**7. Acknowledgment**

14 Electrochemical Cells – New Advances in Fundamental Researches and Applications

electrochemical responses at fractal interface were treated with the help of the analytical solutions to the generalised diffusion equation. In order to provide a guideline in analysing anomalous diffusion coupled with sluggish charge-transfer reaction at fractal interface, i.e., non-diffusion-controlled transfer process across fractal interface, this review covered the recent results concerned to the effect of surface roughness on non-diffusion-controlled transfer process within the intercalation electrodes. It has been shown, that the numerical analysis of diffusion towards and from fractal interface can be used as a powerful tool to elucidate the transport phenomena of mass (ion for electrolyte and atom for intercalation

A theoretical method based on limited scale power law form of the interfacial roughness power spectrum and the solution of diffusion equation under the diffusion-limited boundary conditions on rough interfaces was developed by Kant and Jha (Kant & Jha, 2007). The results were compared with experimentally obtained currents for nano- and microscales of roughness and are applicable for all time scales and roughness factors. Moreover, this work unravels the connection between the anomalous intermediate power law regime

Kinetic response of surfaces defined by finite fractals has been addressed in the context of interaction of finite time independent fractals with a time-dependent diffusion field by a novel approach of Cantor Transform that provides simple closed form solutions and smooth transitions to asymptotic limits (Nair & Alam, 2010). In order to enable automatic simulation of electrochemical transient experiments performed under conditions of anomalous diffusion in the framework of the formalism of integral equations, the adaptive Huber method has been extended onto integral transformation kernel representing fractional

The fractal dimension can be simply estimated using the kinetics-sensitive voltcoulometry introduced by Thurzo and co-workers (Thurzo et al., 1999). On the basis of the multipoint analysis principles the transient charge is sampled at three different events in the interval between subsequent excitation pulses and the sampled values are combined according the appropriate filtering scheme. The third sampling event chosen at the end of measuring period and slow potential scans make the observation of non-Cottrellian responses easier.

as the fractal dimension can be simply determined from two voltcoulograms obtained for

The electrode surface attributes have a profound influence on the kinetic of electron transfer. The continued progress in material research has induced the marked progress in the preparation of electrochemical electrodes with enhanced sensitivity or selectivity. If such a sophisticated electrode with microstructured, nanostructured or electroactive surface is used a special attention should be paid to a careful examination of changes initiated in the diffusion towards its surface. Newly designed types of electrochemical electrodes often result in more or less marked deviations from the ideal Cottrell behaviour. Various modifications of the relationship (Equation (1)) have been investigated to describe the processes in real electrochemical cells. A raising awareness of the importance of a detailed

that enters the power-law time dependence of the transient charge, as well

electrode) across fractal interface whatever controls the overall transfer process.

exponent and the morphological parameters of limited scales of fractality.

diffusion (Bieniasz, 2011).

two distinct sets of sampling events (Gmucová et al., 2002).

The parameter

**6. Conclusion** 

This work was supported by the ASFEU project Centre for Applied Research of Nanoparticles, Activity 4.2, ITMS code 26240220011, supported by the Research & Development Operational Programme funded by the ERDF and by Slovak grant agency VEGA contract No.: 2/0093/10.
