**4. Modified electrodes**

6 Electrochemical Cells – New Advances in Fundamental Researches and Applications

microelectrode was developed by Jaworski and co-workers (Jaworski et al., 1999). Myland and Oldham have shown that on macroelectrodes the Cottrellian dependence can be preserved even when supporting electrolyte is absent. The limiting current, however, was shown to depart in magnitude from the Cottrellian prediction by a factor (greater or less than unity) that depends on the charge numbers of the salt's ions and that of the electroproduct (Myland & Oldham, 1999). A generalized theory of the steady-state voltammetric response of a microelectrode in the absence of supporting electrolyte and for any values of diffusion coefficients of the substrate and the product of an electrode process

The influence of supporting electrolyte on the drugs detection was studied and data obtained using cyclic voltammetry, steady-state voltammetry and voltcoulometry on the same analyte were compared to each other by Orlický and co-workers. Under unsupported conditions different detection limits of the above mentioned methods were observed. Some species were easily observed by the kinetics-sensitive voltcoulometry even for concentrations near or under the sensitivity limit of voltammetric methods (Orlický et al., 2003). Thus, systems obeing deviations from Cottrell behaviour should find their application in sensorics. Later, it has been revealed that the dopamine diffusion current towards a carbon fiber microelectrode fulfills, within experimental errors and for concentration similar to those in a rat striatum, the behaviour theoretically predicted by the Cottrell equation. Nevertheless, under unsupported or weakly supported conditions non-Cottrellian responses were observed. Moreover, markedly non-Cottrellian responses were observed for dopamine concentrations lower or higher than the physiological ones in the rat striatum. It has been also shown, that the non-Cottrellian behaviour of diffusion current involves the nonlinearity of the dopamine calibration curve obtained by kinetics-sensitive voltcoulometry, while voltammetric calibration curve remains linear (Gmucová et al., 2004). Similarly, Caban and co-workers analysed the contribution of migration to the transport of polyoxometallates in the gels by methods of different sensitivity to migration (Caban et al.,

Mathematical models of the ion transport regarded as the superposition of diffusion and migration in a potential field were analyzed by Hasanov and Hasanoglu (Hasanov & Hasanoglu, 2008). Based on the Nernst-Planck equation the authors have derived explicit analytical formulae for the concentration of the reduced species and the current response in the case of pure diffusive as well as diffusion–migration model, for various concentrations at initial conditions. The proposed approach can predict an influence of ionic diffusivities, valences, and initial and boundary concentrations to the behaviour of non-Cottrellian current response. In addition to these, the analytical formulae obtained can also be used for numerical and digital simulation methods for Nernst-Planck equations. The mathematical model of the nonlinear ion transport problem, which includes both the diffusion and migration, was solved by the same authors (Hasanov & Hasanoglu, 2009). They proposed a numerical iteration algorithm for solving the nonlocal identification problem related to nonlinear ion transport. The presented computational results are consistent with

The quantitative understanding of generalized Cottrellian response of moderately supported electrolytic solution at rough electrode/electrolyte interface was enabled with the Srivastav's and Kant's work (Srivastav & Kant, 2010). Here, the effect of the uncompensated

was presented by Hyk and Stojek (Hyk & Stojek, 2002).

experimental results obtained on real systems.

2006).

Modified electrodes include electrodes where the surface was deliberately altered to impart functionality distinct from the base electrode. During last decades a large number of different strategies for physical and chemical electrode modification have been developed, aimed at the enhancement in the detection of species under interest. Particularly in biosciences and environmental sciences such electrodes became of great importance. One of the issues raised in the research of redox processes taking place at modified electrodes has been the analysis of changes in the diffusion towards their altered surfaces.

Historically, liquid and solid electrochemistry grew apart and developed separately for a long time. Appearance of novel materials and methods of thin films preparation lead to massive development of chemically modified electrodes (Alkire et al., 2009). Such electrodes represent relatively modern approach to electrode systems with thin film of a selected chemical bonded or coated onto the electrode surface. A wide spectrum of their possible applications turned the spotlight of electrochemical research towards the design of electrochemical devices for applications in sensing, energy conversion and storage, molecular electronics etc. Only several examples of possible electrode coatings are mentioned in this chapter, all of them in close contact with the study of the electron transfer kinetic on them.

