A class of singular first order differential equations with applications in reaction-diffusion

Agências Financiadoras: FCT e MIUR

The solvation and electrochemical behaviour of Copper acetylacetonate complexes in ionic liquids

The behavior of copper(II) complexes of pentane-2,4-dione and 1,1,1,5,5,5-hexafluoro-2,4-pentanedione, [Cu(acac)(2) (1) and [Cu(HFacac)(2)(H2O)] (2), in ionic liquids and molecular organic solvents, was studied by spectroscopic and electrochemical techniques. The electron paramagnetic resonance characterization (EPR) showed well-resolved spectra in most solvents. In general the EPR spectra of [Cu(acac)(2)] show higher g(z) values and lower hyperfine coupling constants, A(z), in ionic liquids than in organic solvents, in agreement with longer Cu-O bond lengths and higher electron charge in the copper ion in the ionic liquids, suggesting coordination of the ionic liquid anions. For [Cu(HFacac)(2)(H2O)] the opposite was observed suggesting that in ionic liquids there is no coordination of the anions and that the complex is tetrahedrically distorted. The redox properties of the Cu(II) complexes were investigated by cyclic voltammetry (CV) at a Pt electrode (d = 1 mm), in bmimBF(4) and bmimNTf(2) ionic liquids and, for comparative purposes, in neat organic solvents. The neutral copper(II) complexes undergo irreversible reductions to Cu(I) and Cu(0) species in both ILs and common organic solvents (CH2Cl2 or acetonitrile), but, in ILs, they are usually more easier to reduce (less cathodic reduction potential) than in the organic solvents. Moreover, 1 and 2 are easier to reduce in bmimNTf(2) than in bmimBF(4) ionic liquid. (C) 2013 Elsevier B.V. All rights reserved.

The solvation and redox behaviour of mixed ligand COPPER(II) complexes of acetylacetonate and aromatic dimines in ionic liquids

The behavior of two cationic copper complexes of acetylacetonate and 2,2'-bipyridine or 1,10-phenanthroline, [Cu(acac)(bipy)]Cl (1) and [Cu(acac)(phen)]Cl (2), in organic solvents and ionic liquids, was studied by spectroscopic and electrochemical techniques. Both complexes showed solvatochromism in ionic liquids although no correlation with solvent parameters could be obtained. By EPR spectroscopy rhombic spectra with well-resolved superhyperfine structure were obtained in most ionic liquids. The spin Hamiltonian parameters suggest a square pyramidal geometry with coordination of the ionic liquid anion. The redox properties of the complexes were investigated by cyclic voltammetry at a Pt electrode (d = 1 mm) in bmimBF(4) and bmimNTf(2) ionic liquids. Both complexes 1 and 2 are electrochemically reduced in these ionic media at more negative potentials than when using organic solvents. This is in agreement with the EPR characterization, which shows lower A(z) and higher g(z) values for the complexes dissolved in ionic liquids, than in organic solvents, due to higher electron density at the copper center. The anion basicity order obtained by EPR is NTf2-, N(CN)(2)(-), MeSO4- and Me2PO4-, which agrees with previous determinations. (C) 2013 Elsevier B.V. All rights reserved.

Travelling wave profiles in some models with nonlinear diffusion

We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.

Laser-induced diffusion decomposition in Fe-V thin-film alloys

We investigate the origin of ferromagnetism induced in thin-film (similar to 20 nm) Fe-V alloys by their irradiation with subpicosecond laser pulses. We find with Rutherford backscattering that the magnetic modifications follow a thermally stimulated process of diffusion decomposition, with formation of a-few-nm-thick Fe enriched layer inside the film. Surprisingly, similar transformations in the samples were also found after their long-time (similar to 10(3) s) thermal annealing. However, the laser action provides much higher diffusion coefficients (similar to 4 orders of magnitude) than those obtained under standard heat treatments. We get a hint that this ultrafast diffusion decomposition occurs in the metallic glassy state achievable in laser-quenched samples. This vitrification is thought to be a prerequisite for the laser-induced onset of ferromagnetism that we observe. 2014 Elsevier B.V. All rights reserved.