The interfacial conformation of polypropylene glycols and foam behaviour

The foam behaviour of low molecular weight polypropylene glycols (PPG) was investigated as a function of concentration and molecular weight (190–2000 g mol⁻¹). For each polypropylene glycol, foam stability increases with concentration and passes through a maximum, beyond which foamability is suppressed as the solubility limit of the glycol is exceeded and droplets of glycol form. Light-scattering data as well as static and dynamic surface tension results provide the key information leading to these interpretations. A maximum in foamability was observed for the PPG molecules with increasing molecular weight (caused by a change in molecular conformation at the interface). This suppresses the Marangoni effect and leads to a decrease in foam stability.     

Fluorinated Copolymer-Oxide Hybrids

A fluorinated copolymer/metal oxide hybrid is fabricated by refluxing a high hydroxyl content fluorinated copolymer with tetraethoxysilane. The resulting organic-inorganic hybrids are transparent throughout the entire compositional range if processed with HCl as a catalyst. They exhibit a continuous variation in hardness, hydrophobicity, and abrasion resistance, intermediary between the properties of the pure polymer and that of a silica gel. The catalyst has a strong influence over the microstructure of the hybrid. ²⁹Si MAS-NMR indicates the presence of highly condensed silica clusters within the structure of the hybrid. If a Nd(III) alkoxide is used instead of TEOS, a Nd ³⁺-doped fluoropolymer is obtained. These results indicate that when a fluorinated copolymer contains groups amenable to hydrolysis and condensation, cross-linking with a metal alkoxide is possible, leading to an interesting families of hybrids.     

Structure of a poly(2,5‐benzimidazole)/phosphoric acid complex

As‐cast films of poly(2,5‐benzimidazole) exhibit uniplanar orientation in which the planes of the aromatic rings lie parallel to the film surface. Upon doping with phosphoric acid, the original crystalline order is lost, but the doped film can be stretched to produce films with uniaxial orientation. After thermal annealing at 540 °C, nine Bragg reflections are resolved in the fiber diagram, and these are indexed by an orthorhombic unit cell with the dimensions a = 18.1 Å, b = 3.5 Å, and c = 11.4 Å, containing four monomer units of two chains. The absence of odd‐order 00l reflections points to a 2₁ chain conformation, which is probably planar so that the aromatic units can be stacked along the b axis. The water and phosphoric acid contents of the crystalline structure cannot be determined exactly because of the presence of extensive amorphous regions that probably have different solvation. The best agreement between the observed and calculated intensities is for an idealized structure containing two phosphoric acids and two water molecules per unit cell. However, the phosphoric acid is probably present mainly in the form of pyrophosphoric acid and its higher oligomers. In addition, the X‐ray data are consistent with a more disordered structure containing chains with random (up and down) polarity and a lack of c‐axis registry. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2576–2585, 2004     

Cotangent cohomology of Stanley-Reisner rings

Simplicial complexes X provide commutative rings A(X) via the Stanley- Reisner construction. We calculated the cotangent cohomology, i.e., T¹ and T² of A(X) in terms of X. These modules provide information about the deformation theory of the algebro geometric objects assigned to X.     

Preparing New Science Teachers for Urban Classrooms : Consensus Within an Expert Community

Preparing future science teachers for U.S. city classrooms is an important yet poorly understood process. The purpose of this study was to determine the philosophies and practices of university ‐based science educators associated with programs supplying teachers for metropolitan school systems. Through an iterative process of mailed questionnaires, 20 participants rated their views on issues pertinent to science teacher education. The responses to questionnaires were used in the creation of items for each subsequent round. The three rounds of questionnaires contained Likert ‐scale and open‐ended questions. For many issues, there was consistently high consensus among the expert panelists, including the presence of students for whom English is a second or new language, the importance of science education professors remaining connected to urban school issues, and practices often affiliated with reform (e.g., alternative assessment, nature of science). Several issues emerged as having low regard by the participants, including the role of student ethnicity on teaching strategies, providing instruction about reading strategies within science teacher preparation, and the value of professors having themselves taught science in urban settings.     

