Upcycling of Polybutadiene Facilitated by Selenium-Mediated Allylic Amination

Accumulation of end-of-life plastics presents ongoing environmental concerns. One strategy to solve this grand challenge is to invent new techniques that modify post-consumer waste and impart new functionality. While promising approaches for the chemical upcycling of commodity polyolefins and polyaromatics exist, analogous approaches to repurpose unsaturated polymers (e.g., polybutadiene) are scarce. In this work, we propose a method to upcycle polybutadiene, one of the most widely used commercial rubbers, via a mild, metal-free allylic amination reaction. The resulting materials have tunable thermal and surface wetting properties as a function of both sulfonamide identity and grafting density. Importantly, this approach maintains the parent alkene microstructure without evidence of olefin reduction, olefin transposition, and/or chain scission. Based on these findings, we anticipate future applications in the remediation of complex elastomers and vulcanized rubbers.     

A Comparison of Textbooks' Presentation of Fractions

In the United States, fractions are an important part of the middle school curriculum, yet many middle school students struggle with fraction concepts. Teachers also have difficulty with the conceptual understanding needed to teach fractions and rely on textbooks when making instructional decisions. This reliance on textbooks, the idea that teaching and learning of fractions is a complex process, and that fraction understanding is the foundation for later topics such as proportionality, algebra, and probability, makes it important to examine the variation in presentation of fraction concepts in U.S. textbooks, especially the difference between traditional and standards‐based curricula. The purpose of this study is to determine if differences exist in the presentation of fractions in conventional and standards‐based textbooks and how these differences align with the recommendations of National Council of Teachers of Mathematics, Common Core State Standards, and the research on the teaching and learning of fractions.     

On the extensional vibrations of rotating bars

The extensional equations of motion for a cantilever bar rotating about an axis fixed in space are derived. It is shown that the form of the non-linear strain-displacement relation is important in determining the nature of the relationship between the frequency of extensional oscillations and the rotational speed. In particular, the frequency may or may not increase monotonically with rotational speed, depending on the degree of hardening in the effective extensional spring. The determination whether an instability occurs as the rotational speed increases is beyond the limits of engineering beam theory.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Axial instability of rotating rods revisited

For strain sufficiently small such that Hooke's Law is valid, it is shown that only a linear model for axial deformation of rotating rods can be derived. As discussed in the literature, this linear model exhibits an instability when the angular speed reaches a certain critical value. However, unless this linear model is valid for large strain, it is impossible to determine whether this instability really exists; because, as the angular speed is increased, the strain becomes large well short of the critical speed. Next, axial deformation of rotating rods is analyzed using two strain energy functions to model non-linear elastic behavior. The first of these functions is the usual quadratic strain energy function augmented with a cubic term. With this model it is shown that no instability exists if the non-linearity is stiffening (i.e. if the coefficient of the cubic term is positive), although the strain can become large. If the non-linearity is of the softening variety, then the critical angular speed drops as the degree of softening increases. Still, the strains are large enough that, except for rubber-like materials, a non-linear elastic model is not likely to be appropriate. The second strain energy function is based on the square of the logarithmic strain and yields a softening model. It quite accurately models the behavior of certain rubber rods which exhibit the instability within the validated range of elongation.     

A Study of Highly Qualified Science Teachers' Career Trajectory in the Deep,Rural South: Examining a Link Between Deprofessionalization and Teacher Dissatisfaction

Science teacher retention, attrition, and migration continue to perplex educational scholars, political entities, as well as the general public. This study utilized an interpretive methodological design to generate assertions regarding career choice made by highly qualified science teachers in the deep, rural South through analysis of documents, interviews, focus groups, and observation. Generally considered “difficult to staff” because of location, socioeconomics, and demographics, Wilson County High School is an exemplar in science teacher retention and student achievement. Findings presented include how the science department at Wilson County improved student learning outcomes as well as the reasons why two of the highly qualified science teachers at this school were considering leaving the profession they love.     

Structure‐guided RP‐HPLC chromatography of diastereomeric α‐helical peptide analogs substituted with single amino acid stereoisomers

An α‐helical model peptide (Ac‐EAEKAAKE‐X‐EKAAKEAEK‐amide) was used as a template to examine the efficacy of conventional reversed‐phase high‐performance liquid chromatography (RP‐HPLC) in separating peptide analogs with single substitutions (at position X) of diasteromeric amino acids Ile, allo‐Ile, d ‐Ile and d ‐allo‐Ile. We compared differences in peptide retention behavior on a C₈ column and a C₁₈ column at different temperatures. We demonstrated how subtle differences in peptide secondary structure affected by the different substitutions of amino acids with identical overall hydrophobicity enabled effective resolution of these peptide analogs. We also demonstrated the ability of RP‐HPLC to separate Ile‐ and allo‐Ile‐substituted analogs of a 26‐residue α‐helical antimicrobial peptide (AMP), with the substitution site towards the C‐terminus of the α‐helix. These peptides show different values of antibacterial activity and hemolytic activity, and different selectivity against bacteria and human cells. Our results underline the ability of RP‐HPLC to resolve even difficult diasteromeric peptide mixtures as well as its value in monitoring very subtle hydrophobicity changes in de novo‐designed AMP. Copyright © 2013 John Wiley & Sons, Ltd.     

Stereospecific Synthesis of S,S-Statine and its Congeners

Statine (STA, 8) and its cyclohexyl analog (ACHPA, 9) are obtained by a stereospecific synthesis via tetramic acid chemistry. Amides of STA and ACHPA, useful for the synthesis of antihyperten-sive renin inhibitors, are prepared directly from the intermediate activated lactams 7 by nucleophilic ring opening with amines.