On a question of A. Kameyama concerning self-similar metrics

A. Kameyama introduced the concept of self-similar topological system and asked the following fundamental question: given a topological self-similar system (K,_{(fi)i∈{1,2,...,N}})$(K,{(f_i)}_{i\in \{1,2,...,N\}})$, does there exist a metric on K   comparable to the topology such that all the functions _fi$f_i$ are contractions? We modify Kameyama's question (which has a negative answer for an arbitrary topological self-similar system) by weakening the requirement that the functions in the topological self-similar system be contractions to requiring that they be φ  -contractions. More precisely we give an affirmative answer to the following question: given a topological self-similar system (K,_{(fi)i∈{1,2,...,N}})$(K,{(f_i)}_{i\in \{1,2,...,N\}})$ does there exist a metric δ on K   which is compatible with the original topology and a comparison function φ:[0,∞)→[0,∞)$\phi :[0,\infty )\to [0,\infty )$ such that all the functions _fi:(K,δ)→(K,δ)$f_i:(K,\delta )\to (K,\delta )$ are φ  -contractions? Consequently the iterated function system ((K,d),_{(fi)i∈{1,2,...,N}})$((K,d),{(f_i)}_{i\in \{1,2,...,N\}})$, where d is a metric on K compatible with the original topology on K, is φ-hyperbolic.     

An Efficient Strategy to Drive Nanoparticles into Carbon Nanotubes and the Remarkable Effect of Confinement on Their Catalytic Performance

Are you in? Bimetallic PtRu nanoparticles have been selectively confined inside or deposited outside carbon nanotubes (see picture). The confined nanoparticles display significantly higher selectivity and catalytic activity in hydrogenation reactions.

     

A DNA-binding copper(I) metallosupramolecular cylinder that acts as an artificial nuclease

The DNA binding of a dicationic pyridylimine-based dicopper(I) metallosupramolecular cylinder is reported together with its ability to act as an artificial nuclease. The cylinder binds strongly to DNA; more strongly than the spherical dication [Ru(phen)(3)](2+) (phen=1,10-phenanthroline), but more weakly than the corresponding tetracationic cylinders. DNA coiling effects are not observed with this dication, in contrast to the situation with the previously reported tetracationic cylinder involving a similar ligand. Linear dichroism (LD) data suggests that the dicopper cylinder binds in a different orientation from that of the tetracationic iron cylinder. Furthermore, the dicopper cylinder shows DNA-cleavage activity in the presence of peroxide. Of particular note is that the cylinder displays a marked and unusual ability to cleave both DNA strands at the same site, probably reflecting its dinuclear nature and possibly its mode of binding to the DNA.     

DFT studies on the magnetic exchange across the cyanide bridge

Exchange coupling across the cyanide bridge in a series of novel cyanometalate complexes with CuII-NC-MIII (M = Cr and low-spin Mn, Fe) fragments has been studied using the broken-symmetry DFT approach and an empirical model, which allows us to relate the exchange coupling constant with sigma-, pi-, and pi*-type spin densities of the CN- bridging ligand. Ferromagnetic exchange is found to be dominated by pi-delocalization via the CN- pi pathway, whereas spin polarization with participation of sigma orbitals (in examples, where the dz2 orbital of MIII is empty) and pi* orbitals of CN- yields negative spin occupations in these orbitals, and reduces the CuII-MIII exchange coupling constant. When the dz2 orbital of MIII is singly occupied, an additional positive spin density appears in the sigma(CN) orbital and leads to an increase of the ferromagnetic Cu-NC-M exchange constant. For low-spin [MIII(CN)6]3- complexes, the dz2 orbital occupancy results in high-spin metastable excited states, and this offers interesting aspects for applications in the area of molecular photomagnetism. The DFT values of the exchange coupling parameters resulting from different occupations of the t2g orbitals of low-spin (t2g5) FeIII are used to discuss the effect of spin-orbit coupling on the isotropic and anisotropic exchange coupling in linear Cu-NC-Fe pairs.     

Large-scale synthesis of alkyne-linked tripodal porphyrins via palladium-mediated coupling conditions

Suzuki and Sonogashira couplings have been used in short and efficient sequences to give access to a new family of porphyrin trimers on a practical scale.     

