Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.     

Strategies for the development of a voltammetric sensor for the determination of hydrogen peroxide at high concentrations

Different strategies are presented for the development of a voltammetric sensor for in-line measurement and monitoring of H₂O₂ in high concentrations (up to 30 g/l) as used in textile bleaching systems. When using macroelectrodes, signal saturation is observed even at medium concentrations. Some improvement can be achieved by hydrodynamic electrodes like ring-disk electrodes. Satisfactory results up to the desired level in practical solutions (possessing only limited conductivity) are obtained with Pt-microelectrodes.     

Analysis of Paeoniae Radix by high-performance liquid chromatography-electrospray ionization-mass spectrometry.

A method has been developed for the qualitative analysis of paeonol, paeoniflorin and their derivatives in Paeoniae Radix by high-performance liquid chromatography-electrospray ionization-mass spectrometry (HPLC-ESI-MS). Gradient elution with acetonitrile-water solvent system was employed in an HPLC-ESI-MS study. The negative-ion ESI mode was suitable for these compounds. The peaks were identified by their mass spectra, UV spectra and fragments of their MS2 spectra. The structures of three unknown compounds are inferred in this paper.     

Competitive influence of atactic polystyrene and supercritical carbon dioxide on the conformation of syndiotactic polystyrene

The crystallization behavior of miscible syndiotactic polystyrene (sPS) and atactic polystyrene (aPS) blends with different sPS/aPS weight ratios was investigated in supercritical CO₂ by using Fourier‐transform infrared spectroscopy, differential scanning calorimetry, and wide‐angle X‐ray diffraction. Supercritical CO₂ and aPS exhibited different effects on the conformational change of sPS and competed with each other. Increasing the content of amorphous aPS in the blends made its effect on the conformational change of sPS gradually surpass that of supercritical CO₂. Supercritical CO₂ favored the formation of the helical conformation of sPS in lower temperature range and the all trans planar conformation in higher temperature range, instead of forming the latter one only in higher temperature range in ambient atmosphere. However, increasing aPS content in the blends pushed the range for forming the helical conformation to lower temperature and made the all trans planar conformation dominant in aPS/sPS 25/75 blend after treating in supercritical CO₂ above 60 °C. The all trans planar zigzag conformation was more favorable than the helical conformation after mixing aPS in sPS in supercritical CO₂. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1755–1764, 2007     

Synthesis and characterization of liquid crystalline side‐chain block copolymers containing luminescent 4,4′‐bis(biphenyl)fluorene pendants

A series of new liquid crystalline homopolymers, copolymers, and block copolymers were polymerized from styrene‐macroinitiator ( SMi ) and methacrylates with pendent 4,4′‐bis(biphenyl)fluorene ( M1 ) and biphenyl‐4‐ylfluorene ( M2 ) groups through atom transfer radical polymerization (ATRP). The number‐average molecular weights (Mn) of polymers P1 ‐ P4 were 10,007, 14,852, 6,275, and 10,463 g mol^?1 with polydispersity indices values of 1.21, 1.15, 1.31, and 1.22, respectively. All polymers exhibit the nematic phase. The thermal, mesogenic, and photoluminescent properties of all polymers were investigated. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4564–4572, 2007     

Interfacial dynamics‐based modelling of turbulent cavitating flows,Part‐2: Time‐dependent computations

The interfacial dynamics‐based cavitation model, developed in Part‐1, is further employed for unsteady flow computations. The pressure‐based operator‐splitting algorithm (PISO) is extended to handle the time‐dependent cavitating flows with particular focus on the coupling of the cavitation and turbulence models, and the large density ratio associated with cavitation. Furthermore, the compressibility effect is important for unsteady cavitating flows because in a water–vapour mixture, depending on the composition, the speed of sound inside the cavity can vary by an order of magnitude. The implications of the issue of the speed of the sound are assessed with alternative modelling approaches. Depending on the geometric confinement of the nozzle, compressibility model and cavitation numbers, either auto‐oscillation or quasi‐steady behaviour is observed. The adverse pressure gradient in the closure region is stronger at the maximum cavity size. One can also observe that the mass transfer process contributes to the cavitation dynamics. Compared to the steady flow computations, the velocity and vapour volume fraction distributions within the cavity are noticeably improved with time‐dependent computations. Copyright © 2004 John Wiley & Sons, Ltd.     

Crystallographic report: Crystal structure of tetra(4‐methyl‐5‐imidazole‐carboxyaldehyde)zinc(II) diperchlorate

The central zinc(II) atom in the title complex is tetrahedrally coordinated by four nitrogen atoms derived from 4‐methyl‐5‐imidazolecarboxyaldehyde ligands with Zn? N in the range 2.007(3) to 2.026(4) Å. Copyright © 2003 John Wiley & Sons, Ltd.     

Crystallographic report: Crystal structure of a one‐dimensional zinc(II) coordination polymer containing 4,4′‐biphenyldicarboxylate hemihydrate

A one‐dimensional zinc(II) coordination polymer has been constructed from zinc(II), 4,4′‐biphenyldicarboxylate and pyridine in which each zinc(II) atom is coordinated by two pyridine ligands and two monodentate 4,4′‐biphenyldicarboxylate ligands that define a distorted tetrahedral geometry. Copyright © 2003 John Wiley & Sons, Ltd.     

Simultaneous determination of trace cadmium and mercury in Chinese herbal medicine by non-dispersive atomic fluorescence spectrometry using intermittent flow vapor generator.

A method was proposed for the simultaneous determination of trace cadmium and mercury by vapor generation non-dispersive atomic fluorescence spectrometry using an intermittent flow system. The effects of the parameters on the performance were studied systematically. The parameters such as acid concentration of the reaction medium, flow rate of the carrier gas and shield gas, the observation height and the atomizer temperature, etc. which affected the sensitivity, were optimized. Ascorbic acid, cobalt ion and thiourea were used as enhancement reagents or masking agents to enhance the generation efficiency of the volatile species of Cd and Hg. The mechanisms of their effects on vapor generation were investigated. In the presence of thiourea and ascorbic acid, the influences of some coexisting elements on the determination of cadmium and mercury were investigated. The detection limits (3sigma) were 0.010 microg l(-1) for Cd and 0.019 microg l(-1) for Hg, respectively. The relative standard deviations for Cd and Hg at 1.00 microg l(-1) were 2.6% and 0.97% (n = 11), respectively. The proposed method has been satisfactorily applied to the determination of trace cadmium and mercury in Chinese herbal medicine.     

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems

Finite element analysis of fluid flow with moving free surface has been performed in 2‐D and 3‐D. The new VOF‐based numerical algorithm that has been proposed by the present authors (Int. J. Numer. Meth. Fluids, submitted) was applied to several 2‐D and 3‐D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby‐cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2‐D and 3‐D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non‐uniform grid systems and can be extended to 3‐D free surface flow problems without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd.