Solid‐State Gas Sensors Developed from Functional Difluoroboradiazaindacene Dyes

This article describes the synthesis and characterization of several new difluoroboradiazaindacene (BODIPY?) dyes functionalized at the central 8‐position by a phenyliodo, phenylheptynoate or phenylheptynoic fragment and at the 3‐ or 3/5‐position(s) by 4‐dimethylaminophenylstyryl residue(s). Single‐crystal structural determinations confirm the planarity of the dyes, while the absorption and fluorescence spectroscopic properties are highly sensitive to the state of protonation (or alkylation) of the terminal anilino donor group(s). Reversible color tuning from green to blue for absorption and from colorless (i.e., near‐IR region) to red for fluorescence is obtained on successive addition of acid and base. The difunctionalized derivative is especially interesting in this respect and shows two well‐resolved pK_a values of 5.10 and 3.04 in acetonitrile. Addition of the first proton causes only small spectral changes and deactivates the molecule towards addition of the second proton. It is this latter step that accommodates the large change in absorption and emission properties, due to the reversible extinction of the intramolecular charge‐transfer character inherent to this type of dye. The main focus of the work is the covalent anchoring of the dyes to inert, porous polyacrylate beads so as to form a solid‐state sensor suitable for analysis of gases or flowing liquids. The final material is highly stable—its performance is undiminished after more than one year—and fully reversible over many cycles. The sensitivity is such that reactions can be followed by the naked eye and the detection limit is about 600 ppb for HCl and about 80 ppb for ammonia. Trace amounts of diphosgene can be detected, as can alkylating agents. The sensing action is indiscriminate and also operates when the beads are dispersed in aqueous media.     

The Big Freeze: Water and the Scientific Process

In recent years there has been increasing movement toward laboratory exercises that are inquiry-based, requiring students to assume more active roles in the learning process. A laboratory experiment was developed in this light, framed around a simple question, “Which freezes faster, hot water or cold water?” The experiment was used at the beginning of the general chemistry year-long course sequence and served as an introduction to the scientific process. Students were each asked to develop a hypothesis and then design a simple experiment to determine which freezes faster, hot water or cold water, using small cold baths to freeze the water. A strength of this experiment is that students not only design and perform the experiments, but at the end they evaluate each other’s methods.     

FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension

We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. Moreover, using a weaker notion of approximation, we show the existence of a fully polynomial-time approximation scheme for the problem of maximizing or minimizing an arbitrary polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. A conference version of this article, containing a part of the results presented here, appeared in Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, Miami, FL, January 22–24, 2006, pp. 743–748. The first author gratefully acknowledges support from NSF grant DMS-0608785, a 2003 UC-Davis Chancellor’s fellow award, the Alexander von Humboldt foundation, and IMO Magdeburg. The remaining authors were supported by the European TMR network ADONET 504438.     

Systematic investigation of hexadecapole collectivity in even-even nuclei

Energies of the first 2⁺, 3⁻ and 4⁺ states of even-even nuclei are plotted against proton and neutron number. Using this systematics, shell effects and the corresponding quadrupole and hexadecapole collectivity and deformation effects are compared and contrasted. Also, the correspondingB(E2),B(E3) andB(E4) values are plotted against neutron number and their very different systematics compared. Among the new results are the presence of hexadecapole collectivity at the 82 proton and neutron closed shells and the presence of the maximum values ofB(E4) at neutron numbers 10, 90–92 and 140–146. Finally, the systematics of the hexadecapole (K=4⁺) vibrations is compared with that of the quadrupole (K=2⁺) gamma vibrations in the quadrupole deformed rare earth region. This research has been supported by the National Sciences and Engineering Research Council of Canada at McMaster University and by the Department of Atomic Energy, Government of India, at Banaras Hindu University.     

The crystal and molecular structure of 9-methylphenanthro[4,3-a]dibenzothiophene

The crystal structure of 9-methylphenanthro[4,3-a]dibenzothiophene, C₂₅H₁₆S, M_r = 348.47, has been determined. Monoclinic, P2₁/c, a = 11.364(3), b, = 14.257(3), c = 11.575(2)Å, β = 116.26(2)°, V = 1681.9(7)ų, Z = 4, D_x = 1.38 g/cc, MoKα radiation λ = .71069 Å, F(000) = 728, T = 163K, R = .0458 for 2330 reflections. The structure compares favorably with that of hexahelicene and methylated derivatives. The thiophene moiety increases the helical core radius and decreases the pitch with respect to hexahelicene and its derivatives.     

Ramanujan-Slater type identities related to the moduli 18 and 24

We present several new families of Rogers-Ramanujan type identities related to the moduli 18 and 24. A few of the identities were found by either Ramanujan, Slater, or Dyson, but most are believed to be new. For one of these families, we discuss possible connections with Lie algebras. We also present two families of related false theta function identities.     

Molecular dynamics simulation comparison of atomic scale intermixing at the amorphous Al2O3/semiconductor interface for a-Al2O3/Ge, a-Al2O3/InGaAs, and a-Al2O3/InAlAs/InGaAs

The structural properties of a-Al₂O₃/Ge, a-Al₂O₃/In_0.5Ga_0.5As and a-Al₂O₃/In_0.5Al_0.5As/InGaAs interfaces were investigated by density-functional theory (DFT) molecular dynamics (MD) simulations. Realistic a-Al₂O₃ samples were generated using a hybrid classical-DFT MD “melt and quench” approach. The interfaces were formed by annealing at 700 K/800 K and 1100 K with subsequent cooling and relaxation. The a-Al₂O₃/Ge interface demonstrates pronounced interface intermixing and interface bonding exclusively through Al–O–Ge bonds generating high interface polarity. In contrast, the a-Al₂O₃/InGaAs interface has no intermixing, Al–As and O–In/Ga bonding, low interface polarity due to nearly compensating interface dipoles, and low substrate deformation. The a-Al₂O₃/InAlAs interface demonstrated mild intermixing with some substrate Al atoms being adsorbed into the oxide, mixed Al–As/O and O–Al/In bonding, medium interface polarity, and medium substrate deformation. The simulated results demonstrate strong correlation to experimental measurements and illustrate the role of weak bonding in generating an unpinned interface for metal oxide/semiconductor interfaces.