Symmetry-breaking substitutions of [Re(CN)8]3- into the centered, face-capped octahedral clusters (CH3OH)24M9M'6(CN)48 (M = Mn, Co; M = Mo, W)

The diamagnetic complex [Re(CN)8]3- is shown to react with Mn2+ ions in methanol to generate the centered, face-capped octahedral cluster (CH3OH)24Mn9Re6(CN)48, which is structurally analogous to (CH3OH)24Mn9Mo6(CN)48. Related reactions involving stoichiometric mixtures of octacyanometalate complexes generate the substituted species (CH3OH)24Mn9Mo5Re(CN)48, (CH3OH)24Co9Mo5Re(CN)48, (CH3OH)24Mn9Mo3Re3(CN)48, (CH3OH)24Mn9W5Re(CN)48 and (CH3OH)24Co9W5Re(CN)48, in which the O(h) symmetry of the cluster core is broken. Reassessment of the magnetic properties of the Mn9Mo6(CN)48 cluster confirm that it possesses a ground state spin of S = 39/2, but does not exhibit single-molecule-magnet behavior. Lowering the symmetry of the molecule by substitutions of ReV at one or three of the MoV sites does not lead to an overall increase in the magnetic anisotropy, as probed by ac magnetic susceptibility measurements. A similar result occurs for the other substituted species, with the important exception of the new single-molecule magnet (CH3OH)24Co9W5Re(CN)48, for which the spin reversal barrier is significantly reduced relative to that observed previously in (CH3OH)24Co9W6(CN)48.     

Upper bound for the magnetic force gradient in graphite

In this work we investigate possible ferromagnetic order on the graphite surface by using magnetic force microscopy (MFM). Our data show that the tip-sample interaction along the steps is independent of an external magnetic field. Moreover, by combining kelvin probe force microscopy and MFM, we are able to separate the electrostatic and magnetic interactions along the steps obtaining an upper bound for the magnetic force gradient of 16 μN/m. Our experiments suggest the absence of ferromagnetic signal in graphite at room temperature.     

Arrangements of minors in the positive Grassmannian and a triangulation of the hypersimplex

The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. In this paper, we investigate an even richer structure of possible equalities and inequalities between the minors in the positive Grassmannian. It was previously shown that arrangements of equal minors of largest value are in bijection with the simplices in a certain triangulation of the hypersimplex that was studied by Stanley, Sturmfels, Lam and Postnikov. Here, we investigate the entire set of arrangements and its relations with this triangulation. First, we show that second largest minors correspond to the facets of the simplices. We then introduce the notion of cubical distance on the dual graph of the triangulation and study its relations with the arrangement of t-th largest minors. Finally, we show that arrangements of largest minors induce a structure of a partially ordered set on the entire collection of minors. We use this triangulation of the hypersimplex to describe a two-dimensional grid structure on this poset.     

Preparation,Characterization and Application of Modified Surfaces with 3,5-Bis(3,5-dinitrobenzoyl-amino) benzoic acid

Summary: The spontaneous adsorption of the dendron 3,5-Bis (3,5-dinitrobenzoylamino) benzoic acid (D-NO₂) onto gold and carbon electrodes produced conductive surfaces with electroactive chemical functions. A comparative electrochemical behavior of both electrodes after dendron immobilization led us to conclude that the self-assembly of D-NO₂ on carbon is faster and stronger. Considering this advantage, the surface of magnetic maghemite nanoparticles (MNPs) was modified using D-NO₂. Firstly, MNPs were modified with APS as silane coupling agent and afterwards, D-NO₂ was covalently attached to the surface, achieving nitro-functionalized MNPs. Subsequently, the immobilization of these modified MNPs onto glassy carbon surfaces was explored to generate a novel platform promising for biosensors development.     

Synthesis and Properties of Dendronized Chitosan

Summary: Chitosan films and microspheres were prepared and their surfaces were functionalized with first generation dendritic molecules. The films were modified by Weisocyanate dendron, while Behera's and bis Behera's amine dendrons were used to modify the microspheres. Prior to dendronization films were prepared by blending chitosan with 18% of polyvinyl pyrrolidone (PVP), and casting the resulting mixture. The degree of dendronization reached was 28%. The microspheres were prepared by coacervation/precipitation, after which the surfaces were activated with either epychlorohydrine (ECH) or 1,4-butanediol diglycidyl ether (BDGE). The oxirane groups were utilized to form covalent bonds between chitosan and dendrons. The degree of dendronization yielded with Behera's amine was 60% for both activating agents. When bis Behera's amine was used, the dendronization reached values of 15 and 21% when ECH or BDGE were used, respectively. The dendronized products were characterized through spectroscopic and microscopic studies and by determination of swelling indexes. Only one of the surfaces was dendronized in every film, which therefore presented a hydrophobic and a hydrophilic surface. Since these films maintain the properties of chitosan, they offer interesting potential as dressings for exuding wounds. The different surfaces make the microspheres potentially applicable as carriers for delivery and controlled release of drugs.     

Conjugacy Classes,Class Sums and Character Tables for Hopf Algebras

We extend the notion of conjugacy classes and class sums from finite groups to semisimple Hopf algebras and show that the conjugacy classes are obtained from the factorization of H as irreducible left D(H)-modules. For quasitriangular semisimple Hopf algebras H, we prove that the product of two class sums is an integral combination of the class sums up to d ^?2 where d = dim H. We show also that in this case the character table is obtained from the S-matrix associated to D(H). Finally, we calculate explicitly the generalized character table of D(kS ₃), which is not a character table for any group. It moreover provides an example of a product of two class sums which is not an integral combination of class sums.