Preparation and evaluation of solid-phase microextraction fibres based on functionalized latex nanoparticle coatings for trace analysis of inorganic anions

The use of a functionalized latex nanoparticle coating as a new sorbent phase for solid-phase microextraction (SPME) was examined. By means of electrostatic absorption onto ionized silanol groups, a fused-silica rod was coated with polymeric nanoparticles functionalized with quaternary ammonium groups. Optimum conditions for the preparation of the coated fibre are presented. The fibre was used for the extraction of a mixture of seven anions from water samples which are analysed by coupling the SPME fibre to an ion chromatographic system via a special interface. The results obtained proved the suitability of this novel coating as a new SPME fibre. A linear calibration for the target analytes was achieved over the concentration range from 5 μg L⁻¹ to 5 mg L⁻¹ (r² > 0.988), while limits of detection for these ions were all below 3.7 μg L⁻¹ (S/N = 3). The reproducibility of a single fibre (n = 4) under similar conditions was between 7 and 12%, while the fibre to fibre reproducibility (n = 5) was between 8.9 and 14%.     

Compaction and tensile forces determine the accuracy of folding landscape parameters from single molecule pulling experiments

We establish a framework for assessing whether the transition state location of a biopolymer, which can be inferred from single molecule pulling experiments, corresponds to the ensemble of structures that have equal probability of reaching either the folded or unfolded states (P(fold)=0.5). Using results for the forced unfolding of a RNA hairpin, an exactly soluble model, and an analytic theory, we show that P(fold) is solely determined by s, an experimentally measurable molecular tensegrity parameter, which is a ratio of the tensile force and a compaction force that stabilizes the folded state. Applications to folding landscapes of DNA hairpins and a leucine zipper with two barriers provide a structural interpretation of single molecule experimental data. Our theory can be used to assess whether molecular extension is a good reaction coordinate using measured free energy profiles.     

On the Tanaka formula for the derivative of self-intersection local time of fractional Brownian motion

The derivative of self-intersection local time (DSLT) for Brownian motion was introduced by Rosen (2005) and subsequently used by others to study the L²$L^2$ and L³$L^3$ moduli of continuity of Brownian local time. A version of the DSLT for fractional Brownian motion (fBm) was introduced in Yan et al. (2008); however, the definition given there presents difficulties, since it is motivated by an incorrect application of the fractional Itô formula. To rectify this, we introduce a modified DSLT for fBm and prove existence using an explicit Wiener chaos expansion. We will then argue that our modification is the natural version of the DSLT by rigorously proving the corresponding Tanaka formula. This formula corrects a formal identity given in both Rosen (2005) and Yan et al. (2008). In the course of this endeavor we prove a Fubini theorem for integrals with respect to fBm. The Fubini theorem may be of independent interest, as it generalizes (to Hida distributions) similar results previously seen in the literature. As a further byproduct of our investigation, we also provide a small correction to an important technical second-moment bound for fBm which has appeared in the literature many times.     

Asymptotically liberating sequences of random unitary matrices

A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we exhibit many other systems of random unitary matrices that, when used for conjugation, lead to freeness. We do so by first proving a general result asserting “asymptotic liberation” under quite mild conditions, and then we explain how to specialize these general results in a striking way by exploiting Hadamard matrices. In particular, we recover and generalize results of the second-named author and of Tulino, Caire, Shamai and Verdú.     

Electron-stimulated production of molecular hydrogen at the interfaces of amorphous solid water films on Pt(111)

The electron-stimulated production of molecular hydrogen (D(2), HD, and H(2)) from amorphous solid water (ASW) deposited on Pt(111) is investigated. Experiments with isotopically layered films of H(2)O and D(2)O are used to profile the spatial distribution of the electron-stimulated reactions leading to hydrogen within the water films. The molecular hydrogen yield has two components that have distinct reaction kinetics due to reactions that occur at the ASW/Pt interface and the ASW/vacuum interface, but not in the bulk. However, the molecular hydrogen yield as a function of the ASW film thickness in both pure and isotopically layered films indicates that the energy for the reactions is absorbed in the bulk of the films and electronic excitations migrate to the interfaces where they drive the reactions.     

What Does Davidson Reject When He Rejects Conceptual Schemes?

According to a common line of criticism, Donald Davidson’s argument in “On the Very Idea of a Conceptual Scheme” is invalid because it moves illicitly from the relatively weak thesis that conceptual schemes cannot be incommensurable to the stronger thesis that the idea of a conceptual scheme itself is incoherent. I argue in this paper that such objections fail because they misunderstand the position that Davidson’s argument is intended to rule out. According to the “scheme-content dualism” Davidson targets, conceptual schemes differ only if they are incommensurable with one another. Thus, if Davidson has successfully shown the idea of incommensurability to be incoherent (as the critics in question grant), then he has shown “the very idea of a conceptual scheme” to be incoherent, as well.     

3D molecular imaging SIMS

Thin monolayer and bilayer films of spin cast poly(methyl methacrylate) (PMMA), poly(2-hydroxyethyl methacrylate) (PHEMA), poly(lactic) acid (PLA) and PLA doped with several pharmaceuticals have been analyzed by dynamic SIMS using SF₅⁺ polyatomic primary ion bombardment. Each of these systems exhibited minimal primary beam-induced degradation under cluster ion bombardment allowing molecular depth profiles to be obtained through the film. By combing secondary ion imaging with depth profiling, three-dimensional molecular image depth profiles have been obtained from these systems. In another approach, bevel cross-sections are cut in the samples with the SF₅⁺ primary ion beam to produce a laterally magnified cross-section of the sample that does not contain the beam-induced damage that would be induced by conventional focussed ion beam (FIB) cross-sectioning. The bevel surface can then be examined using cluster SIMS imaging or other appropriate microanalysis technique.     

Oxadiazole-metal interface: from isolated molecules to pi-stacking

Derivatives of 2,5-diaryl-1,3,4-oxadiazole are used widely for electron transport in organic light emitting diodes (OLED). This study addresses the structure of 2,5-diphenyl-1,3,4-oxadiazole (PPD) molecules on Cu(111) using scanning tunneling microscopy (STM) and density function theory (DFT): at incomplete coverage, PPD molecules are found horizontally on the surface; once the surface area is insufficient to accommodate all adsorbates in this fashion, a pi-stacked film of vertically arranged molecules is formed. In contrast to bulk PPD, in this film, the molecules are arranged face-to-face at a separation of square root(3a0) = 4.4 A as imposed by the substrate interatomic spacing along the [-2 1 1] direction.     

Dense Egyptian fractions

Every positive rational number has representations as Egyptian fractions (sums of reciprocals of distinct positive integers) with arbitrarily many terms and with arbitrarily large denominators. However, such representations normally use a very sparse subset of the positive integers up to the largest denominator. We show that for every positive rational there exist representations as Egyptian fractions whose largest denominator is at most and whose denominators form a positive proportion of the integers up to , for sufficiently large ; furthermore, the proportion is within a small factor of best possible.     

Alternating-Sign Matrices and Domino Tilings (Part II)

We continue the study of the family of planar regions dubbed Aztec diamonds in our earlier article and study the ways in which these regions can be tiled by dominoes. Two more proofs of the main formula are given. The first uses the representation theory of GL(n). The second is more combinatorial and produces a generating function that gives not only the number of domino tilings of the Aztec diamond of order n but also information about the orientation of the dominoes (vertical versus horizontal) and the accessibility of one tiling from another by means of local modifications. Lastly, we explore a connection between the combinatorial objects studied in this paper and the square-ice model studied by Lieb.