On the Cartan–Jacobson Theorem

The well-known Cartan–Jacobson theorem claims that the Lie algebra of derivations of a Cayley algebra is central simple if the characteristic is not 2 or 3. In this paper we have studied these two cases, with the following results: if the characteristic is 2, the theorem is also true, but, if the characteristic is 3, the derivation algebra is not simple. We have also proved that in this last case, there is a unique nonzero proper seven-dimensional ideal, which is a central simple Lie algebra of type A₂, and the quotient of the derivation algebra modulo this ideal turns out to be isomorphic, as a Lie algebra, to the ideal itself. The original motivation of this work was a series of computer-aided calculations which proved the simplicity of derivation algebras of Cayley algebras in the case of characteristic not 3. These computations also proved the existence of a unique nonzero proper ideal (which turns out to be seven-dimensional) in the algebra of derivations of split Cayley algebras in characteristic 3.     

Nanoindentation on carbon thin films obtained from a C60 ion beam

Raman spectra, atomic force microscope (AFM) images, hardness (H) and Young's modulus (E) measurements were carried out in order to characterize carbon thin films obtained from a C₆₀ ion beam on silicon substrates at different deposition energies (from 100 up to 500 eV). The mechanical properties were studied via the nanoindentation technique. It has been observed by Raman spectroscopy and AFM that the microstructure presents significant changes for films deposited at energies close to 300 eV. However, these remarkable changes have not been noticeable on the mechanical properties: apparently H and E increase with higher deposition energy up to ∼11 and ∼116 GPa, respectively. These values are underestimated if the influence of the film roughness is not taken into account.     

Photoinitiated polymerization in bicontinuous microemulsions: Fluorescence monitoring

The photopolymerization of bicontinuous microemulsions was simultaneously monitored with differential scanning calorimetry and fluorescence. The kinetics and mechanism of the reaction were studied throughout the entire photopolymerization reaction. The role played by the surfactant in the kinetics and morphology was studied. The nature of the surfactant changed the autoacceleration process and final conversion. The behavior was explained as a result of the differences in the interfacial properties. Anionic cetyltrimethylammonium bromide (CTAB) gave rise to a more flexible interfacial film than anionic sodium dodecyl sulfate (SDS), resulting in competition between the intramolecular and intermolecular reactions in the former systems. As cyclization did not contribute to the increase in the degree of crosslinking, SDS photopolymerization gave solids with a more rigid microstructure. Fluorescence methodology was applied to monitor bicontinuous microemulsion polymerization and to reveal the microstructure and morphology development during photopolymerization. The microemulsion composition was designed to prepare nanoporous, crosslinked materials. Even though the nanostructure of the precursor microemulsions was not retained because of phase separation during polymerization, mesoporous solids were obtained. Their morphologies depended on the nature of the surfactant, and membranes with open cells were successfully prepared with CTAB, whereas more complex morphologies resulted with SDS. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5291–5303, 2006     

Lightly crosslinked,mesomorphic networks obtained through the reaction of dimeric,liquid‐crystalline epoxy–imine monomers and heptanedioic acid

We reacted various dimeric, liquid‐crystalline epoxy–imine monomers, differing in the length of the central aliphatic spacer or the dipolar moments, with heptanedioic acid. The resulting systems showed a liquid‐crystalline phase in some cases, depending on the dimer and on the reaction conditions. The systems were characterized with respect to their mesomorphic properties and then were submitted to dynamic mechanical thermal analysis in both fixed‐frequency and frequency‐sweep modes in the shear sandwich configuration. The arrangement in the liquid‐crystalline phase seemed to be mainly affected both by the polarization of the mesogen and by the reaction temperature, which favored the liquid‐crystalline arrangement when it was lying in the range of stability of the dimer mesophase. In agreement with other recent literature data, dynamic mechanical thermal analysis results suggested that the presence of the mesogen directly incorporated into the main chain increased the lifetimes of the elastic modes both in the isotropic phase and in the liquid‐crystalline phase with respect to side‐chain liquid‐crystalline elastomers and that the time–temperature superposition principle did not hold through the liquid‐crystalline‐to‐isotropic transition. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44:6270–6286, 2006     

Vinyl‐terminated side‐chain liquid‐crystalline polyethers containing mesogenic benzylideneaniline moieties

