Joo-Young Go

A study on the simulated diffusion-limited current transient of a self-affine fractal electrode based upon the scaling property

Abstract The power law relation I ( t )∝ t − α , α =( D f −1)/2 between current I and time t has been widely used to analyse current transient (chronoamperometric) behaviour during atomic/ionic diffusion towards the electrode with a fractal dimension D f , irrespective of whether the electrode has a self-similar fractal structure or at best a self-affine fractal structure. We show that the self-affine fractal dimension D f,sa (or Hurst exponent H ) is not always the sufficient condition required for describing the atomic/ionic diffusion behaviour to the self-affine fractal electrode: the current transient exhibits a more negative power dependence of current on time before temporal outer cut-off of fractality with increasing morphological amplitude (roughness factor) of the self-affine fractal electrode, rather than a unique power dependence corresponding to D f,sa . It is particularly noted that the current transients from the electrodes with comparatively large amplitudes are roughly characterised by a two-stage power dependence before temporal outer cut-off of fractality. In the present work, a practical method has been suggested to interpret the anomalous current transient from the self-affine fractal electrodes with various amplitudes. This method includes the determination of the apparent self-similar scaling properties of the self-affine fractal structure by the triangulation method.

A study on ionic diffusion towards self-affine fractal electrode by cyclic voltammetry and atomic force microscopy

Ionic diffusion towards a self-affine fractal electrode was investigated experimentally using both cyclic voltammetry and atomic force microscopy (AFM). For this purpose, three kinds of self-affine fractal Pt film electrodes were first prepared by dc sputtering of Pt on such substrate materials with different roughnesses as polished Al2O3, etched Ni and unpolished Al2O3. Then, the surface morphologies of the electrode specimens were examined by using AFM and cyclic voltammograms (CVs) were measured on the electrode specimens in a 30 wt.% glycerol+70 wt.% (0.01 M K4[Fe(CN)6]+0.5 M Na2SO4) solution at various scan rates. Finally, the fractal dimensions of the electrode surfaces were determined from analyses of AFM images and the power relation between peak current and scan rate in the CVs. All the fractal dimensions determined from the CVs were much smaller than the self-affine fractal dimensions determined by the perimeter–area method. Assuming that the self-affine fractal surface can have a self-similar scaling property, the apparent self-similar fractal dimensions of the self-affine fractal electrodes were determined by a triangulation method. These values agreed well with the fractal dimensions determined from the CVs. From the above results, it is concluded that ionic diffusion towards a self-affine fractal electrode should be described in terms of the apparent self-similar fractal dimension rather than the self-affine fractal dimension.

Electrochemistry of insertion materials for hydrogen and lithium

Electrochemical Methods.- Hydrogen Absorption into and Subsequent Diffusion through Hydride-Forming Metals.- Hydrogen Transport under Impermeable Boundary Conditions.- Hydrogen Trapping inside Metals and Metal Oxides.- Generation of Internal Stress during Hydrogen and Lithium Transport.- Abnormal Behaviors in Hydrogen Transport: Importance of Interfacial Reactions.- Effect of Cell-impedance on Lithium Transport.- Lithium Transport through Electrode with Irregular/Partially-Inactive Interfaces.

Investigation of Stresses Generated during Lithium Transport through the RF Sputter-Deposited Li1 − δ CoO2 Film by a DQCR Technique

In this work, stresses generated during lithium transport through radio-frequency (rfl sputter-deposited Li 1-δ CoO 2 films with different thicknesses were investigated by a double quartz crystal resonator (DQCR) technique. For this purpose, in situ resonant frequency changes of the Li 1-δ CoO 2 -coated AT- and BT-cut quartz crystals were first recorded along with the galvanostatic charge (lithium deintercalation) and discharge (lithium intercalation) curves obtained in a I M LiClO 4 -propylene carbonate solution. From the measured resonant frequency changes, the lateral stresses of the Li 1-δ CoO 2 films were then estimated as a function of lithium stoichiometry, (1-δ). Compressive and tensile stresses were developed in the Li 1-δ CoO 2 films during the lithium deintercalation and intercalation, respectively. The remarkable variation of compressive and tensile stresses with lithium stoichiometry appeared in a two-phase (a Li-poor α-phase and a Li-rich β-phase) region. Compressive and tensile stresses decreased in absolute magnitude with increasing film thickness. The contribution of the electrostrictive stress to the total stress was theoretically calculated to be about 2.2 × 10 -3 %. From the extremely small contribution of the electrostrictive stress, it is strongly suggested that the stresses result mainly from the volume contraction and expansion of the Li 1-δ CoO 2 films due to the lithium intercalation and deintercalation, respectively. Furthermore, the relaxation of the compressive stress was developed during the lithium deintercalation in a single α-phase region, causing the cracking of the Li 1-δ CoO 2 films.

