Synthesis and orientation study of a magnetically aligned liquid‐crystalline chitin/poly(acrylic acid) composite

A high magnetic field of 5 T was used to fabricate a magnetically aligned, optically anisotropic, liquid‐crystalline chitin/poly(acrylic acid) composite. The aligned mesophase was fixed by photoinitiated free‐radical polymerization. From an examination of polarized optical micrographs and an X‐ray diffraction study, a high degree of orientation of 0.70 was observed for the composite with a higher liquid‐crystalline chitin concentration (10.70 wt %); the orientation was reduced with a decreased chitin concentration at a given acrylic acid concentration. The X‐ray data for the developed composite showed a uniplanar orientation for the chitin crystallites, with its molecular long axes perpendicular to the direction of the magnetic field. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 711–714, 2003     

Force field and 13C-NMR investigations of substituted cyclopentanes. A concept for the adaption of 13C NMR shifts to varying torsional arrangements in flexible conformers

MM2 Exploration of the conformational space for methylcyclopentane, in contrast to cyclopentanone yields more and flatter minima than known previously. Calculations of cyclopentanes with substituents X = F, Cl, CHMe₂, and CMe₃ with two stable conformations indicate <2° torsional angle changes with the different substituents. Cyclopentanes bearing not more than 2 substituents can accommodate all groups in pseudoequatorial positions without changing the basic envelope and twist chair geometries significantly. A model for ¹³C-shift calculation is proposed in which shift increments for the different torsional arrangements are obtained by linear interpolation between corresponding cyclohexane values. After correction for the nonequivalent carbon shifts in the hydrocarbon itself, again using the linear interpolation, a significant improvement of the shift correlations is observed. For disubstituted cyclopentanes these predict the shifts within ± 1.7 ppm with Me, CHMe₂, CMe₃, Cl, Br and OH as substituents. Configurational assignments are difficult with 1,3-di-substituted cyclopentanes, but straightforward with 1,2-di- and trisubstituted compounds. Thus, due to the presence of smaller torsional angles between, e.g. diequatorial vicinal substituents in the 1,2- cis series as compared to the trans compounds, the latter show deshielding, particularly at C2, by 1–4 ppm. Several epimers are stereo-selectively prepared by suitable ketone reduction and displacement methods.     

Hermite–Birkhoff–Obrechkoff four-stage four-step ODE solver of order 14 with quantized step size

A four-stage Hermite–Birkhoff–Obrechkoff method of order 14 with four quantized variable steps, denoted by HBOQ(14)4, is constructed for solving non-stiff systems of first-order differential equations of the form y^′=f(t,y)$y^{\prime }=f(t,y)$ with initial conditions y(_t0)=_y0$y\left(t_0\right)=y_0$. Its formula uses y^′$y^{\prime }$, y^″$y^{″}$ and y^?$y^{?}$ as in Obrechkoff methods. Forcing a Taylor expansion of the numerical solution to agree with an expansion of the true solution leads to multistep- and Runge–Kutta-type order conditions which are reorganized into linear Vandermonde-type systems. To reduce overhead, simple formulae are derived only once to obtain the values of Hermite–Birkhoff interpolation polynomials in terms of Lagrange basis functions for 16 quantized step size ratios. The step size is controlled by a local error estimator. When programmed in C ++, HBOQ(14)4 is superior to the Dormand–Prince Runge–Kutta pair DP(8,7)13M of order 8 in solving several problems often used to test higher order ODE solvers at stringent tolerances. When programmed in Matlab, it is superior to ode113 in solving costly problems, on the basis of the number of steps, CPU time, and maximum global error. The code is available on the URL www.site.uottawa.ca/~remi.     

Preparation of nanoscale cellulose materials with different morphologies by mechanical treatments and their characterization

Rod-like cellulose nanowhiskers and spherical cellulose nanoparticles were prepared from wood-pulp-derived cellulose powder by mechanical refining processes such as high-pressure homogenization (HPH) and ball-milling (BM). The nanowhiskers obtained by the HPH method were found to be 200–500 nm long and 11–16 nm wide. The diameters of the nanoparticles were in the range 40–200 nm, depending on the BM time, and were reduced to 25–50 nm after extra HPH. By adjusting the BM time, cellulose nanoparticles having different polymorphs with similar morphologies were prepared. The X-ray diffraction patterns revealed the recrystallization of cellulose I (1 h of BM time) or cellulose II (4–8 h of BM time) in ball-milled nanoparticles after water washing and solvent exchange treatments. The nanowhisker widths derived from the specific surface areas (SSA) by adsorption methods such as Congo red dye, nitrogen, and water vapor, sorptions were in agreement with those obtained from transmission electron microscopy and atomic force microscopy images. Similar SSA values were obtained for micro- and nano-scale cellulose materials using water vapor adsorption methods, and the SSAs of nanoparticles obtained by different adsorption methods are also discussed.     

