Combinatorial Lie bialgebras of curves on surfaces

Goldman (Invent. Math. 85(2) (1986) 263) and Turaev (Ann. Sci. Ecole Norm. Sup. (4) 24 (6) (1991) 635) found a Lie bialgebra structure on the vector space generated by non-trivial free homotopy classes of curves on a surface. When the surface has non-empty boundary, this vector space has a basis of cyclic reduced words in the generators of the fundamental group and their inverses. We give a combinatorial algorithm to compute this Lie bialgebra on this vector space of cyclic words. Using this presentation, we prove a variant of Goldman's result relating the bracket to disjointness of curve representatives when one of the classes is simple. We exhibit some examples we found by programming the algorithm which answer negatively Turaev's question about the characterization of simple curves in terms of the cobracket. Further computations suggest an alternative characterization of simple curves in terms of the bracket of a curve and its inverse. Turaev's question is still open in genus zero.     

Synthesis and coordination properties of new macrocyclic ligands: equilibrium studies and crystal structures

The synthesis and characterization of two new macrocyclic ligands, the bis-macrocyclic compound 2,6-bis(1,4,13-triaza-7,10-dioxacyclopentadec-1-ylmethyl)phenol (L) and 38-methoxy-1,4,13,16,19,28-hexaaza-7,10,22,25-tetraoxatricyclo[14.14.7.1(32,36)]octatriconta-32,34,Delta(36,38)-triene (L1) are reported. Equilibrium studies of basicity and coordination properties toward metal ions such as Cu(II), Zn(II), Cd(II) and Pb(II) were performed for ligand by potentiometric measurements in aqueous solution (298.1 +/- 0.1 K, I= 0.15 mol dm(-3)). L behaves as a hexaprotic base (logK(1)= 10.93, logK(2)= 9.70, logK(3)= 8.79, logK(4)= 8.05, logK(5)= 6.83, logK(6)= 2.55). All metal ions form stable mono- and dinuclear complexes: logK(MLH(-1))= 25.61 for Cu(II), 15.37 for Zn(II), 12.58 for Cd(II) and 13.79 for Pb(II); logK(M(2)LH(-1))= 31.61 for Cu(II), 23.38 for Zn(II), 24.49 for Cd(II) and 23.68 for Pb(II). All these dinuclear species show a great tendency to add the OH(-) group: the equilibrium constant for the addition reaction was found to be logK(M(2)LH(-1)OH)= 4.77 for Cu(II), 5.66 for Zn(II), 2.8 for Cd(II) and 3.18 for Pb(II). In the case of Ni(II), kinetic inertness prevents the possibility of solution studies. The dinuclear solid adducts [Ni(2)H(-1)L(N(3))(3)].EtOH and [Cu(2)H(-1)L(N(3))](ClO(4))(2) were characterized by X-ray analysis.     

Self-intersections in combinatorial topology: statistical structure

Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the minimum number of transversal self-intersection points of representatives of the class. We prove that if a class is chosen at random from among all classes of m letters, then for large m the distribution of the self-intersection number approaches the Gaussian distribution. The theorem was strongly suggested by a computer experiment with four million curves producing a very nearly Gaussian distribution.     

Unusual Inherent Electrochemistry of Graphene Oxides Prepared Using Permanganate Oxidants

Graphene and graphene oxides are materials of significant interest in electrochemical devices such as supercapacitors, batteries, fuel cells, and sensors. Graphene oxides and reduced graphenes are typically prepared by oxidizing graphite in strong mineral acid mixtures with chlorate (Staudenmaier, Hofmann) or permanganate (Hummers, Tour) oxidants. Herein, we reveal that graphene oxides pose inherent electrochemistry, that is, they can be oxidized or reduced at relatively mild potentials (within the range ±1 V) that are lower than typical battery potentials. This inherent electrochemistry of graphene differs dramatically from that of the used oxidants. Graphene oxides prepared using chlorate exhibit chemically irreversible reductions, whereas graphene oxides prepared through permanganate‐based methods exhibit very unusual inherent chemically reversible electrochemistry of oxygen‐containing groups. Insight into the electrochemical behaviour was obtained through cyclic voltammetry, chronoamperometry, and X‐ray photoelectron spectroscopy experiments. Our findings are of extreme importance for the electrochemistry community as they reveal that electrode materials undergo cyclic changes in charge/discharge cycles, which has strong implications for energy‐storage and sensing devices.     

3D printing for aqueous and non-aqueous redox flow batteries

Additive manufacturing technologies, generally grouped under the name of 3D printing, are experiencing an explosion of interest during the last few years. The possibility of fast prototyping enabled by 3D printing has been recognized as a crucial booster for device fabrication and general scientific advancements. In this review, attention is focused on the latest developments in the field of redox flow batteries which are, similar to other energy related devices, characterized by the recent adoption of 3D printing methods for the fabrication of key components. Whether simply to investigate flow phenomena, test new designs or fabricate final-product components with custom features, the use of 3D printing can critically drive this field of research towards better performing energy-storage systems. The latest and most representative examples of redox flow battery studies will be discussed, categorized in relation to the electrolyte used and whether the devices are employed in aqueous or non-aqueous applications.     

Selective Detection of Mg2+ for Sensing Applications in Drinking Water

A new series of ligands containing the 2-(2-hydroxy-3- naphthyl)-4-methylbenzoxazole (HNBO) fluorophore showed selectivity for Mg²⁺ ions, without the interference of Ca²⁺. The most promising representative L3 resulted the best performing sensor for Mg²⁺ both in solution and embedded in an all-solid-state optode, especially towards real samples of drinkable water.     

A macrocyclic ligand able to bind gallium(III) by preorganized pendant arms; coordination and kinetic studies

The equilibria and kinetics of the binding of gallium(III) to 4-(N),10-(N)-bis[2-(3-hydroxo-2-oxo-2-H-pyridine-1-y1)acetamido]-1,7-dimethyl-1,4,7,10-tetraazacyclododecane (L) were investigated in acidic medium at ionic strength 1 M (NaClO4). Spectrophotometric titrations in the UV region revealed that L is able to bind Ga3+ also at high H+ concentration. The kinetic (stopped-flow) experiments are interpreted on the basis of three parallel reaction paths (i) M3+ + H2L2+ = M(H2L)5+ where M(H2L)5+ is in a steady state, (ii) M(OH)2+ + H2L2+ = M(HL)4+ + H2O and (iii) M(OH)2+ + HL+ = ML3+ + H2O. The first-order rate constants for conversion of the outer-sphere into the inner-sphere complexes are similar to those of the Ga(III)/tropolone system which is known to react according to the dissociative Id mechanism and to the relevant rate constants for water exchange at the metal ion. The effects of pH on the UV-Vis absorption, fluorescence emission properties and NMR spectral features on the Ga(III)/L system were also investigated. Spectrophotometric titrations in the UV region reveal that, in acid medium the prevailing species is M(HL)4+ whereas the chelate ML3+ prevails for [H+] < 0.01 M. The results indicate metal coordination at the oxygen atoms of the 3-hydroxo-2-oxopyridine residues.     

Natural products in combinatorial chemistry: an andrographolide-based library

The generation of a natural-product-based library starting from andrographolide is described. Utilizing andrographolide itself in parallel solution-phase synthesis leads to a 360-membered library. The initial transformation of the starting material via ozonolysis is followed by the conversion into a suitable template by introduction of a thiazole moiety. Subsequent decoration at two points of diversity yields the desired natural product derivatives. The selection of actually synthesized compounds is based on a virtually generated library and the assessment of its members with respect to physicochemical parameters, thus ensuring pharmacological relevance of the compounds.