Fractal Approach to Rough Surfaces and Interfaces in Electrochemistry

The real objects found in nature have complex structures which Euclidean geometry can not characterize. After Mandelbrot developed a new geometry, i.e., fractal geometry, which provides a new paradigm for understanding many physical phenomena in nature, fractal geometry has been widely used in a number of fields, e.g., science, art, economics, etc. Especially, in science, the characterization of the rough surfaces and interfaces using fractal geometry has played an important role in understanding the anomalous behavior of rough surfaces and interfaces. There are three kinds of fractals as shown in Figure 1. The first one is a surface fractal, i.e., a dense object with a fractal

A Review of Surface Energy of Solid Electrodes with Emphasis on Its Controversial Issues in Interfacial Electrochemistry

A classical Lippmann equation valid for liquid electrodes can not describe the interfacial properties of solid electrodes due to the elastic surface strain on solid electrodes. Although there have been many attempts to derive the thermodynamic equations for solid electrodes Outing the past few decades, their validity has been still questioned by many researchers. In practice, although there are various experimental techniques to measure surface energy of solid electrodes, the results obtained by each technique are rather inconsistent due to the complexity of the surface strain on solid electrodes. This article covers these controversial issues in surface energy of solid electrodes. After giving brief summaries of the definition of the important thermodynamic parameters and the derivation of the thermodynamic equations for solid electrodes, the several experimental methods were introduced for the measurement of surface energy of solid electrodes. And then we discussed in detail the inconsistent results in the measurement of the potential of zero charge (pac) and the potential of electrocapillary maximum (ecm).

Hydrogen Trapping Inside Metals and Metal Oxides

The anomalous behavior of hydrogen in terms of its solubility and diffusivity in metals and oxides has been the subject of repeated investigations [1–6]. The diffusion coefficients of hydrogen in metals reported in the literature have usually been determined under the assumption that the hydrogen concentration is governed by Fick’s law. Figure 5.1 summarizes some of the experimental data on the diffusivity of hydrogen reported in the literature [1]. It should be noted that small values of the diffusion coefficient were obtained for work-hardened samples (designated as curves 6). Figure 5.1 indicates that the diffusion coefficient is a function of other variables besides the temperature and that these neglected variables are in some way related to the work hardening experienced by the specimen. There are, therefore, some doubts about the validity of Fick’s law and the simple physical model of random motion through the electrode.

Characterization of Surface Roughness and Inhomogeneity of Hot-Rolled Carbon Steels by Using Image Analysis Method and Electrochemical Impedance Spectroscopy

The present work is concerned with characterization of surface roughness and inhomogeneity of four kinds of hot-rolled carbon steels in terms of the fractal dimension and the depression parameter by using image analysis method and electrochemical impedance spectroscopy, respectively. From the analysis of the 3D AFM image, it is realized that all the hot-rolled steel surfaces show the self-affine fractal property. The values of the fractal dimension of the hot-rolled steels were determined by the analyses of the AFM images on the basis of both the perimeter-area method and the triangulation method. In addition, the Nyquist plots were found to be depressed from a perfect semicircle form. From the experimental findings, the changes in the values of the fractal dimension and the depression parameter with chemical composition have been discussed in terms of the change in the value of hardness of base steel.

Lithium Transport Through Electrode with Irregular/Partially Inactive Interfaces

Fractal geometry is a tool employed to define real objects in nature which cannot be characterized by Euclidean geometry. It was conceptualized by Mandelbrot [1] and has been widely used in various fields such as science, art [2–4], economics [5–8], etc. Especially, in science, the secret of the anomalous phenomena which take place on rough and irregular surfaces has been unlocked with the help of fractal geometry.

Hydrogen Transport Under Impermeable Boundary Conditions

The hydrogen injection reaction into metals and oxides involves hydrogen absorption, followed by hydrogen diffusion through the bulk electrode. There are two models that describe hydrogen absorption in an alkaline solution: (1) the one-step (direct) mechanism and (2) the two-step mechanisms [1–3].