The role of capillary and surface forces in the crossover behavior of solid nanoparticles at liquid interfaces

We investigate the interaction between a nanoparticle and an oil-water interface with particular emphasis on the particle crossing through the interface. The formation of a three-phase contact line is investigated in two cases, namely in the presence and in the absence of surface forces. We carefully examine the interplay between capillary and surface forces in such systems. Two instabilities of the interface (snap-in/snap-out) as the particle is moved through the interface are identified and quantitatively described. While the snap-in instability was observed in some AFM studies, the precise interface position and configuration relative to the particle at the instability depends on the nature of the surface forces present in the system. After the snap-in, the particle is adsorbed and must overcome an energy barrier due to the interface deformation in order to cross-over to the other liquid. We make quantitative predictions on the interface configuration at the instabilities and the free energy barrier height. The roles of particle size and different interaction parameters characterizing the system in determining the magnitude of the energy barrier for crossing and in the formation of a three-phase contact line are discussed. Ultimately, this study will enable us to make quantitative predictions on capillary effects in nanoparticle-microemulsions mixtures and other colloidal systems. For particles in the micrometer range and larger the capillary forces dominate over the surface forces and dictate how the snap-in occurs. However, the situation becomes different for particle sizes smaller than about 100 nm. The presence of surface forces modifies the interface configuration and the free energy jump at the snap-in instability.     

Columnar self-assembled ureido crown ethers: an example of ion-channel organization in lipid bilayers

The self-assembly of ureido crown-ether derivatives has been examined in homogeneous solution, in the solid state, and in planar bilayer membranes. The self-assembly is driven by head-to-tail hydrogen bonding between the urea functional groups. Dimers and higher oligomers are formed in CDCl3 solution as assessed by the change in the ureido NH chemical shift as a function of concentration. Single-crystal X-ray diffraction shows that an antiparallel association of the ureas produces columnar channels composed of face-to-face crown ethers. Powder X-ray diffraction studies also show the presence of a minor phase based upon a parallel urea association leading to an alternative columnar arrangement of the crown ethers. In bilayer membranes at low concentration of ureido crown ether added, membrane disruption is observed together with rare single-channel openings, but at higher concentration, a rich array of interconverting channel conductance states is observed. The channel results are interpreted as arising from discreet stacks of ureido crown ethers where the transport of cations would occur via the macrocycles, admixed with larger pores formed by association of the crown ether headgroups around a central large pore.     

Noncovalent interactions within a synthetic receptor can reinforce guest binding

Structural and thermodynamic data are presented on the binding properties of anion receptors containing two covalently linked cyclopeptide subunits that bind sulfate and iodide anions with micromolar affinity in aqueous solution. A synchrotron X-ray crystal structure of the sulfate complex of one receptor revealed that the anion is bound between the peptide rings of the biscyclopeptide. Intimate intramolecular contacts between the nonpolar surfaces of the proline rings of the individual receptor moieties in the complex suggest that hydrophobic interactions within the receptor that do not directly involve the guest contribute to complex stability. This finding is supported by a microcalorimetric analysis of the solvent dependence of complex stability, which showed that increasing the water content of the solvent has only a weak influence on the Gibbs energy of binding. Hence, the increasing amount of energy required for desolvating the binding partners in solutions containing more water is almost compensated by the increasingly favorable hydrophobic interactions. Further observations that suggest that guest-induced intra-receptor interactions contribute to guest binding are (i) anion binding of a monomeric cyclopeptide lacking the covalent linkage between the two rings leads to the formation of 2:1 complexes; (ii) in the crystal structure of the 2:1 iodide complex of this monotopic receptor, a similar arrangement of the two cyclopeptide rings has been found as in the sulfate complex of the biscyclopeptide; (iii) complex formation of the monomeric cyclopeptide in aqueous solution is highly cooperative with a large stability constant corresponding to the formation of the 2:1 complexes from relatively instable 1:1 complexes; (iv) the monomeric cyclopeptide forms only 1:1 anion complexes in DMSO where hydrophobic interactions do not take place; and (v) introducing polar hydroxy groups on the proline rings of the monomeric cyclopeptide disrupts cooperativity causing the formation of only 1:1 complexes even in aqueous solution. Taken together these observations demonstrate that, in addition to direct receptor-substrate interactions, noncovalent interactions between the two subunits of such biscyclopeptides contribute significantly to anion complex stability. Reinforcement of molecular recognition through intra-receptor interactions should be an attractive new strategy to boost host-guest affinities.