Mechanistic studies of the electro-oxidation pathway of ammonia in several room-temperature ionic liquids

A mechanistic study of the direct oxidation of ammonia has been reported in several room-temperature ionic liquids (RTILs), namely, [C(4)mim][BF4], [C(4)mim][OTf], [C(2)mim][NTf2], [C(4)mim][NTf2], and [C(4)mim][PF6], on a 10 mu m diameter Pt microdisk electrode. In four of the RTILs studied, the cyclic voltammetric analysis suggests that ammonia is initially oxidized to nitrogen, N-2, and protons, which are transferred to an ammonia molecule, forming NH4+ via the protonation of the anion(s) (A(-)). In contrast, NH4+ is formed first in [C(4)mim][PF6], followed by the protonated anion(s), HA. In all five RTILs, both HA and NH4+ are reduced at the electrode surface, forming hydrogen gas, which is then oxidized. The effect of changing the RTIL anion is discussed, and this may have implications in the defining of pK(a) in RTIL media. This work also has implications in the possible amperometric sensing of ammonia gas.

An electrochemical study of the oxidation of hydrogen at platinum electrodes in several room temperature ionic liquids

The electrochemical oxidation of dissolved hydrogen gas has been studied in a range of room-temperature ionic liquids (RTILs), namely [C(2)mim][NTf2], [C(4)mim][NTf2], [N-6,N-2,N-2,N-2][NTf2], [P-14,P-6,P-6,P-6][NTf2], [C(4)mpyrr][NTf2], [C(4)mim][BF4], [C(4)mim][PF6], [C(4)mim][OTf], and [C(6)mim]Cl on a platinum microdisk electrode of diameter 10 mu m. In all cases, except [C(6)mim]Cl, a broad quasi-electrochemically reversible oxidation peak between 0.3 to 1.3 V vs Ag was seen prior to electrode activation ([C(6)mim]Cl showed an almost irreversible wave). When the electrode was pre-anodized (

Electroreduction of Chlorine Gas at Platinum Electrodes in Several Room Temperature Ionic Liquids: Evidence of Strong Adsorption on the Electrode Surface Revealed by Unusual Voltammetry in Which Currents Decrease with Increasing Voltage Scan Rates

Voltammetry is reported for chlorine, Cl-2, dissolved in various room temperature ionic liquids using platinum microdisk electrodes. A single reductive voltammetric wave is seen and attributed to the two-electron reduction of chlorine to chloride. Studies of the effect of voltage scan rate reveal uniquely unusual behavior in which the magnitude of the currents decrease with increasing scan rates. A model for this is proposed and shown to indicate the presence of strongly adsorbed species in the electrode reaction mechanism, most likely chlorine atoms, Cl*((ads)).

SuperWASP observations of long timescale photometric variations in cataclysmic variables

Aims: We investigated whether the predictions and results of Stanishev et al. (2002, A&A, 394, 625) concerning a possible relationship between eclipse depths in PX And and its retrograde disc precession phase, could be confirmed in long term observations made by SuperWASP. In addition, two further CVs (DQ Her and V795 Her) in the same SuperWASP data set were investigated to see whether evidence of superhump periods and disc precession periods were present and what other, if any, long term periods could be detected. Methods: Long term photometry of PX And, V795 Her and DQ Her was carried out and Lomb-Scargle periodogram analysis undertaken on the resulting light curves. For the two eclipsing CVs, PX And and DQ Her, we analysed the potential variations in the depth of the eclipse with cycle number. Results: The results of our period and eclipse analysis on PX And confirm that the negative superhump period is 0.1417 ± 0.0001d. We find no evidence of positive superhumps in our data suggesting that PX And may have been in a low state during our observations. We improve on existing estimates of the disc precession period and find it to be 4.43 ± 0.05d. Our results confirm the predictions of Stanishev et al. (2002). We find that DQ Her does not appear to show a similar variation for we find no evidence of negative superhumps or of a retrograde disc precession. We also find no evidence of positive superhumps or of a prograde disc precession and we attribute the lack of positive superhumps in DQ Her to be due to the high mass ratio of this CV. We do however find evidence for a modulation of the eclipse depth over a period of 100 days which may be linked with solar-type magnetic cycles which give rise to long term photometric variations. The periodogram analysis for V795 Her detected the likely positive superhump period 0.1165d, however, neither the 0.10826d orbital period nor the prograde 1.53d disc precession period were seen. Here though we have found a variation in the periodogram power function at the positive superhump period, over a period of at least 120 days.

The electrochemical reduction of the purines guanine and adenine at platinum electrodes in several room temperature ionic liquids