Electron transfer induced dissociations of 2- and 4-alkyl cyclohexadienones

Several 2- and 4-alkylcyclohexadienones were prepared and shown to accept electrons to produce ketyl radical anions that dissociated rapidly at room temperature to release carbon-centered radicals and an aromatic phenoxide type anion. In the PET process with benzyl-substituted cyclohexadienones, initiated with triethylamine, the benzyl radicals dimerised or abstracted an H-atom from solvent. In electrochemical reductions, and in reductions with alkali metals in liquid ammonia, the benzyl radicals were further reduced to anions.     

Self-Interactions of Strands and Sheets

Physical strands or sheets that can be modelled as curves or surfaces embedded in three dimensions are ubiquitous in nature, and are of fundamental importance in mathematics, physics, biology, and engineering. Often the physical interpretation dictates that self-avoidance should be enforced in the continuum model, i.e., finite energy configurations should not self-intersect. Current continuum models with self-avoidance frequently employ pairwise repulsive potentials, which are of necessity singular. Moreover the potentials do not have an intrinsic length scale appropriate for modelling the finite thickness of the physical systems. Here we develop a framework for modelling self-avoiding strands and sheets which avoids singularities, and which provides a way to introduce a thickness length scale. In our approach pairwise interaction potentials are replaced by many-body potentials involving three or more points, and the radii of certain associated circles or spheres. Self-interaction energies based on these many-body potentials can be used to describe the statistical mechanics of self-interacting strands and sheets of finite thickness.     

Perspectives on Advanced Mathematical Thinking

This article sets the stage for the following 3 articles. It opens with a brief history of attempts to characterize advanced mathematical thinking, beginning with the deliberations of the Advanced Mathematical Thinking Working Group of the International Group for the Psychology of Mathematics Education. It then locates the articles within 4 recurring themes: (a) the distinction between identifying kinds of thinking that might be regarded as advanced at any grade level, and taking as advanced any thinking about mathematical topics considered advanced; (b) the utility of characterizing such thinking for integrating the entire curriculum; (c) general tests, or criteria, for identifying advanced mathematical thinking; and (d) an emphasis on advancing mathematical practices. Finally, it points out some commonalities and differences among the 3 following articles.     

The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning.     

Fluorination of diamond — C4F9I and CF3I photochemistry on diamond (100)

The radiation-induced decomposition of C₄F₉I and CF₃I overlayers at 119 K on diamond (100) surfaces has been shown to be an efficient route to fluorination of the diamond surface. X-ray photoelectron spectroscopy has been used for photoactivation as well as for studying the photodecomposition of the fluoroalkyl iodide molecules, the attachment of the photofragments to the diamond surface, and the thermal decomposition of the fluoroalkyl ligands. Measured chemical shifts agree well with ab initio calculations of both C 1s and F 1s binding energies. It is found that chemisorbed CF₃ groups on diamond (100) decompose by 300 K whereas C₄F₉ groups decompose over the range 300 to 700 K and this reactivity difference is rationalized on steric grounds. Both of these thermal decomposition processes produce surface C---F bonds on the diamond. The surface C---F species thermally decompose over a wide temperature range extending up to 1500 K. Hydrogen passivation of the diamond surface is ineffective in preventing free radical attack from the photodissociated products of the fluoroalkyl iodides; I atoms produced photolytically abstract H from surface C---H bonds to yield hydrogen iodide at 119 K allowing diamond fluorination. The attachment of chemisorbed F species to the diamond (100) surface causes band bending as the surface states are occupied as a result of chemisorption. This results in a shift to higher binding energy of the diamond-related C 1s levels present in the surface and subsurface regions which are sampled by XPS on the diamond. The use of photoactivation of fluoroalkyl iodides for the fluorination of diamond surfaces provides a convenient route compared to other methods involving the action of atomic F, molecular F₂, XeF₂ and F-containing plasmas.