#### **4.1 Micro- and nanoparticle modified electrodes**

Marked deviations from Cottrellian behaviour were encountered in the theoretical study (Thompson et al., 2006) describing the diffusion of charge over the surface of a microsphere resting on an electrode at a point, in the limit of reversible electrode kinetics. A realistic physical problem of truncated spheres on the electrode surface was modelled in the above mentioned work, and the effect of truncation angle on chronoamperometry and voltammetry was explored. It has been shown that the most Cottrell-like behaviour is observed for the case of a hemispherical particle resting on the surface, but only at short times is the diffusion approximated well by a planar diffusion model. Concurrently, Thompson and Compton have developed a model for the voltammetric response due to surface charge injection at a single point on the surface of a microsphere on whose surface the electro-active material is confined. The cyclic voltammetric response of such system was investigated, the Fickian diffusion constrained on spherical surfaces showed strong deviations from the responses expected for planar diffusion. The Butler–Volmer condition

A Review of Non-Cottrellian Diffusion Towards Micro- and Nano-Structured Electrodes 9

kinetics the authors stated that for the nanoparticle arrays, the mechanism is likely to be a rate-determining electron transfer followed by a chemical step. As the kinetics displayed by the nanoparticle arrays show changed kinetics from that of a silver macrodisk, they have inferred a change in the mechanism of the rate-determining step for the reduction of 4 nitrophenol in acidic media between the macro- and nanoscales (Campbell et al., 2010). Zhou and co-workers have found the shape and size of voltammograms obtained on silver nanoparticle modified electrodes to be extremely sensitive to the nanoparticle coverage, reflecting the transition from convergent to planar diffusion with increased coverage (Zhou et al., 2010). A system of iron oxide nanoparticles with mixed valencies deposited on photovoltaic amorphous hydrogenated silicon was studied by the kinetic sensitive voltcoulometry by Gmucová and co-workers. This study was motivated by the previously observed orientation ordering in similar system of nanoparticles involved by a laser irradiation under the applied electric field (Gmucová et al., 2008a). A significant dependence of the kinetic of the redox reactions, in particular oxidation reaction of ferrous ions, was observed as a consequence of the changes in the charged deep states density in amorphous

Both the preparation and application of carbon nanotubes modified electrodes have been reviewed by Merkoçi, and by Wildgoose and co-workers (Merkoçi, 2006; Wildgoose et al., 2006). The comparative study of electrochemical behaviour of multiwalled carbon nanotubes and carbon black (Obradović et al., 2009) has revealed that although the electrochemical characteristics of properly activated carbon black approaches the characteristics of the carbon nanotubes, carbon nanotubes are superior, especially regarding the electron-transfer properties of the nanotubes with corrugated walls. The kinetics of electron-transfer reactions depends on the morphology of the samples and is faster on the bamboo-like structures, than on the nanotubes with smooth walls. Different oxidation properties of coenzyme NADH on carbon fibre microelectrode and carbon fibre microelectrode modified with branching carbon

Thin-layer cells, thin films and membrane systems show theoretical *I-t* responses that deviate from Cottrell behaviour. Although the diffusion was often assumed to be the only transport mechanism of the electroactive species towards polymer coated electrodes, the migration can contribute significantly. The bulk resistance of film corresponds to a resistance in series with finite diffusional element(s) and leads to ohmic *I-t* curves at short times. Subsequently, this resistance and the interacting depletion regions give rise to the non-Cottrellian behaviour of thin systems. According to Aoki, when an electrode is coated with a conducting polymer, the Nernst equation in a stochastic process is defined (Aoki, 1991). In such a case the electrode potential is determined by the ratio of the number of conductive (oxidized) species to that of the insulating (reduced) species experienced at the interface which is formed by electric percolation of the conductive domain to the substrate electrode. Examples of evaluating the potential for the case where the film has a random distribution of the conductive and insulating species were presented for three models: a one-

nanotubes have been reported by Zhao and co-workers (Zhao et al., 2010).

dimensional model, a seven-cube model and a cubic lattice model.

hydrogenated silicon (Gmucová et al., 2008b).

