SINGULARITY THEORY AND FORCED SYMMETRY BREAKING IN EQUATIONS

A theory of bifurcation equivalence for forced symmetry breaking bifurcation problems is developed. We classify (O(2), 1) problems of corank 2 of low codimension and discuss examples of bifurcation problems leading to such symmetry breaking.

On the open-circuit interaction between methanol and oxidized platinum electrodes

In the present work, results of the interaction between methanol and oxidized platinum surfaces as studied via transients of open-circuit potentials are presented. The surface oxidation before the exposure to interaction with 0.5 M methanol was performed at different polarization times at 1.4 V vs reversible hydrogen electrode (RHE). In spite of the small changes in the initial oxide content, the increase of the pre-polarization time induces a considerable increase of the time needed for the oxide consumption during its interaction with methanol. The influence of the identity of the chemisorbing anion on the transients was also investigated in the following media: 0.1 M HClO4, 0.5 M H2SO4, and 0.5 M H2SO4 + 0.1 mM Cl-. It was observed that the transient time increases with the energy of anion chemisorption and, more importantly, without a change in the shape of the transient, meaning that free platinum sites are available at the topmost layer all over the transient and not only in the potential region of small oxide `coverage`. The impact of the pre-polarization time and the effect of anion chemisorption on the transients are rationalized in terms of the presence of surface and subsurface oxygen driven by place exchange.

Stabilizing Nonstationary Electrochemical Time Series

Electrochemical systems are ideal working-horses for studying oscillatory dynamics. Experimentally obtained time series, however, are usually associated with a spontaneous drift in some uncontrollable parameter that triggers transitions among different oscillatory patterns, despite the fact that all controllable parameters are kept constant. Herein we present an empirical method to stabilize experimental potential time series. The method consists of applying a negative galvanodynamic sweep to compensate the spontaneous drift and was tested for the oscillatory electro-oxidation of methanol on platinum. For a wide range of applied currents, the base system presents spontaneous transitions from quasi-harmonic to mixed mode oscillations. Temporal patterns were stabilized by galvanodynamic sweeps at different rates. The procedure resulted in a considerable increase in the number of oscillatory cycles from 5 to 20 times, depending on the specific temporal pattern. The spontaneous drift has been associated with uncompensated oscillations, in which the coverage of some adsorbed species are not reestablished after one cycle; i.e., there is a net accumulation and/or depletion of adsorbed species during oscillations. We interpreted the rate of the galvanodynamic sweep in terms of the time scales of the poisoning processes that underlies the uncompensated oscillations and thus the spontaneous slow drift.

Nanogravimetric study of the complex voltammetric response in the electro-oxidation of methanol on platinum

Instead of a time-invariant voltammetric profile, many electrochemical systems display a cycle-dependent current-potential response. This phenomenon has been referred to as complex voltammetric response and it has been observed during the electro-oxidation of several molecules such as methanol, ethanol, propanol and hydrogen. There are currently two explanations for the surface mechanism underlying this behavior. In one scenario, the complex voltammogram would result from the specific kinetic pathway taken during the forward sweep. In the other explanation, the phenomenon is discussed in terms of the interplay among the surface roughening and subsequent relaxation, and the ohmic drop coupled to a negative differential resistance. We report in this paper a nanogravimetric investigation of the complex voltammetric response in the electro-oxidation of methanol on platinum electrode in both acidic and alkaline media. Different periodic patterns composed of intercalated small and large hysteresis cycles were observed as a function of the applied voltage and the series resistance between the working electrode and the potentiostat. Independently, nanogravimetric results indicated no detectable difference in the delta-frequency versus voltage profile between small and large hysteresis cycles. These findings were interpreted as experimental evidence of the secondary, if any, role played by the very electrochemical reaction on the emergence of complex voltammetric response. (C) 2009 Elsevier Ltd. All rights reserved.