Particle/electrolyte interface

The model is most vulnerable in the way it accounts for the number of particles that collide with the electrode [50, 115], In the model, the mass transfer of particles to the cathode is considered to be proportional to the mass transfer of ions. This greatly oversimplifies the behavior of particles in the vicinity of an interface. Another difficulty with the model stems from the reduction of the surface-bound ions. Since charge transfer cannot take place across the non-conducting particle-electrolyte interface, reduction is only possible if the ion resides in the inner Helmholtz layer [116]. Therefore, the assumption that a certain fraction of the adsorbed ions has to be reduced, implies that metal has grown around the particle to cover an identical fraction of the surface. Especially for large particles, it is difficult to see how such a particle, embedded over a substantial fraction of its diameter, could return to the plating bath. Moreover, the parameter itr, that determines the position of the codeposition maximum, is an artificial concept. This does not imply that the bend in the polarisation curve that marks the position of itr is illusionary. As will be seen later on, in the case of copper, the bend coincides with the point of zero-charge of the electrode. 

Electrophoretic techniques have found wide applicability in the biomedical areas. Electrophoresis is the migration of colloidal particles in an electrolyte under the influence of an electric field. The zeta potential across the colloidal particle/electrolyte interface may be obtained from the electrophoretic mobility (p) according to the equation ... 

Typically, the largest voltage loss in a cell occurs in the catalyst layers. Electrochemical reactions run at the catalyst particle/electrolyte interface. Consider for definiteness, Pt particles. 

The potential difference across the mobile part of the diffuse-charge layer is frequently called the zeta potential, = E(0) — E(oo). Its value depends on the composition of the electrolytic solution as well as on the nature of the particle-hquid interface. 

FIG. 1 Geometries of electrolyte interfaces, (a) A planar electrode immersed in a solution with ions, and with the ion distrihution in the double layer, (b) Particles with permanent charges or adsorbed surface charges, (c) A porous electrode or membrane with internal structures, (d) A polyelectrolyte with flexible and dynamic structure in solution, (e) Organized amphophilic molecules, e.g., Langmuir-Blodgett film and microemulsion, (f) Organized polyelectrolytes with internal structures, e.g., membranes and vesicles. 

The general way in which a Galvani potential is established is similar in all cases, but special features are observed at the metal-electrolyte interface. The transition of charged species (electrons or ions) across the interface is possible only in connection with an electrode reaction in which other species may also be involved. Therefore, equilibrium for the particles crossing the interface [Eq. (2.5)] can also be written as an equilibrium for the overall reaction involving all other reaction components. In this case the chemical potentials of aU reaction components appear in Eq. (2.6) (for further details, see Chapter 3). 

An important result of this study is the conclusion of a particle-size-dependent COads surface mobility. The value obtained for large Ft particles is significantly smaller than Deo at a solid/gas interface. However, Kobayashi and co-workers, using solid state NMR, performed measurements of the tracer diffusion coefficient Deo at the solid/electrolyte interface and for Ft-black particles (about 5nm grain... 

One of the most distinguishing features of semiconductor nanoparticles for use in photoelectrocatalysis is the absence of band bending at the semiconductor-electrolyte interface, see Fig. 4.2. In contrast to bulk behavior, for a colloidal semiconductor or a semiconductor comprised of a nanociystalline network in contact with an electrolyte the difference in potentials between the center (r = 0) of the particle and a distance r from the center can be expressed [83] ... 

Figure 4.12 is an illustration of the potential distribution for n-type semiconductor particles at the semiconductor-electrolyte interface. There are two limiting cases of equation (4.8.11) for photo-induced electron transfer in semiconductors. For large particles the potential drop within the semiconductor is defined by ... 

Fig. 4.12 Diagram illustrating space charge layer formation in microcrystalline and nanocrystalline particles in equilibrium in a semiconductor-electrolyte interface. The nanoparticles are almost completely depleted of charge carriers with negligibly small band bending.

Fig. 108a-c. Proposed equivalent circuits for. a an empty and b a semiconductor-particle-coated BLM. Porous structure of the semiconductor particles allowed c the simplification of the equivalent circuit. Rm, RH, and Rsol are resistances due to the membrane, to the Helmholtz electrical double layer, and to the electrolyte solutions, while C and CH are the corresponding capacitances Rf and Cf are the resistance and capacitance due to the particulate semiconductor film R m and Cm are the resistance and capacitance of the parts of the BLM which remained unaltered by the incorporation of the semiconductor particles R and Csc are the space charge resistance and capacitance at the semiconductor particle-BLM interface and Rss and C are the resistance and capacitance due to surface-state on the semiconductor particles in the BLM [652]... 

The argument is so general that its particularization for the metal/electrolyte interface was only for convenience. One could have carried out the discussion with equal validity for the gas/electrolyte or the glass (container)/electrolyte boundary of the electrolyte. Of course, one would have had to note the difference between the particles that constitute gases and glass and those that compose a metal. In all these systems, the conclusion would be reached that forces are direction dependent at the phase boundary and therefore new and compromise arrangements are assumed by the particles (of the two phases) in the phase boundary. If the particles are charged or are dipoles, not only is there a redistribution of particles but also an electrification of the interface and the development of a potential difference across it... 

In nanosized particle film electrodes, photogenerated holes can be rapidly transferred to the semiconductor/electrolyte interface and there be captured by the redox species in the electrolyte. In this way, the recombination losses can be diminished. This is of great importance for semiconductors like hematite with a very short hole diffusion length (2-4 nm). Another advantage is the large internal surface area, which characterize nanostructured semiconductor film electrodes. The latter decreases the current density per unit area of semiconductor / electrolyte interface. 

Fig. 10.28. Model of charge carrier separation and charge transport in a nanocrystalline film. The electrolyte has contact with the individual nanocrystallites. Illumination produces an electron-hole pair in one crystallite. The hole transfers to the electrolyte and the electron traverses several crystallites before reaching the substrate. Note that the photogenerated hole always has a short distance (about the radius of the particle) to pass before reaching the semiconductor/electrolyte interface wherever the electron-hole pair is created in the nanoporous film. The probability for the electron to recombine will, however, depend on the distance between the photoexcited particle and the tin-coated oxide back-contact. (Reprinted with permission from A. Hagfeldt and Michael Gratzel, Light-Induced Redox Reactions in Nanocrystalline Systems Chem. Rev. 95 49-68, copyright 1995, American Chemical Society.)...

Directly applying Gubkin s concept of a plasma cathode, Koo et al. produced isolated metal nanoparticles by reduction of a platinum salt at the free surface of its aqueous solution [39]. The authors used an AC discharge as cathode over the surface of an aqueous solution of ITPtCk. Platinum particles with a diameter of about 2 nm were deposited at the plasma liquid electrolyte interface by reduction with free electrons from the discharge. 

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