An optimization study of PtSn/C catalysts applied to direct ethanol fuel cell: Effect of the preparation method on the electrocatalytic activity of the catalysts

The aim of this work was to perform a systematic study of the parameters that can influence the composition, morphology, and catalytic activity of PtSn/C nanoparticles and compare two different methods of nanocatalyst preparation, namely microwave-assisted heating (MW) and thermal decomposition of polymeric precursors (DPP). An investigation of the effects of the reducing and stabilizing agents on the catalytic activity and morphology of Pt75Sn25/C catalysts prepared by microwave-assisted heating was undertaken for optimization purposes. The effect of short-chain alcohols such as ethanol, ethylene glycol, and propylene glycol as reducing agents was evaluated, and the use of sodium acetate and citric acid as stabilizing agents for the MW procedure was examined. Catalysts obtained from propylene glycol displayed higher catalytic activity compared with catalysts prepared in ethylene glycol. Introduction of sodium acetate enhanced the catalytic activity, but this beneficial effect was observed until a critical acetate concentration was reached. Optimization of the MW synthesis allowed for the preparation of highly dispersed catalysts with average sizes lying between 2.0 and 5.0 nm. Comparison of the best catalyst prepared by MW with a catalyst of similar composition prepared by the polymeric precursors method showed that the catalytic activity of the material can be improved when a proper condition for catalyst preparation is achieved. (C) 2012 Elsevier B.V. All rights reserved.

No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the 2d gluon propagator

We study general properties of the Landau-gauge Gribov ghost form factor sigma(p(2)) for SU(N-c) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d = 3, 4 with respect to the d = 2 case. In particular, considering any (sufficiently regular) gluon propagator D(p(2)) and the one-loop-corrected ghost propagator, we prove in the 2d case that the function sigma(p(2)) blows up in the infrared limit p -> 0 as -D(0) ln(p(2)). Thus, for d = 2, the no-pole condition sigma(p(2)) < 1 (for p(2) > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, D(0) = 0. On the contrary, in d = 3 and 4, sigma(p(2)) is finite also if D(0) > 0. The same results are obtained by evaluating the ghost propagator G(p(2)) explicitly at one loop, using fitting forms for D(p(2)) that describe well the numerical data of the gluon propagator in two, three and four space-time dimensions in the SU(2) case. These evaluations also show that, if one considers the coupling constant g(2) as a free parameter, the ghost propagator admits a one-parameter family of behaviors (labeled by g(2)), in agreement with previous works by Boucaud et al. In this case the condition sigma(0) <= 1 implies g(2) <= g(c)(2), where g(c)(2) is a "critical" value. Moreover, a freelike ghost propagator in the infrared limit is obtained for any value of g(2) smaller than g(c)(2), while for g(2) = g(c)(2) one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for sigma(p(2)) and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form factor sigma(p(2)). Using these bounds we find again that only in the d = 2 case does one need to impose D(0) = 0 in order to satisfy the no-pole condition. The d = 2 result is also supported by an analysis of the Dyson-Schwinger equation using a spectral representation for the ghost propagator. Thus, if the no-pole condition is imposed, solving the d = 2 Dyson-Schwinger equations cannot lead to a massive behavior for the gluon propagator. These results apply to any Gribov copy inside the so-called first Gribov horizon; i.e., the 2d result D(0) = 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.