Interface film-solution

A discussion of the charge transfer reaction on the polymer-modified electrode should consider not only the interaction of the mediator with the electrode and a solution species (as with chemically modified electrodes), but also the transport processes across the film. Let us assume that a solution species S reacts with the mediator Red/Ox couple as depicted in Fig. 5.32. Besides the simple charge transfer reaction with the mediator at the interface film/solution, we have also to include diffusion of species S in the polymer film (the diffusion coefficient DSp, which is usually much lower than in solution), and also charge propagation via immobilized redox centres in the film. This can formally be described by a diffusion coefficient Dp which is dependent on the concentration of the redox sites and their mutual distance (cf. Eq. (2.6.33). 

Let us imagine a piece of silver with an AgCl film to be immersed in a Cl solution. Two phase boundaries will form, one between the metal and the film and the other between the film and the solution. The interface metal/film is permeable for Ag but not for CP ions or electrons. It is impermeable to CP ions because they cannot be inserted into the metal lattice and electrons cannot pass through because silver chloride does not conduct electrons. Therefore, a Galvani potential difference will form there that is determined only by the chemical potentials of the Ag" ions in both phases. These are fixed values, so the Galvani potential difference will also have a fixed value. The interface film/solution is permeable to both CP and Ag" so that Ag and CP ions compete to set the Galvani potential difference. However, free Ag ions in a CP solution can only be present in extremely low concentrations, so they are hopelessly outnumbered by the CP ions. This is why only the CP ions determine the potential difference at this interface. 

Then the diffusion equation for the fluctuation of the metal ion concentration is given by Eq. (68), and the mass balance at the film/solution interface is expressed by Eq. (69). These fluctuation equations are also solved with the same boundary condition as shown in Eq. (70). 

If substrate diffusion becomes rate determining, only a small fraction of the film at the film/solution interface will be used. On the other hand, if charge diffusion becomes rate determining, the catalytic reaction can take place only in a film fraction close to the electrode surface. Each of these effects will render parts of the film superfluous, and it is obvious that there is no sense in designing very thick redox films, rather there is an optimal layer thickness to be expected depending on the individual system. 

Several approaches have been undertaken to construct redox active polymermodified electrodes containing such rhodium complexes as mediators. Beley [70] and Cosnier [71] used the electropolymerization of pyrrole-linked rhodium complexes for their fixation at the electrode surface. An effective system for the formation of 1,4-NADH from NAD+ applied a poly-Rh(terpy-py)2 + (terpy = terpyridine py = pyrrole) modified reticulated vitreous carbon electrode [70]. In the presence of liver alcohol dehydrogenase as production enzyme, cyclohexanone was transformed to cyclohexanol with a turnover number of 113 in 31 h. However, the current efficiency was rather small. The films which are obtained by electropolymerization of the pyrrole-linked rhodium complexes do not swell. Therefore, the reaction between the substrate, for example NAD+, and the reduced redox catalyst mostly takes place at the film/solution interface. To obtain a water-swellable film, which allows the easy penetration of the substrate into the film and thus renders the reaction layer larger, we used a different approach. Water-soluble copolymers of substituted vinylbipyridine rhodium complexes with N-vinylpyrrolidone, like 11 and 12, were synthesized chemically and then fixed to the surface of a graphite electrode by /-irradiation. The polymer films obtained swell very well in aqueous... 

Catalysis at multilayered electrode coatings is then addressed. Besides the rate of the catalytic reaction within the film and the diffusion of the substrate and products between the bulk of the bathing solution and the film-solution interface, the current response depends on two additional factors permeation of the substrate through the film, and transport of electrons through the film. Analysis of the first of these factors also involves a discussion of the inhibition of the electrode electron transfer that the presence of a film on the electrode surface may cause, whether the electrode is covered by a monolayer or by a thicker film. This discussion also addresses the important case where inhibition is due to deposition onto the electrode surface of one of the reaction products. 

In zone R, all three phenomena that take place in the film are fast compared to the diffusion of the substrate from the bulk of the solution to the film-solution interface. The concentrations of both Q and A are constant through the film. The RDEV response is similar to that of a monolayer coating (Section 4.3.2), except that more catalytic material is present on the surface of the electrode (it is multiplied by the number of layers in the multilayered coating). A linear Koutecky-Levich plot is obtained from the intercept, from which the kinetics of the catalytic reaction can be characterized. 

If electron transport is fast, the system passes from zone R to zone S+R and then to zone SR. In the latter case there is a mutual compensation of diffusion and chemical reaction, making the substrate concentration profile decrease within a thin reaction layer adjacent to the film-solution interface. This situation is similar to what we have termed pure kinetic conditions in the analysis of an EC reaction scheme adjacent to the electrode solution interface developed in Section 2.2.1. From there, if electron transport starts to interfere, one passes from zone SR to zone SR+E and ultimately to zone E, where the response is controlled entirely by electron transport. 

