Interfacial potential dependance

Pm, the solution-membrane or solution - in-sula-tor interfacial potential, depends on the activity of the ions in the analyte solution according to the Nemst-Nikolsky equation [Eq. (6), Section 28.2.3.1.1] for ISFETs with an additional membrane, or according to a similar equation (see below) for ISFETs with a solution - insulator interface. 

At each interface the interfacial potential will depend upon the chemical potentials of the species involved in the equilibrium. Thus at the Zn/Zn electrode there will be a tendency for zinc ions in the lattice to lose electrons and to pass across the interface and form hydrated ions in solution this tendency is given by the chemical potential of zinc which for pure zinc will be a constant. Similarly, there will be a tendency for hydrated Zn ions in solution to lose their hydration sheaths, to gain electrons and to enter the lattice of the metal this tendency is given by the chemical potential of the Zn ions, which is related to their activity. (See equation 20.155.) Thermodynamically... 

This potential depends on the interfacial tension am of a passivated metal/electrolyte interface shifting to the lower potential side with decreasing am. The lowest film breakdown potential AEj depends on the surface tension of the breakdown site at which the film-free metal surface comes into contact with the electrolyte. A decrease in the surface tension from am = 0.41 J m"2 to nonmetallic inclusions on the metal surface, will cause a shift of the lowest breakdown potential by about 0.3 V in the less noble direction. 

These three equations (11), (12), and (13) contain three unknown variables, ApJt kn and sr The rest are known quantities, provided the potential-dependent photocurrent (/ph) and the potential-dependent photoinduced microwave conductivity are measured simultaneously. The problem, which these equations describe, is therefore fully determined. This means that the interfacial rate constants kr and sr are accessible to combined photocurrent-photoinduced microwave conductivity measurements. The precondition, however is that an analytical function for the potential-dependent microwave conductivity (12) can be found. This is a challenge since the mathematical solution of the differential equations dominating charge carrier behavior in semiconductor interfaces is quite complex, but it could be obtained,9 17 as will be outlined below. In this way an important expectation with respect to microwave (photo)electro-chemistry, obtaining more insight into photoelectrochemical processes... 

Figure 14. PMC potential dependence, calculated from analytical formula (18) for different interfacial rate constants for minority carriers S = 1 cm, minority carrier flux toward interface I,- 1 cm-2s 1, a= 780enr1, L = 0.01 cm, 0=11.65 cmV, Ld = 2x 0"3cm), (a) sr = 0 and different charge-transfer rates (inserted in the figures in cm s 1), (b) Constant charge-transfer rate and different surface recombination rates (indicated in the figure).

Figure 16 shows such PMC peaks in the depletion region for electrodes of Si,9 WSez8 and ZnO.12 They all appear near the onset of anodic photocurrents. They have different shapes, which, however, can easily be explained with the assumption of potential-dependent interfacial charge-transfer and charge recombination rates. 

As outlined at the beginning of this chapter, combined photocurrent and microwave conductivity measurements supply the information needed to determine three relevant potential-dependent quantities the surface concentration of excess minority carriers (Aps), the interfacial recombination rate (sr), and the interfacial charge-transfer rate ( r). By inserting the... 

Therefore, no experimental knowledge is available on interfacial reaction mechanisms under such conditions. These now become accessible via PMC measurements. As theory shows [Fig. 13(b)], the PMC signals in the accumulation region are controlled by potential-dependent surface recombination and charge-transferrates, as well as by the bulk lifetime of charge carriers. 

The fact that a potential-dependent lifetime peak for PMC transients has been found which coincides with the stationary PMC peak in the depletion region near the onset of photocurrents (Fig. 22) is very relevant since the stationary PMC peak is determined by the interfacial rate constants of charge carriers (Figs. 13 and 14) this should also be the case for the transient PMC peak. To demonstrate this correlation, the following formalism can be developed10 ... 

Equation (40) relates the lifetime of potential-dependent PMC transients to stationary PMC signals and thus interfacial rate constants [compare (18)]. In order to verify such a correlation and see whether the interfacial recombination rates can be controlled in the accumulation region via the applied electrode potentials, experiments with silicon/polymer junctions were performed.38 The selected polymer, poly(epichlorhydrine-co-ethylenoxide-co-allyl-glycylether, or technically (Hydrine-T), to which lithium perchlorate or potassium iodide were added as salt, should not chemically interact with silicon, but can provide a solid electrolyte contact able to polarize the silicon/electrode interface. 

On the basis of our theoretical considerations and preliminary experimental work, it is hoped that fast processes of charge carriers will become directly measurable in functioning photoelectrochemical cells, Typical semiconductor electrodes are not the only systems accessible to potential-dependent microwave transient measurements. This technique may also be applied to the interfacial processes of semimetals (metals with energy gaps) or thin oxide or sulfide layers on ordinary metal electrodes. 

VII. OXIDES AND SENSITIZATION CELLS 1. Potential Dependence of Interfacial Rate Constants... 

Since the potential-dependent photocurrent and the potential-dependent PMC signal were measured and potential-dependent interfacial rate constant kr can be determined. It turns out that it increases exponentially with the electrode potential applied... 

In this chapter we have attempted to summarize and evaluate scientific information available in the relatively young field of microwave photoelectrochemistry. This discipline combines photoelectrochemical techniques with potential-dependent microwave conductivity measurements and succeeds in better characterizing the behavior ofphotoinduced charge carrier reactions in photoelectrochemical mechanisms. By combining photoelectrochemical measurements with microwave conductivity measurements, it is possible to obtain direct access to the measurement of interfacial rate constants. This is new for photoelectrochemistry and promises better insight into the mechanisms of photogenerated charge carriers in semiconductor electrodes. 

The form of the kinetic equation depends on the way in which the surface potential X varies with electrode potential E. When the surface potential is practically constant, the first factor in Eq. (14.24) will also be constant, and the potential dependence of the reaction rate is governed by the second factor alone. The slope b of the polarization curve will be RT/ F (i.e., has the same value as that found when the same reaction occurs at a metal electrode). When in another case a change in electrode potential E produces an equally large change in surface potential (i.e., E = x + const), while there is practically no change in interfacial potential. Then Eq. (14.24) changes into... 

FIGURE 32.4 Potential dependence of the interfacial tension J and the capacity C for the interface between solutions of 5mM tetrabutylammonium tetraphenylborate in 1,2-dichloroethane and lOOmM LiCl in water. The potential scale E represents the Galvani potential difference relative to the standard ion transfer potential for tetraethylammonium ion, cP o EA+ = 0.02 V. 

Campbell, S. D. and Hdber, A. C. (1999) Nanometer-scale probing of potential-dependent electrostatic forces, adhesion, and interfacial friction at the electrode/ electrolyte interface. Langmuir, 15, 891-899. 

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