Abstract
An oscillation system was observed during an electroless copper electrodeposition. The cathodic electrode at electrodeposition was a pretreated nonconductive printed circuit substrate in electroless bath. The current was oscillating while the copper concentration or potential between working electrode and reference electrode was varied. The mathematics model was proposed as the coupling of rates of diffusion of the electrolytic ion and the surface reaction. The nonlinearity was introduced by a dis-continuity of surface reaction rate constant attributed to the concentration overpotential. Then, the computed results showed the parameter sensitive periodic and gradually developed into chaotic oscillation. Time series of potential or copper concentration on the electrode surface were obtained. The oscillation patterns were characterized and verified by Fourier transformation and resulting power spectrum. The phase portraits of potential against potential with a time delay or concentration against potential were reconstructed on the phase plane. A strong attractor was found and the basin of attraction was defined. The portrait was embedded as a fractal with the property of self-similarity. The properties of the phase portrait on the fractal geometry were characterized.The mass transport phenomena in porous solids are extensively studied and the diffusion constant can be determined by various methods such as chromatographic measurement, pulsed field gradient n.m.r. technique and the simulation of transient sorption rate data, etc., despite none of them is consistent with each other. But the morphology of porous media is not well characterized in the conventional analysis. However, the fractal geometry has been employed and began to analyze the structure effects of the sorbent or the porous catalytic materials. The Hausdorff fractal dimension of a specific porous solid can be determined by the scales of molecular sizes of adsorbates and corresponding adsorption capacities. Now, a modified Fick's second law based on fractal geometry instead of Euclidean geometry is proposed by introducing the fractal dimension of the porous solid. Following the methodology of the analysis of transient sorption rate data, we can find the diffusivity of the adsorbate in the adsorbent by this new consideration. Some porous catalytic particles, which are classified as zeolite A, X, ZSM5, Dowex, and carbon molecular sieve, are studied and characterized. The diffusivities of some paraffin and aromatic hydrocarbons in these solids are obtained and compared with the results by conventional Euclidean formulation and n.m.r. technique and showed the agreement in the order of magnitude with the n.m.r. technique. This new consideration on diffusion may be a helpful approach in determining the kinetics of transport in porous solids.