Similarly, in the SR situation, the substrate concentration profile is squeezed within a reaction layer adjacent to the film-solution interface, whose thickness is equal to ->/Ds/kCe. In the ER situation, the substrate concentration profile is squeezed within a reaction layer adjacent to the film-solution interface whose thickness is equal to ->/DejKkC. In both cases there is no point in thickening the film beyond these values. Doing so would not only be useless but also deleterious, since a further increase in the film thickness would make the system pass into the SR+E or ER+S zone, adding an additional limitation to the current caused by electron transport or substrate diffusion, respectively. 

From the electrode to the film-solution interface, the following boundary conditions apply ... 

A consequence of the fact that the diffusion layer is much thicker than the enzyme film is that the fluxes in the solution are negligible compared to the fluxes in the film. The two time-dependent integral equations relating the fluxes and the concentrations at the film-solution interface may be thus be... 

We examine an electron transfer of hydrated redox particles (outer-sphere electron transfer) on metal electrodes covered with a thick film, as shown in Fig. 8-41, with an electron-depleted space charge layer on the film side of the film/solution interface and an ohmic contact at the metal/film interface. It appears that no electron transfer may take place at electron levels in the band gap of the film, since the film is sufficiently thick. Instead, electron transfer takes place at electron levels in the conduction and valence bands of the film. 

In the active state, the dissolution of metals proceeds through the anodic transfer of metal ions across the compact electric double layer at the interface between the bare metal and the aqueous solution. In the passive state, the formation of a thin passive oxide film causes the interfadal structure to change from a simple metal/solution interface to a three-phase structure composed of the metal/fUm interface, a thin film layer, and the film/solution interface [Sato, 1976, 1990]. The rate of metal dissolution in the passive state, then, is controlled by the transfer rate of metal ions across the film/solution interface (the dissolution rate of a passive semiconductor oxide film) this rate is a function of the potential across the film/solution interface. Since the potential across the film/solution interface is constant in the stationary state of the passive oxide film (in the state of band edge level pinning), the rate of the film dissolution is independent of the electrode potential in the range of potential of the passive state. In the transpassive state, however, the potential across the film/solution interface becomes dependent on the electrode potential (in the state of Fermi level pinning), and the dissolution of the thin transpassive film depends on the electrode potential as described in Sec. 11.4.2. 

In the stationary state of anodic dissolution of metals in the passive and transpassive states, the anodic transfer of metallic ions metal ion dissolution) takes place across the film/solution interface, but the anodic transfer of o Q en ions across the Qm/solution interface is in the equilibrium state. In other words, the rate of film formation (the anodic transfer oS metal ions across the metal lm interface combined with anodic transfer of osygen ions across the film/solution interface) equals the rate of film dissolution (the anodic transfer of metal ions across the film/solution interface combined with cathodic transfer of oitygen ions across the film/solution interface). 

Thus, in the stationary state, the rate of anodic transfer of metal ions across the metal/film interface equals the rate of anodic transfer of metal ions across the film/solution interface this rate of metal ion transfer represents the dissolution rate of the passive film. The thickness of the passive film at constant potential remains generally constant with time in the stationary state of dissolution, although the thickness of the film depends on the electrode potential and also on the dissolution current of the passive film. 

In the range of potential of the passive state the passive oxide film is in the state of band edge level pinning at the film/solution interface hence, the potential A( )h across the film/solution interface remains constant irrespective of the electrode potential of the passive metal. With increasing anodic polarization and in the... 

Fig. 11-11. Potential at a film/solution interface and potential dfp in a passive film as a fimction of anodic potential of a passive metal electrode in the stationary state the interface is in the state of band edge level pinning to the extent that the Fermi level e, is within the band gap, but the interface changes to the state of Fermi level pinning as e, coincides with the valence band edge Cy.

For metallic iron and nickel electrodes, the transpassive dissolution causes no change in the valence of metal ions during anodic transfer of metal ions across the film/solution interface (non-oxidative dissolution). However, there are some metals in which transpassive dissolution proceeds by an oxidative mode of film dissolution (Sefer to Sec. 9.2.). For example, in the case of chromium electrodes, on whidi the passive film is trivalent chromium oxide (CrgOj), the transpassive dissolution proceeds via soluble hexavalent chromate ions. This process can be... 

