Interaction of scanning probes with semiconductor nanocrystals; physical mechanism and basis for near-field optical imaging

We investigate the modification of photoluminescence (PL) from single semiconductor nanocrystal quantum dots (NCs) in the proximity of metal and semiconducting atomic force microscope (AFM) tips. The presence of the tip alters the radiative decay rate of an emitter via interference and opens efficient nonradiative decay channels via energy transfer to the tip material. These effects cause quenching (or enhancement) of the emitter's PL intensity as a function of its distance from the interacting tip. We take advantage of this highly distance-dependent effect to realize a contrast mechanism for high-resolution optical imaging. AFM tips are optimized as energy acceptors by chemical functionalization with InAs NCs to achieve optical resolution down to 30 nm. The presented experimental scheme offers high-resolution optical information while maintaining the benefits of traditional AFM imaging. We directly measure the PL intensity of single NCs as a function of the tip distance. Our results are in good agreement with calculations made by a classical theoretical model describing an oscillating dipole interacting with a planar mirror.     

Hindman’s theorem and idempotent types

Motivated by a question of Di Nasso, we show that Hindman’s theorem is equivalent to the existence of idempotent types in countable complete extensions of Peano Arithmetic.     

Cultivating Computational Thinking Practices and Mathematical Habits of Mind in Lattice Land

There is a great deal of overlap between the set of practices collected under the term “computational thinking” and the mathematical habits of mind that are the focus of much mathematics instruction. Despite this overlap, the links between these two desirable educational outcomes are rarely made explicit, either in classrooms or in the literature. This paper presents Lattice Land, a computational learning environment and accompanying curriculum designed to support the development of mathematical habits of mind and promote computational thinking practices in high-school mathematics classrooms. Lattice Land is a mathematical microworld where learners explore geometrical concepts by manipulating polygons drawn with discrete points on a plane. Using data from an implementation in a low-income, urban public high school, we show how the design of Lattice Land provides an opportunity for learners to use computational thinking practices and develop mathematical habits of mind, including tinkering, experimentation, pattern recognition, and formalizing hypothesis in conventional mathematical notation. We present Lattice Land as a restructuration of geometry, showing how this new and novel representational approach facilitates learners in developing computational thinking and mathematical habits of mind. The paper concludes with a discussion of the interplay between computational thinking and mathematical habits of mind, and how the thoughtful design of computational learning environments can support meaningful learning at the intersection of these disciplines.     

Long-range electronic-to-vibrational energy transfer from nanocrystals to their surrounding matrix environment

A radiationless transition process of long-range, resonance interconversion of electronic-to-vibrational energy transfer (EVET) is discovered between the band-gap excitation of nanocrystal quantum dots to matrix vibrational overtone modes using fluorescence lifetime measurements. A theoretical analysis based on long-range dipole-dipole nonadiabatic couplings, being distinct from the traditional adiabatic or "static-coupling" pictures, is given and is in qualitative agreement with experiments. EVET should be considered in matrix choices for near-infrared optoelectronic applications of nanocrystals.     

Dynamics of water and sodium in gels under salt‐induced phase transition

Synthetic and biological gels undergo a sharp volume phase transition when subjected to a variety of environmental changes. Water and ion dynamics within swollen and compact phases are critical for understanding fundamental concepts in cellular (specifically neuronal) biophysics, for models of bound, free, or ordered water in complex environments; and for practical applications such as the design of gels for drug release, biomimetics, sensors, or actuators. In this work, we find, for the first time, basic physical parameters that shed light on the interaction of gels with water and electrolytes, across a volume phase transition. Water within a gel can be separated into bound and free populations with high exchange rate. We show that free water dynamics in compact gels are the same as those in pure water. Bound water was found to comprise a single layer around the polymers in both phases, with a correlation time three orders of magnitude higher than that of free water. Most importantly, salt‐induced phase transition was found to be different from a standard coil‐globule transition (e.g., temperature‐induced), with no rejection of bound water as the gel compacts. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1620–1628     

A kinetic study of the oxidation of hydroxamic acids by compounds I and II of horseradish peroxidase: Effect of transition metal ions

Abstract

Oxidation of hydroxamic acids (HXs) generates HNO, and it is not clear whether it is formed also in the presence of metal ions. The kinetics of the oxidation of HXs, such as acetohydroxamic acid, suberohydroxamic acid, and suberoylanilide hydroxamic acid (SAHA), by compounds I and II of horseradish peroxidase (HRP) at pH 7.0 and 25?°C have been studied using rapid-mixing stopped-flow. The kinetics of these reactions were compared to those observed in the presence of Cu(ClO₄)₂, NiSO₄, or ZnSO₄. The rates decrease upon increasing [Cu^II] at constant [HXs], and no oxidation of HX occurs when [HX]/[Cu^II] ≈ 2, implying that HX oxidation in the presence of Cu^II proceeds through the free ligand since the predominant complex is CuX₂. In the case of Ni^II, the oxidation rate decreases upon increasing the ratio [Ni^II]/[HX] beyond 1, where the predominant complex is Ni^IIX⁺, implying that its oxidation is feasible. The effect of Zn^II could be studied only on the rate of HXs oxidation by compound II demonstrating similar behavior to that of Ni^II. HXs were also oxidized catalytically by HRP/H₂O₂ at pH 7.0, demonstrating that metal ions facilitate the formation of HNO while hardly affecting its yield and the extent of HX oxidation.     

