Search results for "Solution of Schrödinger equation for a step potential"
showing 9 items of 9 documents
Application of a Novel Refinement Method for Accurate Determination of Chemical Diffusion Coefficients in Electroactive Materials by Potential Step T…
2005
We describe application of a novel refinement method for an accurate determination of the chemical diffusion coefficient, D, and the generalized kinetic parameter, A, from experimental potentiostatic intermittent titration technique (PITT) data suited for a variety of electrochemically doped electroactive polymers and inorganic intercalation host materials. The proposed, simple, two-step refinement procedure, based on earlier derived analytical expressions for the PITT response, is exemplified by the analysis of chronoamperometric responses to small-amplitude potential perturbation for p- and n-doped poly(fluorenone-bithiophene) (PFDOBT-HH) thin film electrode. The initial p-doping and the …
Spatially limited diffusion coupled with ohmic potential drop and/or slow interfacial exchange: a new method to determine the diffusion time constant…
2004
Abstract We have analyzed chronoamperometric curves, I ( t ), after small-amplitude potential steps Δ E (PITT technique) for the model of linear diffusion of a species inside an electroactive film, taking into account ohmic effects in the external media (solution and electrode) as well as a finite rate of the interfacial exchange. For its short-time interval, t ≪ τ d ( τ d is the diffusion time constant, corresponding to unlimited diffusion from the interface), three approximate analytical expressions have been proposed. One of these represents an interpolation formula between the value of the current at the start of the diffusion process, I (0)=Δ E / R ext (after the end of the EDL chargin…
Introductory Quantum Physics Courses using a LabVIEW multimedia module
2007
We present the development of a LabVIEW multimedia module for introductory Quantum Physics courses and our experience in the use of this application as an educational tool in learning methodologies. The program solves the Time Dependent Schrodinger Equation for arbitrary potentials. We describe the numerical method used for solving this equation, as well as some mathematical tools employed to reduce the calculation time and to obtain more accurate results. As an illustration, we present the evolution of a wave packet for three different potentials: the repulsive barrier potential, the repulsive step potential, and the harmonic oscillator. This application has been successfully integrated in…
AN EXPERIMENTAL PROOF OF THE BACK-SCATTERING MODEL FOR DICHROIC EFFECTS IN VUV PHOTOEMISSION
2002
The energy dependence of the circular dichroism in the angular distribution of photoelectrons (CDAD) was investigated from the shallow Cs 5p core levels. Cesium was prepared in a hexagonal ordered monolayer on W(110). The results are mainly influenced by scattering of the photoelectrons within the adlayer. At low energies, the behavior observed is described by means of a model that treats only the back-scattering of photoelectrons at the potential step between the adlayer and the substrate. It leads to a simple method determining the position of the monolayer with respect to the substrate. In this approach, the back-scattering model is matched with the measured energy dependence of the CDA…
Quantification of electrochromic kinetics by analysis of RGB digital video images
2018
A new, rapid, and practical procedure to obtain quantitative kinetic information of electrochromic materials is proposed. When the transition between two colors on a colored electrode surface is monitorized by digital video, the analysis of pixel color intensity (I) in sequential RGB digital images allows us to precise the half-life time (t1/2) of the color change since a maximum value of the standard deviation of the pixel intensity (σ(I)) is reached. We simulated and analyzed the evolution of standard deviation during an electrochromic transition in different circumstances (kinetic and diffusion control). As an example of application, electrochromic transitions of a thin film model, the P…
Analysis of small-angle scattering patterns from a commercial Al-Li alloy by means of a model incorporating a repulsive step potential
1992
Abstract Small-angle X-ray scattering measurements are reported for a commercial Al-8·49%Li-51% Cu (atomic composition) alloy solution treated at 520°C and thermally aged for several times at several temperatures. Data have been analysed by means of a model of ellipsoidal precipitate particles previously proposed by some of us and by a modification of this model where, in the interparticle interference term, allowance is made for interactions between the precipitate particles at longer range than previously. This was achieved by the introduction, in addition to the hard-sphere interaction potential, of a potential step. Our fits indicate that the precipitate particles interact through a rep…
Primary and secondary distributions after a small-amplitude potential step at disk electrode coated with conducting film
2011
Abstract The set of equations and boundary conditions for the “primary potential/current distribution” after a small-amplitude potential step has been analyzed for a film-coated disk electrode in contact with an electrolyte. The solution of these equations provides the overall short-time resistance of this system, Rtot, which is determined by the short-time resistance of the electrolyte solution in contact with the bare disk electrode, Rs, and the short-time film resistance to the current passage in the normal direction, R f = L f / κ f π r o 2 (ro, disk radius; Lf, film thickness; κf, its specific conductivity). The deviation of Rtot from the sum of these resistances, Rs + Rf, originates f…
Acid versus base peptization of mesoporous nanocrystalline TiO2 films: functional studies in dye sensitized solar cells
2005
We report an analysis of the influence of acid/base conditions employed in the synthesis of TiO2 nanoparticles upon the performance of dye sensitised photoelectrochemical solar cells fabricated from these particles. The functional properties of the TiO2 nanoparticles in these devices are investigated by potential step chronoamperometry, transient laser spectroscopy, and photovoltaic device characterisation. We find that base peptization conditions employed in the sol–gel fabrication of the TiO2 nanoparticles result in a reduction in film electron density under negative applied bias, correlated with slower interfacial recombination losses and a higher device open circuit voltage.