Polyelectrolyte films are comprised of the polyelectrolytes, solvent and ions, the latter mainly located at the film/solution interface, see below. Solvent content in PEMs can beaproximately40% ]94,95], being the actual value dependent on film history (drying and reswelling steps) and for dry films on environmental humidity ]95,96]. PEMs are therefore highly swollen structures, but its water content is below that found in... 

Attenuated total reflectance infrared (ATR-IR) is used to study films, coatings, threads, powders, interfaces, and solutions. (It also serves as the basis for much of the communication systems based on fiber optics.) ATR occurs when radiation enters from a more-dense material (i.e., a material with a higher refractive index) into a material that is less dense (i.e., with a lower refractive index). The fraction of the incident radiation reflected increases when the angle of incidence increases. The incident radiation is reflected at the interface when the angle of incidence is greater than the critical angle. The radiation penetrates a short depth into the interface before complete reflection occurs. This penetration is called the evanescent wave. Its intensity is reduced by the sample which absorbs. 

A laser beam was used for graft polymerization of AAc onto a tetrafluo-roethylene-perfluoroalkyl vinyl ether copolymer film [81]. The film placed in contact with AAc solution was irradiated with KrF laser through the film to excite the film/solution interface. Surface composition of the grafted film determined by XPS revealed an extensive loss of fluorine atom and an increase of oxygen atom in addition to the presence of a Cls line shape, similar to that of AAc monomer. Mirzadeh et al. [82] used pulsed laser beam for the graft polymerization of AAm on a rubber surface in the presence of a photosensitizer, ben-zophenone, or AIBN. 

Successful assembly requires matching features of the template, meaning that wavelength and height have to be of the same dimensions. Additionally, adhesion of particles and surface must be avoided by weak repulsive forces. In this context, polyelectrolyte multilayer-wrinkles are particularly useful, as the wettability of the multilayer is determined by the part of the layer adjacent to the film/solution or film/air interface respectively, while the elastic properties are determined by the total film [84], Thus, elastic constants can be adjusted largely independent from wettability properties. 

Figure 3.9 Schematic illustration of the processes that can occur at a modified electrode, where P represents a reducible substance in a film on the electrode surface and A a species in solution. The processes shown are as follows (1) heterogeneous electron transfer to P to produce the reduced form Q (2) electron transfer from Q to another P in the film (electron diffusion or electron hopping in the film) (3) electron transfer from Q to A at the film/solution interface (4) penetration of A into the film (where it can also react with Q or at the substrate/film interface) (5) movement (mass transfer) of Q within the film (6) movement of A through a pinhole or channel in the film to the substrate, where it can be reduced. From A.J. Bard and L.R. Faulkner, Electrochemical Methods Fundamentals and Applications, 2nd Edition, Wiley, 2001. Reprinted by permission of John Wiley Sons, Inc...

The formal potential, E0/, contains useful information about the ease of oxidation of the redox centers within the supramolecular assembly. For example, a shift in E0/ towards more positive potentials upon surface confinement indicates that oxidation is thermodynamically more difficult, thus suggesting a lower electron density on the redox center. Typically, for redox centers located close to the film/solution interface, e.g. on the external surface of a monolayer, the E0 is within 100 mV of that found for the same molecule in solution. This observation is consistent with the local solvation and dielectric constant being similar to that found for the reactant freely diffusing in solution. The formal potential can shift markedly as the redox center is incorporated within a thicker layer. For example, E0/ shifts in a positive potential direction when buried within the hydrocarbon domain of a alkane thiol self-assembled monolayer (SAM). The direction of the shift is consistent with destabilization of the more highly charged oxidation state. 

The use of galvanostatic transients enabled the measurement of the poten-tiodynamic behavior of Li electrodes in a nearly steady state condition of the Li/film/solution system [21,81], It appeared that Li electrodes behave potentio-dynamically, as predicted by Eqs. (5)—(12), Section III.C a linear, Tafel-like, log i versus T dependence was observed [Eq. (8)], and the Tafel slope [Eq. (10)] could be correlated to the thickness of the surface films (calculated from the overall surface film capacitance [21,81]). From measurements at low overpotentials, /o, and thus the average surface film resistivity, could be measured according to Eq. (11), Section m.C [21,81], Another useful approach is the fast measurement of open circuit potentials of Li electrodes prepared fresh in solution versus a normal Li/Li+ reference electrode [90,91,235], While lithium reference electrodes are usually denoted as Li/Li+, the potential of these electrodes at steady state depends on the metal/film and film/solution interfaces, as well as on the Li+ concentration in both film and solution phases [236], However, since Li electrodes in many solutions reach a steady state stability, their potential may be regarded as quite stable within reasonable time tables (hours —> days, depending on the system s surface chemistry and related aging processes). 

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