Photoinitiated free radical polymerization of vinyl compounds in aqueous solution

A new method for the photochemical initiation of polymerization of vinyl compounds in aqueous solution is described. The photochemically active species is an ion pair complex of the formula Fe³⁺X⁻(X⁻ = OH⁻, CI⁻, N⁻₃, etc.). The light absorption by the ion pair leads to an electron transfer causing reduction of the cation and oxidation of the anion to an atom or free radical X. The latter leads to the initiation of polymerization in accordance with X + CH₂CHR→XCH₂ CHR . The kinetics of the reaction were studied by the measurement of: (a) ferrous ion formed (colorimetrically), (b) monomer disappearance (by titration and by weighting the polymer), (c) the chain length of the polymer (in the case of methyl methacrylate). The dependence of the quantum yield on the light intensity, light absorption fraction, and the concentration of vinyl monomer and ferrous ion added initially was investigated. A complete mechanism, both with regard to the formation of free radicals and the polymerization reaction, was put forward involving: (1) light absorption, (2) a primary dark back reaction, (3) dissociation of the primary product, (4) a secondary dark back reaction, (5) initiation of polymerization by free radicals, (6) propagation of polymerization, and (7) termination by recombination of active polymer endings. The mechanism was verified by the experimental results and some constant ratios were estimated quantitatively.     

Poset algebras over well quasi-ordered posets

A new class of partial order-types, class is defined and investigated here. A poset P is in the class iff the poset algebra F(P) is generated by a better quasi-order G that is included in L(P). The free Boolean algebra F(P) and its free distributive lattice L(P) have been defined in [ABKR]. The free Boolean algebra F(P) contains the partial order P and is generated by it: F(P) has the following universal property. If B is any Boolean algebra and f is any order-preserving map from P into a Boolean algebra B, then f can be extended to a homomorphism of F(P) into B. We also define L(P) as the sublattice of F(P) generated by P. We prove that if P is any well quasi-ordering, then L(P) is well founded, and is a countable union of well quasi-orderings. We prove that the class is contained in the class of well quasi-ordered sets. We prove that is preserved under homomorphic image, finite products, and lexicographic sum over better quasi-ordered index sets. We prove also that every countable well quasi-ordered set is in . We do not know, however if the class of well quasi-ordered sets is contained in . Additional results concern homomorphic images of posets algebras. The third author was supported by the following institutions: Israel Science Foundation (postdoctoral positions at Ben Gurion University 2000–2002), The Fields Institute (Toronto 2002–2004), and by The Nato Science Fellowship (University Paris VII, CNRS-UMR 7056, 2004).     

A combinatorial method for solution-phase synthesis of labeled bivalent beta-turn mimics

Piperidine-functionalized, 1,4-disubstituted-1,2,3-triazoles of generic structure 1 were conceived as "minimalist" mimics of peptidic beta-turn structures. Key features of these molecules include (i) the possibility of incorporating amino acid side chains corresponding to many of the protein amino acids; (ii) a close correspondence of separations of these side chains to i + 1 to i + 2 residues in turns; (iii) facile adjustment of the side-chain vectors on docking while only influencing two critical degrees of freedom; and (iv) some electrostatic polarity. Fifteen monomers of this type were made via copper-mediated cycloaddition reactions. Solution-phase methodologies were devised to assemble these monomers into bivalent compounds in high purity states (typically >85%) so that they could be used in first-pass biological assays without further purification. The skeleton for forming these bivalent compounds is triazine-based. There is a third site which allowed for introduction of a fluorescent label (library of compounds 2) or an alkyne-functionalized triethylene glycol chain (library of compounds 3) included to promote water-solubility and to allow incorporation of probes via copper-mediated cycloaddition reactions. In the event, two 135-membered libraries were prepared, one consisting of compounds 2 and the other of 3. No protecting groups or coupling agents were required; these attributes of the method were important to allow most of the products to be obtained in over 85% purities. The fluorescein-tagged library of compounds 2 was screened in a fluorescence-activated cell sorting (FACS) assay using cells transfected to overexpress one of the following neurotrophin receptors: TrkA, TrkC, and p75. Preliminary findings indicate four compounds 2gm, 2gn, 2gi, and 2gj bound the TrkA receptor selectively; all of these contain a threonine-lysine turn mimic. Thus, a pharmacological probe for the TrkA receptor has been developed.