The synthesis of two vinyl‐terminated side‐chain liquid‐crystalline polyethers containing benzylideneaniline moieties as mesogenic cores was approached in two different ways: by chemically modifying poly(epichlorohydrin) with suitable mesogenic acids or by polymerizing analogous glycidyl ester or glycidyl ether derivatives. In all the conditions tested, the first approach led to materials in which the imine group was hydrolyzed. The second approach led to the desired polymers PG2a and PG2b , but only from the glycidyl ether derivatives and when the initiator was the system that combined polyiminophosphazene base t‐Bu‐P₄ and 3,5‐di‐t‐butylphenol. These polymers were chemically characterized by IR and ¹H and ¹³C NMR spectroscopies. The estimated degrees of polymerization ranged from 30 to 36. The liquid crystalline behavior of the synthesized polymers was studied by differential scanning calorimetry, polarized optical microscopy (POM) and X‐ray diffraction. Both polymers behave like liquid crystals and exhibited a single mesophase, which was recognized as a smectic C mesophase, probably with a bilayer arrangement, i.e., a smectic C₂ mesophase. The crosslinking of both polymers was performed with dicumyl peroxide as initiator, which led to liquid crystalline thermosets. POM and X‐ray diffraction confirmed that the mesophase organization mantained on the crosslinked materials. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1877–1889, 2006     

N,N‐dimethylaminopyridine as initiator in the copolymerization of diglycidylether of bisphenol A with six‐membered cyclic carbonates

N,N‐Dimethylaminopyridine (DMAP) was used as initiator to cure mixtures of diglycidylether of bisphenol A (DGEBA) and 1,3‐dioxan‐2‐one (TMC) or 5,5‐dimethyl‐1,3‐dioxan‐2‐one (DMTMC). The curing was studied by differential scanning calorimetry (DSC) and Fourier transform infrared in the attenuated‐total‐reflection mode (FTIR/ATR). FTIR/ATR was used to monitor the competitive reactive processes and to quantify the evolution of the groups involved in the curing. We observed the formation of five‐membered cyclic carbonates and anionic carbonate groups that remain unreacted at the chain ends. The formation of these groups was explained by the attack of the anionic propagation species on the methylene carbon of the carbonate group, which leads to an alkyl‐oxygen rupture. By performing the cure in the thermobalance we could evaluate the loss of CO₂ produced in the samples containing carbonates. The kinetics were studied by DSC and analyzed with isoconversional procedures. The addition of carbonates slows down the curing rate. Thermogravimetric analysis (TGA) and dynamic mechanical thermal analysis (DMTA) experiments were used to evaluate the properties of the materials obtained. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2873–2882, 2006     

Effect of the environment on the stability of surfactant–polypeptide self‐assembled complexes: Molecular dynamics simulations of stoichiometric complexes formed by N‐dodecyltrimethylammonium and poly(α,L‐glutamate) in chloroform,methanol, and water

A series of molecular dynamics simulations have been performed to study the supramolecular structure of self‐assembled complexes formed by N‐dodecyltrimethylammonium cations and the synthetic polypeptide poly(α,L ‐glutamate). The influence of the type of solvent has been investigated, considering explicit environments of chloroform, water, and methanol on a stoichiometric complex containing 15 residues. In chloroform, the complex stabilizes in a regular structure: the polypeptide adopts an α‐helix conformation that is regularly surrounded by surfactant molecules to form electrostatic interactions through a multiple interaction pattern. However, this structure destabilizes in methanol and water: (a) the α‐helix unfolds in the two solvents and (b) the electrostatic links between the surfactant molecules and the polyanion are disrupted in aqueous solution, although these interactions are still preserved in methanol. The role of the solvent environment in stabilizing or destabilizing the polypeptide secondary structure, the organization of the surfactant molecules, and predominantly the surfactant–polypeptide supramolecular organization is discussed in detail. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1122–1133, 2006     

Magneto-volume effects in Fe–Cu solid solutions

The magnetic properties of Fe–Cu metastable solid solutions have been investigated by means of neutron diffraction and magnetisation measurements. These compounds exhibit ferromagnetic order with Curie temperatures above room temperature for concentrations beyond 40 at% in Fe. The magnetic moment at 5 K can reach values over 2 μ_B, while the high field susceptibility is similar to that found in FCC–FeNi Invar alloys. These features together with the low values for the linear coefficient for thermal expansion in the ferromagnetic region suggest that magneto-volume anomalies, including Invar behaviour, play a major role in the magnetic properties of this system when the crystal structure is face centred cubic. Such behaviour could be explained using theoretical total-band energy calculations.