Asymptotics of Block Toeplitz Determinants and the Classical Dimer Model

We compute the asymptotics of a block Toeplitz determinant which arises in the classical dimer model for the triangular lattice when considering the monomer-monomer correlation function. The model depends on a parameter interpolating between the square lattice (t = 0) and the triangular lattice (t = 1), and we obtain the asymptotics for 0 < t ≤ 1. For 0 < t < 1 we apply the Szegö Limit Theorem for block Toeplitz determinants. The main difficulty is to evaluate the constant term in the asymptotics, which is generally given only in a rather abstract form.     

Copper-assisted oxidation of catechols into quinone derivatives

Catechols are ubiquitous substances often acting as antioxidants, thus of importance in a variety of biological processes. The Fenton and Haber–Weiss processes are thought to transform these molecules into aggressive reactive oxygen species (ROS), a source of oxidative stress and possibly inducing degenerative diseases. Here, using model conditions (ultrahigh vacuum and single crystals), we unveil another process capable of converting catechols into ROSs, namely an intramolecular redox reaction catalysed by a Cu surface. We focus on a tri-catechol, the hexahydroxytriphenylene molecule, and show that this antioxidant is thereby transformed into a semiquinone, as an intermediate product, and then into an even stronger oxidant, a quinone, as final product. We argue that the transformations occur via two intramolecular redox reactions: since the Cu surface cannot oxidise the molecules, the starting catechol and the semiquinone forms each are, at the same time, self-oxidised and self-reduced. Thanks to these reactions, the quinone and semiquinone are able to interact with the substrate by readily accepting electrons donated by the substrate. Our combined experimental surface science and ab initio analysis highlights the key role played by metal nanoparticles in the development of degenerative diseases.

An antioxidant catechol transforms following intramolecular redox reactions into highly reactive oxygen species, a semiquinone and a quinone, on copper.     

Synthesis and Characterization of Multinanometer‐Sized Expanded Dendralenes with an iso‐Poly(triacetylene) Backbone

A series of [n]dendralenes (n =3, 4, 8, 3b – d (Fig. 1)) expanded with buta‐1,3‐diynediyl moieties between the CC bonds were prepared by repetitive acetylenic scaffolding of 3‐(cyclohexylidene)penta‐1,4‐diyne building blocks (Scheme). These remarkably unstable iso‐poly(triacetylene) (iso‐PTA) oligomers were characterized by ¹H‐ and ¹³C NMR (Fig. 3 and Table 1), IR, and UV/VIS (Figs. 4 and 6 and Table 2) spectroscopy, as well as mass spectrometry (Fig. 2). The expanded [8]dendralene contains 40 C(sp)‐ and C(sp²)‐atoms in the backbone and represents the longest iso‐PTA oligomer prepared to date. HOMO‐LUMO Gap energies were determined as a function of oligomeric length (Fig. 5 and Table 3), providing insight into the degree of π‐electron delocalization in these cross‐conjugated chromophores. A continous drop in the HOMO‐LUMO gap with increasing number of monomeric repeating units provides evidence that cross‐conjugation along the oligomeric backbone is effective to some extent. The limiting HOMO‐LUMO gap energy for an infinitely long, buta‐1,3‐diynediyl‐expanded dendralene was extrapolated to about 3.3–3.5 eV. The conformational preferences of the expanded dendralenes were analyzed in semi‐empirical calculations, revealing energetic preferences for planar or slightly twisted s‐cis and ‘U‐shaped' geometries.     

Can the presence of chemically inert species modify the face selectivity in asymmetric induction by cyclodextrins?

Reduction of-cyclodextrin (-CD) aromatic ketone (acetophenone and acetonaphthones) inclusion compounds were carried out in the presence of a large number of chemically inert species as potential co-guests. In several cases, it was observed that stoichiometric molar ratios of these compounds to ketone significantly modify the chiral induction yielding the inverted alcohol enantiomer and increasing the face selectivity. The results were found to depend strongly on the respective structure and shape of both the ketone and the additive, and on the molar ratio of-CD:ketone:third compound. These observations suggest the formation of a three-component inclusion complex in which the geometry of binding of the substrate and its mobility are changed with respect to the binary system.     

Microfluidic platform for combinatorial synthesis in picolitre droplets

This paper presents a droplet-based microfluidic platform for miniaturized combinatorial synthesis. As a proof of concept, a library of small molecules for early stage drug screening was produced. We present an efficient strategy for producing a 7 × 3 library of potential thrombin inhibitors that can be utilized for other combinatorial synthesis applications. Picolitre droplets containing the first type of reagent (reagents A(1), A(2), …, A(m)) were formed individually in identical microfluidic chips and then stored off chip with the aid of stabilizing surfactants. These droplets were then mixed to form a library of droplets containing reagents A(1-m), each individually compartmentalized, which was reinjected into a second microfluidic chip and combinatorially fused with picolitre droplets containing the second reagent (reagents B(1), B(2), …, B(n)) that were formed on chip. The concept was demonstrated with a three-component Ugi-type reaction involving an amine (reagents A(1-3)), an aldehyde (reagents B(1-7)), and an isocyanide (held constant), to synthesize a library of small molecules with potential thrombin inhibitory activity. Our technique produced 10(6) droplets of each reaction at a rate of 2.3 kHz. Each droplet had a reaction volume of 3.1 pL, at least six orders of magnitude lower than conventional techniques. The droplets can then be divided into aliquots for different downstream screening applications. In addition to medicinal chemistry applications, this combinatorial droplet-based approach holds great potential for other applications that involve sampling large areas of chemical parameter space with minimal reagent consumption; such an approach could be beneficial when optimizing reaction conditions or performing combinatorial reactions aimed at producing novel materials.     

Lipophilic phthalocyanines for their potential interest in photodynamic therapy: synthesis and photo-physical properties

Several phthalocyanines with different peripheral substituents were prepared and characterized by MALDI-TOF, ¹H NMR, UV–vis, fluorescence, and singlet oxygen quantum yields and retention time in HPLC normal phase. Zinc was used as a central metal ion to increase the photodynamic therapy efficiency. Phthalonitrile or 4-nitro phthalonitriles were used as starting materials. The influence of lipophilicity on the photophysical and photochemical properties was evaluated.