Diffusion electrode surface

At higher current densities, the primary electron transfer rate is usually no longer limiting instead, limitations arise tluough the slow transport of reactants from the solution to the electrode surface or, conversely, the slow transport of the product away from the electrode (diffusion overpotential) or tluough the inability of chemical reactions coupled to the electron transfer step to keep pace (reaction overpotential). 

The flux of material to and from the electrode surface is a complex function of all three modes of mass transport. In the limit in which diffusion is the only significant means for the mass transport of the reactants and products, the current in a voltammetric cell is given by... 

The detailed mechanism of battery electrode reactions often involves a series of chemical and electrochemical or charge-transfer steps. Electrode reaction sequences can also include diffusion steps on the electrode surface. Because of the high activation energy required to transfer two electrons at one time, the charge-transfer reactions are beheved to occur by a series of one electron-transfer steps illustrated by the reactions of the 2inc electrode in strongly alkaline medium (41). 

The enzyme can be immobilized on the electrode by several techniques (53). The simplest method, first used in 1962, is to trap an enzyme solution between the electrode surface and a semipermeable membrane. Another technique is to immobilize the enzyme in a polymer gel such as polyacrylamide which is coated on the electrode surface. Very thin-membrane films can be obtained by electropolymerization techniques (49,54,55) using polypyrrole, polyindole, or polyphenylenediamine films, among others. These thin films (qv) offer the advantage of improved diffusion of substrate and product that... 

F r d ic Current. The double layer is a leaky capacitor because Faradaic current flows around it. This leaky nature can be represented by a voltage-dependent resistance placed in parallel and called the charge-transfer resistance. Basically, the electrochemical reaction at the electrode surface consists of four thermodynamically defined states, two each on either side of a transition state. These are (11) (/) oxidized species beyond the diffuse double layer and n electrons in the electrode and (2) oxidized species within the outer Helmholtz plane and n electrons in the electrode, on one side of the transition state and (J) reduced species within the outer Helmholtz plane and (4) reduced species beyond the diffuse double layer, on the other. 

Transport of a species in solution to and from an electrode/solution interface may occur by migration, diffusion and convection although in any specific system they will not necessarily be of equal importance. However, at the steady state all steps involved in the electrode reaction must proceed at the same rate, irrespective of whether the rate is controlled by a slow step in the charge transfer process or by the rate of transport to or from the electrode surface. It follows that the rate of transport must equal the rate of charge transfer ... 

Diffusion Layer the thin layer of solution adjacent to an electrode through which transport of species to or from the electrode surface occurs by diffusion rather than by convection. 

The rate of diffusion of the ion to the electrode surface is given by Fick s Second Law as... 

S.3.2 Sol-Gel Encapsulation of Reactive Species Another new and attractive route for tailoring electrode surfaces involves the low-temperature encapsulation of recognition species within sol-gel films (41,42). Such ceramic films are prepared by the hydrolysis of an alkoxide precursor such as, Si(OCH3)4 under acidic or basic condensation, followed by polycondensation of the hydroxylated monomer to form a three-dimensional interconnected porous network. The resulting porous glass-like material can physically retain the desired modifier but permits its interaction with the analyte that diffuses into the matrix. Besides their ability to entrap the modifier, sol-gel processes offer tunability of the physical characteristics... 

Inside a pit in electrolytic solution, anodic dissolution (the critical dissolution current density, and diffusion of dissolved metal hydrates to the bulk solution outside the pit take place simultaneously, so that the mass transfer is kept in a steady state. According to the theory of mass transport at an electrode surface for anodic dissolution of a metal electrode,32 the total increase of the hydrates inside a pit, AC(0) = AZC,<0),is given by the following equation33,34 ... 

As shown in Fig. 33, the decreasing mechanism of this fluctuation is summarized as follows At a place on the electrode surface where metal dissolution happens to occur, the surface concentration of the metal ions simultaneously increases. Then the dissolved part continues to grow. Consequently, as the concentration gradient of the diffusion layer takes a negative value, the electrochemical potential component contributed by the concentration gradient increases. Here it should be noted that the electrochemical potential is composed of two components one comes from the concentration gradient and the other from the surface concentration. Then from the reaction equilibrium at the electrode surface, the electrochemical potential must be kept constant, so that the surface concentration component acts to compensate for the increment of the concen-... 

Since the diffusion layer extends into the bulk of the solution, the main role for mitigating the fluctuation is transferred from the reaction at the electrode surface to the diffusion of dissolved metal ions in the bulk of the solution. Then, other fluctuations (i.e., symmetrical fluctuations) emerge, as proved before, and decay to zero. The average value of the symmetrical fluctuation becomes zero because of its symmetry. So, for average values, we can neglect all the symmetrical fluctuations. 

If the film is nonconductive, the ion must diffuse to the electrode surface before it can be oxidized or reduced, or electrons must diffuse (hop) through the film by self-exchange, as in regular ionomer-modified electrodes.9 Cyclic voltammograms have the characteristic shape for diffusion control, and peak currents are proportional to the square root of the scan speed, as seen for species in solution. This is illustrated in Fig. 21 (A) for [Fe(CN)6]3 /4 in polypyrrole with a pyridinium substituent at the 1-position.243 This N-substituted polypyrrole does not become conductive until potentials significantly above the formal potential of the [Fe(CN)6]3"/4 couple. In contrast, a similar polymer with a pyridinium substituent at the 3-position is conductive at this potential. The polymer can therefore mediate electron transport to and from the immobilized ions, and their voltammetry becomes characteristic of thin-layer electrochemistry [Fig. 21(B)], with sharp symmetrical peaks that increase linearly with increasing scan speed. 

Figure 3.6. Spatial variation of the electrochemical potential, jl02-, of O2 in YSZ and on a metal electrode surface under conditions of spillover (broken lines A and B) and when equilibrium has been established. In case (A) surface diffusion on the metal surface is rate limiting while in case (B) the backspillover process is controlled by the rate, I/nF, of generation of the backspillover species at the three-phase-boundaries. This is the case most frequently encountered in electrochemical promotion (NEMCA) experiments as shown in Chapter 4.

The kinetics of ion backspillover on the other hand will depend on two factors On the rate, I/nF, of their formation at the tpb and on their surface diffusivity, Ds, on the metal surface. As will be shown in Chapters 4 and 5 the rate of electrochemically controlled ion backspillover is normally limited by I/nF, i.e. the slow step is their transfer at the tpb. Surface diffusion is usually fast. Thus, as shown in Chapter 5, for the case of Pt electrodes where reliable surface O diffusivity data exist, obtained by Gomer and Lewis several years ago,76 Ds is at least 4.-10 11 cm2/s at 400°C and thus an O2 ion can move at least 1 pm per s on a Pt(lll) or Pt(110) surface. Therefore ion backspillover from solid electrolytes onto electrode surface is not only thermodynamically feasible, but can also be quite fast on the electrode surface. But does it really take place This we will see in the next Chapter. 

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