Anodic and Cathodic Platinum Dissolution Processes Involve Different Oxide Species

The degradation of Pt-containing oxygen reduction catalysts for fuel cell applications is strongly linked to the electrochemical surface oxidation and reduction of Pt. Here, we study the surface restructuring and Pt dissolution mechanisms during oxidation/reduction for the case of Pt(100) in 0.1 M HClO₄ by combining operando high-energy surface X-ray diffraction, online mass spectrometry, and density functional theory. Our atomic-scale structural studies reveal that anodic dissolution, detected during oxidation, and cathodic dissolution, observed during the subsequent reduction, are linked to two different oxide phases. Anodic dissolution occurs predominantly during nucleation and growth of the first, stripe-like oxide. Cathodic dissolution is linked to a second, amorphous Pt oxide phase that resembles bulk PtO₂ and starts to grow when the coverage of the stripe-like oxide saturates. In addition, we find the amount of surface restructuring after an oxidation/reduction cycle to be potential-independent after the stripe-like oxide has reached its saturation coverage.     

Synthesis,X‐ray characterization and density functional theory studies of N6‐benzyl‐N6‐methyladenine–M(II) complexes (M = Zn,Cd): The prominent role of π–π, C–H···π and anion–π interactions

We report the synthesis and X‐ray characterization of the N⁶‐benzyl‐N⁶‐methyladenine ligand (L) and three metal complexes, namely [Zn(HL)Cl₃]·H₂O ( 1 ), [Cd(HL)₂Cl₄] ( 2 ) and [H₂L]₂[Cd₃(μ‐L)₂(μ‐Cl)₄Cl₆]·3H₂O ( 3 ). Complex 1 consists of the 7H‐adenine tautomer protonated at N3 and coordinated to a tetrahedral Zn(II) metal centre through N9. The octahedral Cd(II) in complex 2 is N⁹‐coordinated to two N⁶‐benzyl‐N⁶‐methyladeninium ligands (7H‐tautomer protonated at N3) that occupy apical positions and four chlorido ligands form the basal plane. Compound 3 corresponds to a trinuclear Cd(II) complex, where the central Cd atom is six‐coordinated to two bridging μ‐L and four bridging μ‐Cl ligands. The other two Cd atoms are six‐coordinated to three terminal chlorido ligands, to two bridging μ‐Cl ligands and to the bridging μ‐L through N3. Essentially, the coordination patterns, degree of protonation and tautomeric forms of the nucleobase dominate the solid‐state architectures of 1 – 3 . Additionally, the hydrogen‐bonding interactions produced by the endocyclic N atoms and NH groups stabilize high‐dimensional‐order supramolecular assemblies. Moreover, energetically strong anion–π and lone pair (lp)–π interactions are important in constructing the final solid‐state architectures in 1 – 3 . We have studied the non‐covalent interactions energetically using density functional theory calculations and rationalized the interactions using molecular electrostatic potential surfaces and Bader's theory of atoms in molecules. We have particularly analysed cooperative lp–π and anion–π interactions in 1 and π⁺–π⁺ interactions in 3 .     

Markov shifts and topological entropy of families of homoclinic tangles

The existence of a homoclinic orbit in dynamical systems implies chaotic behaviour with positive entropy. In this work, we determine explicitly the Markov shifts associated to certain Smale horseshoe homoclinic orbits which allow us to compute a lower bound for the topological entropy that such a system can have. It is done associating a heteroclinic orbit which belongs to the same isotopy class and then determining the Markov partition of the dynamical core of an end periodic mapping.     

Few associative triples,isotopisms and groups

Let Q be a quasigroup. For \(\alpha ,\beta \in S_Q\) let \(Q_{\alpha ,\beta }\) be the principal isotope \(x*y = \alpha (x)\beta (y)\). Put \(\mathbf a(Q)= |\{(x,y,z)\in Q^3;\) \(x(yz)) = (xy)z\}|\) and assume that \(|Q|=n\). Then \(\sum _{\alpha ,\beta }\mathbf a(Q_{\alpha ,\beta })/(n!)^2 = n^2(1+(n-1)^{-1})\), and for every \(\alpha \in S_Q\) there is \(\sum _\beta \mathbf a(Q_{\alpha ,\beta })/n! = n(n-1)^{-1}\sum _x(f_x^2-2f_x+n)\ge n^2\), where \(f_x=|\{y\in Q;\) \( y = \alpha (y)x\}|\). If G is a group and \(\alpha \) is an orthomorphism, then \(\mathbf a(G_{\alpha ,\beta })=n^2\) for every \(\beta \in S_Q\). A detailed case study of \(\mathbf a(G_{\alpha ,\beta })\) is made for the situation when \(G = \mathbb Z_{2d}\), and both \(\alpha \) and \(\beta \) are “natural” near-orthomorphisms. Asymptotically, \(\mathbf a(G_{\alpha ,\beta })>3n\) if G is an abelian group of order n. Computational results: \(\mathbf a(7) = 17\) and \(\mathbf a(8) \le 21\), where \(\mathbf a(n) = \min \{\mathbf a(Q);\) \( |Q|=n\}\). There are also determined minimum values for \(\mathbf a(G_{\alpha ,\beta })\), G a group of order \(\le 8\).     

On the Hahn-Banach Theorem in Certain Linear Quasi-uniform Structures

A Hahn-Banach type theorem in the frame of quasi-normed spaces (a class of linear spaces with a quasi-uniform structure that contains all linear lattices) is given. The classical result for positive functionals follows as a particular case.     

Charge transfer properties of Tröger base derivatives

Two triarylamine centers bridged through an aliphatic bridge feature unexpected charge transfer properties, bearing an important electronic coupling between them in the absence of a π linker; EPR, electrochemistry, electronic spectroscopy and first principles molecular calculations are combined to study the electronic structure of this compound.