Purification of high-throughput organic synthesis libraries by counter-current chromatography

Experiments were performed to evaluate whether counter-current chromatography (CCC) could function as an alternative purification method to reversed-phase high-performance liquid chromatography (RP-HPLC) and normal-phase supercritical fluid chromatography (SFC). RP-HPLC and SFC are the routine methods currently used in our high-throughput purification (HTP) facility for the purification of high-throughput organic synthesis (HTOS) libraries and medicinal chemistry reaction mixtures. Pre-equilibration of the solvent mixture layers was not mandatory for effective chromatography when hexanes–ethyl acetate–methanol–water (HEMW) solvent mixtures were used. Key to the use of CCC for high-throughput applications is the ability to effectively select a solvent system appropriate to each library member. Pilot-scale CCC elution time was used to estimate a starting solvent ratio and RP-HPLC retention time was then used to adjust solvent ratios within a particular library. It was also found that dimethyl sulfoxide (DMSO) and DMSO–methanol were suitable as sample injection solvents when using the HEMW solvent systems.     

Discretization limits of lattice-Boltzmann methods for studying immiscible two-phase flow in porous media

Digital images of porous media often include features approaching the image resolution length scale. The behavior of numerical methods at low resolution is therefore important even for well-resolved systems. We study the behavior of the Shan-Chen (SC) and Rothman-Keller (RK) multicomponent lattice-Boltzmann models in situations where the fluid-fluid interfacial radius of curvature and/or the feature size of the medium approaches the discrete unit size of the computational grid. Various simple, small-scale test geometries are considered, and a drainage test is also performed in a Bentheimer sandstone sample. We find that both RK and SC models show very high ultimate limits: in ideal conditions the models can simulate static fluid configuration with acceptable accuracy in tubes as small as three lattice units across for RK model (six lattice units for SC model) and with an interfacial radius of curvature of two lattice units for RK and SC models. However, the stability of the models is affected when operating in these extreme discrete limits: in certain circumstances the models exhibit behaviors ranging from loss of accuracy to numerical instability. We discuss the circumstances where these behaviors occur and the ramifications for larger-scale fluid displacement simulations in porous media, along with strategies to mitigate the most severe effects. Overall we find that the RK model, with modern enhancements, exhibits fewer instabilities and is more suitable for systems of low fluid-fluid miscibility. The shortcomings of the SC model seem to arise predominantly from the high, strongly pressure-dependent miscibility of the two fluid components.     

A flow injection analysis system for monitoring silver (I) ion and iodine residuals in recycled water from recovery systems used for spaceflight

A laboratory-built flow injection analyzer is reported for monitoring the drinking water disinfectants silver (I) ion and iodine in water produced from NASA's water recovery system. This analyzer uses spectrophotometric detection with a custom made 10 cm optical flow cell. Optimization and interference studies are discussed for the silver (I) ion configuration. Subsequent results using the silver (I) configuration with minor modifications and alternative reagents gave promising results for iodine determinations as well. The estimated MDL values for Ag⁺ and I₂ are 52 μg L⁻¹ Ag⁺ and 2 μg L⁻¹ I₂; the mean percent recoveries were 104% and 96.2% for Ag⁺ and I₂ respectfully; and percent relative standard deviations were estimated at 1.4% for Ag⁺ and 5.7% for I₂. The agreement of this potentially multifunctional analyzer to reference methods for each respective water disinfectant is measured using Bland–Altman analysis as well as more traditional estimates.     

Regioselective C−H Xanthylation as a Platform for Polyolefin Functionalization

Polyolefins that contain polar functional groups are important materials for next‐generation lightweight engineering thermoplastics. Post‐polymerization modification is an ideal method for the incorporation of polar groups into branched polyolefins; however, it typically results in chain scission events, which have deleterious effects on polymer properties. Herein, we report a metal‐free method for radical‐mediated C?H xanthylation that results in the regioselective functionalization of branched polyolefins without coincident polymer‐chain scission. This method enables a tunable degree of polymer functionalization and capitalizes on the versatility of the xanthate functional group to unlock a wide variety of C?H transformations previously inaccessible on branched polyolefins.     

Construction of meaning: urban elementary students’ interpretation of geometric puzzles

Mathematical puzzles have long been employed by parents and teachers to augment the standard mathematics curriculum. This paper reports on a study of urban elementary students engaged in the solution of mathematical puzzles. The work confirms that, given the opportunity, these students will construct their own, logically consistent, interpretations of the puzzle clues. In particular, these students used self-generated rules about alignment and orientation to construct meaning in ambiguous clues. Such exercises in logic bring to light the value of student approaches to problem solving, and the possibility of using these approaches as building blocks from which students might construct knowledge in the standard curriculum.     

Recent trends in carbon nanomaterial-based electrochemical sensors for biomolecules: A review

Carbon nanomaterials are advantageous for electrochemical sensors because they increase the electroactive surface area, enhance electron transfer, and promote adsorption of molecules. Carbon nanotubes (CNTs) have been incorporated into electrochemical sensors for biomolecules and strategies have included the traditional dip coating and drop casting methods, direct growth of CNTs on electrodes and the use of CNT fibers and yarns made exclusively of CNTs. Recent research has also focused on utilizing many new types of carbon nanomaterials beyond CNTs. Forms of graphene are now increasingly popular for sensors including reduced graphene oxide, carbon nanohorns, graphene nanofoams, graphene nanorods, and graphene nanoflowers. In this review, we compare different carbon nanomaterial strategies for creating electrochemical sensors for biomolecules. Analytes covered include neurotransmitters and neurochemicals, such as dopamine, ascorbic acid, and serotonin; hydrogen peroxide; proteins, such as biomarkers; and DNA. The review also addresses enzyme-based electrodes that are used to detect non-electroactive species such as glucose, alcohols, and proteins. Finally, we analyze some of the future directions for the field, pointing out gaps in fundamental understanding of electron transfer to carbon nanomaterials and the need for more practical implementation of sensors.     

Developing the roots of modelling conceptions: ‘mathematical modelling is the life of the world’

A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a Modelling conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity, actions and conceptions of both modelling and mathematics that these beginners to modelling displayed. Understanding the conceptions of mathematics that students might hold or be developing and how these can be influenced in early schooling are essential ingredients in any plans for introducing modelling seriously into primary school classrooms. The majority of the students (22/25) were identified as displaying a developing conception of modelling as a way of problem handling. The three other students displayed the developmental roots of a way of understanding the world conception of modelling. These three students also displayed a Modelling conception of mathematics with one showing indications of developing towards a Life conception of mathematics.     

On k‐ordered graphs

Ng and Schultz [J Graph Theory 1 ( 6 ), 45–57] introduced the idea of cycle orderability. For a positive integer k, a graph G is k‐ordered if for every ordered sequence of k vertices, there is a cycle that encounters the vertices of the sequence in the given order. If the cycle is also a Hamiltonian cycle, then G is said to be k‐ordered Hamiltonian. We give sum of degree conditions for nonadjacent vertices and neighborhood union conditions that imply a graph is k‐ordered Hamiltonian. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 69–82, 2000