Retro–Leapfrog and structure elucidation

Operations on maps are topological-geometrical tools used for transforming a given polyhedral tessellation. Investigation of fullerene structure often needs information on the original map which transformed into a larger molecular structure. Operations leading to the previous, smaller structures are called Retro-operations. They appear particularly useful in studies of structure elucidation or stability of series of fullerenes. The paper presents the first structure affiliation of the well-known C₆₀ fullerene to a family of Leapfrog fullerenes with relatedness being established by map operation. Thus, the tessellation of C₆₀ is described as an Archimedean, joint Sumanene-hexagon covering, in tetrahedral disposition. The other members of family show essentially the same covering and predicted good stability. Related Leapfrog fullerenes showing a disjoint Sumanene covering are also given.     

Electron Transfer Processes at Aryl‐Modified Glassy Carbon Electrode

The effect of a layer of electrochemically grafted 4‐diazo‐N,N‐diethylaniline (DEA) groups on the electron transfer kinetics of redox systems, displaying fast and slow heterogeneous electron transfer rate constants at edge and basal planes of carbon, was investigated. The properties of the modified electrode were characterized by cyclic voltammetry using four different inorganic redox systems (Fe(CN) , Co(phen) , Ru(NH₃) , and IrCl in acidic, neutral, and basic media. Two distinct blocking behaviors and electrostatic effects were observed. More precisely, a strong blocking effect of the grafted layer on Fe(CN) and Co(phen) was found, whereas Ru(NH₃) and IrCl showed to be rather unaffected by the presence of the DEA grafted layer.     

Electron impact mass spectra of 3,5,7-triaryl-and -trialkyl-4H-1,2-diazepines

Electron impact mass spectra of 3,5,7-trisubstituted 4H-1,2-diazepines indicate that aryl substituents lead to N₂ expulsion while alkyl substitutents do not. A common fragmentation pattern is observed and discussed for all alkyldiazepines, most of which are newly reported compounds. Assignments are based on electron impact mass spectra of deuteriated substrates and high resolution mass spectra. A previous interpretation of N₂ expulsion is corrected.     

The Chirality of Icosahedral Fullerenes: a Comparison of the Tripling (leapfrog), Quadrupling (chamfering), and Septupling (capra) Transformations

Fullerene polyhedra of icosahedral symmetry have the midpoints of their 12 pentagonal faces at the vertices of a macroicosahedron and can be characterized by the patterns of their hexagonal faces on the (triangular) macrofaces of this macroicosahedron. The numbers of the vertices in fullerene polyhedra of icosahedral symmetry satisfy the Goldberg equation v=20(h ²+hk+k ²), where h and k are two integers and 0 <h≥ k≥ 0 and define a two-dimensional Goldberg vector G = (h, k). The known tripling (leapfrog), quadrupling (chamfering), and septupling (capra) transformations correspond to the Goldberg vectors (1, 1), (2, 0), and (2, 1), respectively. The tripling and quadrupling transformations applied to the regular dodecahedron generate achiral fullerene polyhedra with the full I _h point group. However, the septupling transformation destroys the reflection operations of the underlying icosahedron to generate chiral fullerene polyhedra having only the I icosahedral rotational point group. Generalization of the quadrupling transformation leads to the fundamental homologous series of achiral fullerene polyhedra having 20 n ² vertices and Goldberg vectors (n, 0). A related homologous series of likewise achiral fullerene polyhedra having 60 n ² vertices and Goldberg vectors (n, n) is obtained by applying the tripling transformation to regular dodecahedral C₂₀ to give truncated icosahedral C₆₀ followed by the generalized operations (as in the case of quadrupling) for obtaining homologous series of fullerenes. Generalization of the septupling (capra) transformation leads to a homologous series of chiral C_20m fullerenes with the I point group and Goldberg vectors G=(h, 1) where m=h ²+h+1.     

A quasistatic contact problem with slip‐dependent coefficient of friction

We consider a mathematical model which describes the bilateral quasistatic contact of a viscoelastic body with a rigid obstacle. The contact is modelled with a modified version of Coulomb's law of dry friction and, moreover, the coefficient of friction is assumed to depend either on the total slip or on the current slip. In the first case, the problem depends upon contact history. We present the classical formulations of the problems, the variational formulations and establish the existence and uniqueness of a weak solution to each of them, when the coefficient of friction is sufficiently small. The proofs are based on classical results for elliptic variational inequalities and fixed point arguments. We also study the dependence of the solutions on the perturbations of the friction coefficient and obtain a uniform convergence result. Copyright © 1999 John Wiley & Sons, Ltd.     

Graft copolymers of polyethylene by atom transfer radical polymerization

Poly(ethylene‐g‐styrene) and poly(ethylene‐g‐methyl methacrylate) graft copolymers were prepared by atom transfer radical polymerization (ATRP). Commercially available poly(ethylene‐co‐glycidyl methacrylate) was converted into ATRP macroinitiators by reaction with chloroacetic acid and 2‐bromoisobutyric acid, respectively, and the pendant‐functionalized polyolefins were used to initiate the ATRP of styrene and methyl methacrylate. In both cases, incorporation of the vinyl monomer into the graft copolymer increased with extent of the reaction. The controlled growth of the side chains was proved in the case of poly(ethylene‐g‐styrene) by the linear increase of molecular weight with conversion and low polydispersity (M_w /M_n < 1.4) of the cleaved polystyrene grafts. Both macroinitiators and graft copolymers were characterized by ¹H NMR and differential scanning calorimetry. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2440–2448, 2000     

Direct fluorescent detection of chromatographically separated amino-acids by means of 9-isothiocyanatoacridines

A new method is presented for fluorescent detection of amino-acids separated on silica gel R plates, by spraying with a 0.1% solution of 9-isothiocyanatoacridine derivatives in dichloromethane or benzene, heating and examining in ultraviolet light at 254 and 336 nm. This method is useful for routine analysis owing to its selectivity and sensitivity.     

Effect of dopant on the physical properties of polymer films for microphotonics

This paper presents experimental results concerning the influence of the additives on the physical properties of polymer films. Metal oxides/inorganic salts were used as additives in vinyl-polymers solutions. The physical properties of the metal doped polymer films can be significantly modified by the composition of the doping elements and the curing conditions of the polymer. Morphologic, electronic, magnetic and optic properties of the doped polymers were analysed by AFM, SEM, Mössbauer spectroscopy and optical measurements. The film composition and the deposition processes were optimized to allow a better control of the optical parameters (refractive index, transmission), to reduce the processing temperatures and to improve the chemical sensitivity of the films for sensor applications. These compounds can be easily spin coated onto a variety of directly patterned semiconductor substrates.     

Higher-dimensional Ahlfors-Beurling type inequalities in Clifford analysis

A generalization to higher dimensions of a classical inequality due to Ahlfors and Buerling is proved. As a consequence, an extension of Alexander's quantitative version of Hartogs-Rosenthal Theorem is derived. Both results are stated and proved within the framework of Clifford analysis.