A note on an additive property of primes.

An elementary construction is given of an infinite sequence of natural numbers, having at least two different decompositions as sum of primes and no prime number appears in more than one of them

Looking for the Stokes Theorem in an elementary trapezoid

The aim of this very short note it to show that even in a totally elementary framework, it is possible to glimpse the Stokes theorem

Reversible phase transformation and doubly-charged anions at the surface of simple cubic RbC60

The simple cubic phase of a RbC60 thin film has been studied using photoelectron spectroscopy. The simple cubic-to-dimer transition is found to be reversible at the film surface. A sharp Fermi edge is observed and a lower limit of 0.5 eV is found for the surface Hubbard U, pointing to a strongly-correlated metallic character of thin-film simple cubic RbC60. A molecular charge state is identified in the valence band and core level photoemission spectra which arises from C602- anions and contributes to the spectral intensity at the Fermi level.Comment: 13 pages, 3 figure

Rapid Solvent-Free Microcrystalline Cellulose Melt Functionalization with L-Lactide for the Fabrication of Green Poly-Lactic Acid Biocomposites

A green approach is proposed to achieve a rapid surface functionalization of microcrystalline cellulose (MCC) in 30 min by a solvent-free grafting by the reaction of L-lactide through compression molding without the need for an inert atmosphere. A sufficient hydrophobization of the MCC surface is achieved with an amount of grafted poly(L-lactic acid) (PLLA) oligomers of 7 wt % with respect to MCC. The obtained PLLA-g-MCC is subsequently melt-compounded with poly(lactic acid) (PLA) through extrusion and injection molding. As a result of higher compatibility and interfacial adhesion of the functionalized filler with PLA, PLA/ MCC-g-PLLA biocomposites with a cellulose content ranging from 4 to 20 wt % exhibit an enhancement in important physicochemical properties (i.e., water vapor barrier, crystallinity, stiffness) compared to both pure PLA and formulations containing an equal or higher amount of nonfunctionalized MCC. At the same time, the materials retain the mechanical strength and resistance to thermal degradation of PLA. The physicochemical characteristics, excellent biocompatibility, and biodegradability of PLA and cellulose and the simplicity, rapidity, and cost-effectiveness of the grafting process render these biocomposites suitable for several applications within the plastics domain including packaging, agriculture, automotive, consumer goods, and household appliances

Characterization of high-quality MgB2(0001) epitaxial films on Mg(0001)

High-grade MgB2(0001) films were grown on Mg(0001) by means of ultra-high-vacuum molecular beam epitaxy. Low energy electron diffraction and x-ray diffraction data indicate that thick films are formed by epitaxially oriented grains with MgB2 bulk structure. The quality of the films allowed angle-resolved photoemission and polarization dependent x-ray absorption measurements. For the first time, we report the band mapping along the Gamma-A direction and the estimation of the electron-phonon coupling constant l ~ 0.55 for the surface state electrons.Comment: 15 text pages, 6 figures Submitted for publicatio

Role of acid-base equilibria in the size, shape, and phase control of cesium lead bromide nanocrystals

A binary ligand system composed of aliphatic carboxylic acids and primary amines of various chain lengths is commonly employed in diverse synthesis methods for CsPbBr3 nanocrystals (NCs). In this work, we have carried out a systematic study examining how the concentration of ligands (oleylamine and oleic acid) and the resulting acidity (or basicity) affects the hot injection synthesis of CsPbBr3 NCs. We devise a general synthesis scheme for cesium lead bromide NCs which allows control over size, size distribution, shape, and phase (CsPbBr3 or Cs4PbBr6) by combining key insights on the acid base interactions that rule this ligand system. Furthermore, our findings shed light upon the solubility of PbBr2 in this binary ligand system, and plausible mechanisms are suggested in order to understand the ligand-mediated phase control and structural stability of CsPbBr3 NCs

Seeding the vertical growth of laterally coherent coordination polymers on the rutile-TiO2(110) surface

Coordination polymers may be synthesized by linear bridging ligands to metal ions with conventional chemistry methods (e.g. in solution). Such complexes can be hardly brought onto a substrate with the chemical, spatial and geometrical homogeneity required for device integration. Instead, we follow an in situ synthesis approach, where the anchoring points are provided by a monolayer of metal(II)-tetraphenylporphyrin (M-TPP, M = Cu, Zn, Co) grown in vacuum on the rutile-TiO2(110) surface. We probed the metal affinity to axial coordination by further deposition of symmetric dipyridyl-naphthalenediimide (DPNDI). By NEXAFS linear polarization dichroism, we show that DPNDI stands up on Zn- and Co-TPP thanks to axial coordination, whereas it lies down on the substrate for Cu-TPP. Calculations for a model pyridine ligand predict strong binding to Zn and Co cations, whose interaction with the O anions underneath is disrupted by surface trans effect. The weaker interactions between pyridine and Cu-TPP are then overcome by the strong attraction between TiO2 and DPNDI. The binding sites exposed by the homeotropic alignment of the ditopic DPNDI ligand on Zn- and Co-TPP are the foundations to grow coordination polymers preserving the lateral coherence of the basal layer

Photo-polymerisable electrospun fibres of N-methacrylate glycol chitosan for biomedical applications

The availability of nanofibrous substrates with engineered properties, such as controlled porosity, mechanical conformability, biodegradation profile and drug release, is of strategic importance in the biomedical sector. Here, we demonstrate that N-methacrylate glycol chitosan, a photo-polymerisable, biocompatible and water-soluble derivative of chitosan, can be easily processed to create non-woven mats of nanofibres with controlled physicochemical characteristics. The produced fibrous mats are characterised by thermal stability, Young's modulus of 140 MPa and ultimate strength of 4 MPa. The degree of cross-linking of the realised fibres regulates their durability and degradation profile under conditions of high humidity, but also allows controlling the delivery over time of active agents encapsulated inside the fibres. We demonstrate that the N-methacrylate glycol chitosan nanofibres are able to release an antimicrobial drug within 24 hours. Moreover, cells proliferation of 85% indicates that non-cytotoxic substances were released from the electrospun mats

Molecular Iodine for a General Synthesis of Binary and Ternary Inorganic and Hybrid Organic-inorganic Iodide Nanocrystals

We report the synthesis of various binary and ternary inorganic and hybrid organic-inorganic iodide nanocrystals starting from molecular iodine (I2). The procedure utilizes a reaction between I2 and oleylamine that yields oleylammonium iodide -the iodide precursor for a subsequent preparation of nanocrystals. The syntheses are facile, carried out under air, in vials heated on a hotplate and deliver nanocrystals with narrow size distributions and, in the case of red and near infrared-emitting lead-based perovskites, with 70-80% photoluminescence quantum yields. The latter were used to fabricate red and infrared bright light-emitting diodes, with external quantum efficiencies (EQE) exceeding 3%