C-C bond unsaturation degree in monosubstituted ferrocenes for molecular electronics investigated by a combined near-edge x-ray absorption fine structure, x-ray photoemission spectroscopy, and density functional theory approach

We present the results of an experimental and theoretical investigation of monosubstituted ethyl-, vinyl-, and ethynyl-ferrocene (EtFC, VFC, and EFC) free molecules, obtained by means of synchrotron-radiation based C 1s photoabsorption (NEXAFS) and photoemission (C 1s XPS) spectroscopies, and density functional theory (DFT) calculations. Such a combined study is aimed at elucidating the role played by the C-C bond unsaturation degree of the substituent on the electronic structure of the ferrocene derivatives. Such substituents are required for molecular chemical anchoring onto relevant surfaces when ferrocenes are used for molecular electronics hybrid devices. The high resolution C 1s NEXAFS spectra exhibit distinctive features that depend on the degree of unsaturation of the hydrocarbon substituent. The theoretical approach to consider the NEXAFS spectrum made of three parts allowed to disentangle the specific contribution of the substituent group to the experimental spectrum as a function of its unsaturation degree. C 1s IEs were derived from the experimental data analysis based on the DFT calculated IE values for the different carbon atoms of the substituent and cyclopentadienyl (Cp) rings. Distinctive trends of chemical shifts were observed for the substituent carbon atoms and the substituted atom of the Cp ring along the series of ferrocenes. The calculated IE pattern was rationalized in terms of initial and final state effects influencing the IE value, with special regard to the different mechanism of electron conjugation between the Cp ring and the substituent, namely the σ/π hyperconjugation in EtFC and the π-conjugation in VFC and EFC.     

Calix[4]arene‐Functionalised Silver Nanoparticles as Hosts for Pyridinium‐Loaded Gold Nanoparticles as Guests

A series of lipophilic gold nanoparticles (AuNPs) circa 5 nm in diameter and having a mixed organic layer consisting of 1‐dodecanethiol and 1‐(11‐mercaptoundecyl) pyridinium bromide was synthesised by reacting tetraoctylammonium bromide stabilised AuNPs in toluene with different mixtures of the two thiolate ligands. A bidentate ω‐alkylthiolate calix[4]arene derivative was instead used as a functional protecting layer on AgNPs of approximately 3 nm. The functionalised nanoparticles were characterised by transmission electron microscopy (TEM), and by UV/Vis and X‐ray photoelectron spectroscopy (XPS). Recognition of the pyridinium moieties loaded on the AuNPs by the calix[4]arene units immobilised on the AgNPs was demonstrated in solution of weakly polar solvents by UV/Vis titrations and DLS measurements. The extent of Au‐AgNPs aggregation, shown through the low‐energy shift of their surface plasmon bands (SPB), was strongly dependent on the loading of the pyridinium moieties present in the organic layer of the AuNPs. Extensive aggregation between dodecanethiol‐capped AuNPs and the Ag calix[4]arene‐functionalised NPs was also promoted by the action of a simple N‐octyl pyridinium difunctional supramolecular linker. This linker can interdigitate through its long fatty tail in the organic layer of the dodecanethiol‐capped AuNPs, and simultaneously interact through its pyridinium moiety with the calix[4]arene units at the surface of the modified AgNPs.     

An Exceptional Set in the Ergodic Theory of Markov Maps of the Interval

It is known that a Markov map T of the unit interval preservesa measure µ, say, equivalent to Lebesgue measure, andthat almost every point of the interval has a forward orbitunder T that is uniformly distributed with respect to µ.In the opposite direction the main result of this paper statesthat there is a set of points having Hausdorff dimension 1 whoseforward orbits are in a certain sense very far from being sodistributed. 1991 Mathematics Subject Classification: 58F08,28A80.     

Killing Symmetries of Generalized Minkowski Spaces, 3: Spacetime Translations in Four Dimensions

In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e., a space endowed with a (in general non-diagonal) metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the translations in such spaces, by confining ourselves (without loss of generality) to the four-dimensional case. In particular, the results obtained are specialized to the case of a deformed Minkowski space (i.e. a pseudoeuclidean space with metric coefficients depending on energy).     

Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems

We determine explicit orbit representatives of reducible Jordan algebras and their corresponding Freudenthal triple systems. This work has direct application to the classification of extremal black hole solutions of ${\mathcal{N}=2}$ , 4 locally supersymmetric theories of gravity coupled to an arbitrary number of Abelian vector multiplets in D = 4, 5 space-time dimensions.     

Lectures on attractors and black holes

A basic survey on some aspects of four‐dimensional black holes (BHs) is given in these lectures. It covers thermodynamical properties as well as the Attractor Mechanism for extremal BHs in an environment of scalar field background. Some relevant formulæ for the critical points of the BH “effective potential” are discussed, and the simplest example uncovering the attractor behavior, the Maxwell‐Einstein‐dilaton supergravity, is analyzed in detail. Observations on similarities between BH entropy (as given by the Bekenstein‐Hawking entropy‐area formula) and multipartite entanglement of qubits in quantum information theory are reported, as well. Finally, among the latest developments, the moduli space of attractor points for 𝒩 ≥ 2 supergravities is also considered. Based on lectures given by S. Ferrara at the International School of Subnuclear Physics, 45th Course: Search for the “Totally Unexpected” in the LHC era, Erice, Italy, 29 August – 7 September 2007 (Directors: G. 't Hooft – A. Zichichi), and at the III Avogadro Meeting on Theoretical Physics, Alessandria, Italy, 19 – 21 December 2007.