分析一直是计算数学领域中的难点.参数化有限元法是曲率流的一类有效计算方法,已经能够成功模拟一些曲面在几类基本的曲率流下的演化过程.本文重点讨论曲率流的参数化有限元逼近,它的产生、发展和当前的一些挑战.     

The density and minimal gap of visible points in some planar quasicrystals

It has previously been observed that the limiting gap distribution of the directions to visible points of planar quasicrystals may vanish near zero, that is, there exist planar quasicrystals with a positive limiting minimal normalised gap between the angles of visible points. The exact values of these limiting minimal normalised gaps have not been determined. In this paper we give explicit formulas for the densities of visible points for planar quasicrystals from several families, which include the Ammann–Beenker point set and the vertex sets of some rhombic Penrose tilings. Combining these results with a known characterisation of the limiting minimal gap in terms of a probability measure on an associated homogeneous space of quasicrystals, we give explicit values of the limiting minimal normalised gap between the angles of visible points for several families of planar quasicrystals, in particular, for the Ammann–Beenker point set and for the vertex sets of some rhombic Penrose tilings. We also compare our results with numerical observations.