The reduction of guanine was studied by microelectrode voltammetry in the room temperature ionic liquids (RTILs) N-hexyltriethylammonium his (trifluoromethanesulfonyl) imide [N-6.2.2.2][N(Tf)(2)], 1-butyl-3-methylimidazolium hexafluorosphosphate [C(4)mim] [PF6], N-butyl-N-methyl-pyrrolidinium bis(trifluoromethanesulfonyl)imide [C(4)mpyrr][N(Tf)(2)], 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide [C-4mim][N(TF)(2)], N-butyl-N-methyl-pyrrolidinium dicyanamide [C(4)mpyrr][N(NC)(2)] and tris(P-hexyl)-tetradecylphosphonium trifluorotris(pentafluoroethyl)phosphate [P-14,P-6,(6,6)][FAP] on a platinum microelectrode. In [N-6,N-2,N-2,N-2][NTf2] and [P-14,P-6,P-6.6][FAP], but not in the other ionic liquids studied, guanine reduction involves a one-electron, diffusion-controlled process at very negative potential to produce an unstable radical anion. which is thought to undergo a dimerization reaction, probably after proton abstraction from the cation of the ionic liquid. The rate of this subsequent reaction depends on the nature of the ionic liquid, and it is faster in the ionic liquid [P-14,P-6,P-6.6[FAP], in which the formation of the resulting dimer can be voltammetrically monitored at less negative potentials than required for the reduction of the parent molecule. Adenine showed similar behaviour to guanine but the pyrimidines thymine and cytosine did not; thymine was not reduced at potentials less negative than required for solvent (RTIL) decomposition while only a poorly defined wave was seen for cytosine. The possibility for proton abstraction from the cation in [N-6,N-2,N-2,N-2],[NTF2] and [P-14,P-6,P-6.6][FAP] is noted and this is thought to aid the electrochemical dimerization process. The resulting rapid reaction is thought to shift the reduction potentials for guanine and adenine to lower values than observed in RTILs where the scope for proton abstraction is not present. Such shifts are characteristic of so-called EC processes where reversible electron transfer is followed by a chemical reaction. (C) 2009 Elsevier B.V. All rights reserved.

Finite domination and Novikov rings: Laurent polynomial rings in two variables

Let C be a bounded cochain complex of finitely generatedfree modules over the Laurent polynomial ring L = R[x, x−1, y, y−1].The complex C is called R-finitely dominated if it is homotopy equivalentover R to a bounded complex of finitely generated projective Rmodules.Our main result characterises R-finitely dominated complexesin terms of Novikov cohomology: C is R-finitely dominated if andonly if eight complexes derived from C are acyclic; these complexes areC ⊗L R[[x, y]][(xy)−1] and C ⊗L R[x, x−1][[y]][y−1], and their variants obtainedby swapping x and y, and replacing either indeterminate by its inverse.

The Riemann-Hilbert method applied to the theory of orthogonal polynomials

Doutoramento em Matemática

Structures algébriques, systèmes superintégrables et polynômes orthogonaux

Cette thèse est divisée en cinq parties portant sur les thèmes suivants: l’interprétation physique et algébrique de familles de fonctions orthogonales multivariées et leurs applications, les systèmes quantiques superintégrables en deux et trois dimensions faisant intervenir des opérateurs de réflexion, la caractérisation de familles de polynômes orthogonaux appartenant au tableau de Bannai-Ito et l’examen des structures algébriques qui leurs sont associées, l’étude de la relation entre le recouplage de représentations irréductibles d’algèbres et de superalgèbres et les systèmes superintégrables, ainsi que l’interprétation algébrique de familles de polynômes multi-orthogonaux matriciels. Dans la première partie, on développe l’interprétation physico-algébrique des familles de polynômes orthogonaux multivariés de Krawtchouk, de Meixner et de Charlier en tant qu’éléments de matrice des représentations unitaires des groupes SO(d+1), SO(d,1) et E(d) sur les états d’oscillateurs. On détermine les amplitudes de transition entre les états de l’oscillateur singulier associés aux bases cartésienne et polysphérique en termes des polynômes multivariés de Hahn. On examine les coefficients 9j de su(1,1) par le biais du système superintégrable générique sur la 3-sphère. On caractérise les polynômes de q-Krawtchouk comme éléments de matrices des «q-rotations» de U_q(sl_2). On conçoit un réseau de spin bidimensionnel qui permet le transfert parfait d’états quantiques à l’aide des polynômes de Krawtchouk à deux variables et on construit un modèle discret de l’oscillateur quantique dans le plan à l’aide des polynômes de Meixner bivariés. Dans la seconde partie, on étudie les systèmes superintégrables de type Dunkl, qui font intervenir des opérateurs de réflexion. On examine l’oscillateur de Dunkl en deux et trois dimensions, l’oscillateur singulier de Dunkl dans le plan et le système générique sur la 2-sphère avec réflexions. On démontre la superintégrabilité de chacun de ces systèmes. On obtient leurs constantes du mouvement, on détermine leurs algèbres de symétrie et leurs représentations, on donne leurs solutions exactes et on détaille leurs liens avec les polynômes orthogonaux du tableau de Bannai-Ito. Dans la troisième partie, on caractérise deux familles de polynômes du tableau de Bannai-Ito: les polynômes de Bannai-Ito complémentaires et les polynômes de Chihara. On montre également que les polynômes de Bannai-Ito sont les coefficients de Racah de la superalgèbre osp(1,2). On détermine l’algèbre de symétrie des polynômes duaux -1 de Hahn dans le cadre du problème de Clebsch-Gordan de osp(1,2). On propose une q - généralisation des polynômes de Bannai-Ito en examinant le problème de Racah pour la superalgèbre quantique osp_q(1,2). Finalement, on montre que la q -algèbre de Bannai-Ito sert d’algèbre de covariance à osp_q(1,2). Dans la quatrième partie, on détermine le lien entre le recouplage de représentations des algèbres su(1,1) et osp(1,2) et les systèmes superintégrables du deuxième ordre avec ou sans réflexions. On étudie également les représentations des algèbres de Racah-Wilson et de Bannai-Ito. On montre aussi que l’algèbre de Racah-Wilson sert d’algèbre de covariance quadratique à l’algèbre de Lie sl(2). Dans la cinquième partie, on construit deux familles explicites de polynômes d-orthogonaux basées sur su(2). On étudie les états cohérents et comprimés de l’oscillateur fini et on caractérise une famille de polynômes multi-orthogonaux matriciels.