Ion-permeable membrane for on-chip preconcentration and separation of cancer marker proteins

Cancer marker proteins have been electrophoretically concentrated and then separated in a microfluidic device. On-chip preconcentration was achieved using an ion-permeable membrane, consisting of acrylamide, N,N'-methylene-bisacrylamide and 2-(acrylamido)-2-methylpropanesulfonate. This negatively charged membrane was photopolymerized in the microdevice near the injection intersection. Anionic proteins were excluded from the porous membrane based on both size and charge, which concentrated target components in the injection intersection prior to separation by microchip capillary electrophoresis (μ-CE). Bovine serum albumin was used in the initial characterization of the system and showed a 40-fold enrichment in the μ-CE peak with 4 min of preconcentration. Adjustment of buffer pH enabled baseline resolution of two cancer biomarkers, α-fetoprotein (AFP) and heat shock protein 90 (HSP90), while fine control over preconcentration time limited peak broadening. Our optimized preconcentration and μ-CE approach was applied to AFP and HSP90, where enrichment factors of >10-fold were achieved with just 1 min of preconcentration. Overall, the process was simple and rapid, providing a useful tool for improving detection in microscale systems.     

Variable-step variable-order 3-stage Hermite-Birkhoff-Obrechkoff DDE solver of order 4 to 14

This article presents a solver for delay differential equations (DDEs) called HBO414DDE based on a hybrid variable-step variable-order 3-stage Hermite-Birkhoff-Obrechkoff ODE solver of order 4 to 14. The current version of our method solves DDEs with state dependent, non-vanishing, small, vanishing and asymptotically vanishing delays, except neutral type and initial value DDEs. Delayed values are computed using Hermite interpolation, small delays are dealt with by extrapolation, and discontinuities are located by a bisection method. HBO414DDE was tested on several problems and results were compared with those of known solvers like SYSDEL and the recent Matlab DDE solver ddesd and statistics show that it gives, most of the time, a smaller relative error than the other solvers for the same number of function evaluations.     

Strong-stability-preserving 3-stage Hermite-Birkhoff time-discretization methods

Strong-stability-preserving (SSP) time-discretization methods have a nonlinear stability property that makes them particularly suitable for the integration of hyperbolic conservation laws. A collection of SSP explicit 3-stage Hermite-Birkhoff methods of orders 3 to 7 with nonnegative coefficients are constructed as k-step analogues of third-order Runge-Kutta methods, incorporating a function evaluation at two off-step points. Generally, these new methods have larger effective CFL coefficients than the hybrid methods of Huang with the same step number k. They have larger maximum scaled step sizes than hybrid methods on Burgers' equations.     

Determination of Low Cyanide Levels Using a Deposited-on-Wire Silver/Silver Selenide Electrode

Because of extreme toxicity, cyanide is important in water quality control,and cyanide-selective electrode method is one of the best methods for fast determination of cyanide content. In this paper, a silver/silver selenide electrode is prepared quickly by holding a silver wire in vapours of molten selenide. The electrodes were tested in following steps.     

One-step 5-stage Hermite-Birkhoff-Taylor ODE solver of order 12

A one-step 5-stage Hermite-Birkhoff-Taylor method, HBT(12)5, of order 12 is constructed for solving nonstiff systems of differential equations y^′=f(t,y), y(t₀)=y₀, where y∈Rⁿ. The method uses derivatives y^′ to y⁽⁹⁾ as in Taylor methods combined with a 5-stage Runge-Kutta method. Forcing an expansion of the numerical solution to agree with a Taylor expansion of the true solution to order 12 leads to Taylor- and Runge-Kutta-type order conditions which are reorganized into Vandermonde-type linear systems whose solutions are the coefficients of the method. HBT(12)5 has a larger interval of absolute stability than Dormand-Prince DP(8, 7)13M and Taylor method T12 of order 12. The new method has also a smaller norm of principal error term than T12. It is superior to DP(8, 7)13M and T12 on the basis the number of steps, CPU time and maximum global error on common test problems. The formulae of HBT(12)5 are listed in an appendix.