**4.2 Carbon nanotubes modified electrodes** 

**4.3 Thin film or membrane modified electrodes** 

was imposed for the electron transfer kinetics. It was found that the peak-to-peak separations differ from those expected for the planar-diffusion model, as well as the peak currents and the asymmetry of the voltammetric wave at higher sweep rates indicate the heterogeneous kinetics. The wave shape was explained by the competing processes of divergent and convergent diffusion (Thompson & Compton, 2006). Later, the electrochemical catalytic mechanism at a regularly distributed array of hemispherical particles on a planar surface was studied using simulated cyclic voltammetry (Ward et al., 2011). As is known, a high second-order rate constant can lead to voltammetry with a split wave. The conditions under which anomalous 'split-wave' phenomenon in cyclic voltammogram is observed were elucidated in the above-mentioned work.

In recent years significant attention is paid to the use of nanoparticles in many areas of electrochemistry. Underlying this endeavour is an expectation that the changed morphology and electronic structure between the macro- and nanoscales can lead to usefully altered electrode reactions and mechanisms. Thus, the use of nanoparticles in electroanalysis became an area of research which is continually expanding. Within both the trend towards the miniaturisation of electrodes and the ever-increasing progress in preparation and using nanomaterials, a profound development in electroanalysis has been connected with the design and characterisation of electrodes which have at least one dimension on the nanoscale.

In a nanostructured electrode, a larger portion of atoms is located at the electrode surface as compared to a planar electrode. Nanoparticle modified electrodes possess various advantages over macroelectrodes when used for electroanalysis, e.g., electrocatalysis, higher effective surface area, enhancement of mass transport and control over electrode microenvironment. An overview of the investigations carried out in the field of nanoparticles in electroanalytical chemistry was given in two successive papers (Welch & Compton, 2006; Campbell & Compton, 2010). Particular attention was paid to examples of the advantages and disadvantages nanoparticles show when compared to macroelectrodes and the advantages of one nanoparticle modification over another. From the works detailed in these reviews, it is clear that metallic nanoparticles have much to offer in electroanalysis due to the unique properties of nanoparticulate materials (e.g., enhanced mass transport, high surface area, improved signal-to-noise ratio). The unique properties of nanoparticulate materials can be exploited to enhance the response of electroanalytical techniques. However, according to the authors, at present, much of the work is empirical in nature. Belding and co-workers have compared the behaviour of nanoparticle-modified electrodes with that of conventional unmodified macroelectrodes (Belding et al., 2010). Here, a conclusion has been made that the voltammetric response from a nanoparticle-modified electrode is substantially different from that expected from a macroelectrode.

The first measurement of comparative electrode kinetics between the nano- and macroscales has been recently reported by Campbell and co-workers. The electrode kinetics and mechanism displayed by the nanoparticle arrays were found to be qualitatively and quantitatively different from those of a silver macrodisk. As was argued by Campbell and co-workers, the electrochemical behaviour of nanoparticles can differ from that of macroelectrodes for a variety of reasons. The most significant among them is that the size of the diffusion layer and the diffuse double layer at the nanoscale can be similar and hence diffusion and migration are strongly coupled. By comparison of the extracted electrode kinetics the authors stated that for the nanoparticle arrays, the mechanism is likely to be a rate-determining electron transfer followed by a chemical step. As the kinetics displayed by the nanoparticle arrays show changed kinetics from that of a silver macrodisk, they have inferred a change in the mechanism of the rate-determining step for the reduction of 4 nitrophenol in acidic media between the macro- and nanoscales (Campbell et al., 2010). Zhou and co-workers have found the shape and size of voltammograms obtained on silver nanoparticle modified electrodes to be extremely sensitive to the nanoparticle coverage, reflecting the transition from convergent to planar diffusion with increased coverage (Zhou et al., 2010). A system of iron oxide nanoparticles with mixed valencies deposited on photovoltaic amorphous hydrogenated silicon was studied by the kinetic sensitive voltcoulometry by Gmucová and co-workers. This study was motivated by the previously observed orientation ordering in similar system of nanoparticles involved by a laser irradiation under the applied electric field (Gmucová et al., 2008a). A significant dependence of the kinetic of the redox reactions, in particular oxidation reaction of ferrous ions, was observed as a consequence of the changes in the charged deep states density in amorphous hydrogenated silicon (Gmucová et al., 2008b).
