Electrical analog, interfaces

This chapter will be concerned with the kinetics of charge transfer across an electrically charged interface and the transport and chemical processes accompanying this phenomenon. Processes at membranes that often have analogous features will be considered in Chapter 6. The interface that is most often studied is that between an electronically conductive phase (mostly a metal electrode) and an electrolyte, and thus these systems will be dealt with first. 

Figure 28 Randles circuit that serves as an electrical analog of the corroding interface.

An electrochemical cell is a type of electrical circuit. As such, it may be modeled with an electrical analog circuit. The potentiometric cell can be considered to be an electrical potential applied to a capacitor and a resistor in series. The capacitor represents the interface between the electrode and the solution, the applied potential is the solution Eh, and the resistor represents the heterogeneous kinetics of the aqueous redox species. The term "heterogeneous kinetics" denotes electron transfer between different phases, in this case aqueous species and the noble-metal electrode. The time required for the capacitor to equilibrate with the applied potential depends on the size of the capacitor and the electrical current. 

Figure I. (a) Experimental arrangement for the measurement of freezing potentials (10 K, resistor not in circuit) and currents (10 K. resistor shunting the phases), V = electrometer C = recorder, (b) Electric analog of the system in the shunt case, Rb = interface barrier resistance = external shunt resistance Rj = ice resistance Ri = solution resistance Rm = ice metal interface resistance c = interface charge separation...

Based on the case of the semiinfinite solid, one may foretell the temperature history, temperature gradient, and heating rate of the stratified fluid portion beneath the liquid—vapor interface where numerous succeeding initial and boundary conditions are to be imposed in the manner of trial and error, where these conditions are to vary with time for any one given situation, or where a variation of thermal properties must be taken into account, the electrical-analog method may better be adapted to the problem with respect to time involved in solution attainment. 

The calomel electrode Hg/HgjClj, KCl approximates to an ideal non-polarisable electrode, whilst the Hg/aqueous electrolyte solution electrode approximates to an ideal polarisable electrode. The electrical behaviour of a metal/solution interface may be regarded as a capacitor and resistor in parallel (Fig. 20.23), and on the basis of this analogy it is possible to distinguish between a completely polarisable and completely non-polarisable... 

A detailed analysis of this behavior, as well as its analogy to the mercury-KF solution system, can be found in several papers [1-3,8,14]. The ions of both electrolytes, existing in the system of Scheme 13, are practically present only in one of the phases, respectively. This allows them to function as supporting electrolytes in both solvents. Hence, the above system is necessary to study electrical double layer structure, zero-charge potentials and the kinetics of ion and electron reactions at interface between immiscible electrolyte solutions. 

Although a family of OgS - Jig8 values are allowed under Equation 7 the actual equilibrium state of the oxide/solution interface will be determined by the dissociation of the surface groups and the properties of the electrolyte or the diffuse double layer near the surface. For surfaces that develop surface charges by different mechanisms such as for semiconductor, there will be an equation of state or charge-potential relationship that is analogous to Equation 7 which characterizes the electrical response of the surface. 

Show that Eq. (QQ) applies for the electrical circuit analogy in Fig. 5.16 with the individual conductances and resistances defined as shown (but excluding the interface reaction). 

Equilibrium is reached when the driving force for the diffusion (the concentration gradient) is compensated for by the electric field (the potential gradient). Under these equilibrium conditions, there is an equilibrium net charge on each side of the junction and an equilibrium potential difference d< >e. This process is analogous to the way charge transfer across a nonpolarizable electrode/solution interface results in the establishment of an equilibrium potential difference across the interface. 

Experiments demonstrate that along crystal imperfections such as dislocations, internal interfaces, and free surfaces, diffusion rates can be orders of magnitude faster than in crystals containing only point defects. These line and planar defects provide short-circuit diffusion paths, analogous to high-conductivity paths in electrical systems. Short-circuit diffusion paths can provide the dominant contribution to diffusion in a crystalline material under conditions described in this chapter. 

The experimental set-up is shown in Fig. 7-1 an electrochemical interface with low level noise and a transfer function analyzer (TFA) were used for measurements of the EHD impedance. A matched two-channels 24 db/octave low pass filter (F) was used to remove HF noise and the ripple due to electric network supply, this analog filtering allows the TFA to operate with an increased sensitivity. These instruments were controlled by a computer, which recorded the data. 

A test system, controlled by personal computer (PC), was developed to evaluate the performance of the sensors. A schematic of this system is shown in Figure 3. The signals from the sensors were amplified by a multi-channel electrometer and acquired by a 16 bit analog to digital data acquisition board at a resolution of 0.0145 mV/bit. The test fixture provided the electrical and fluid interface to the sensor substrate. It contained channels which directed the sample, reference and calibrator solutions over the sensors. These channels combined down stream of the sensors to form the liquid junction as shown in Figure 1. Contact probes were used to make electrical connection to the substrate. Fluids were drawn through the test fixture by a peristaltic pump driven by a stepper motor and flow of the different fluids was controlled by the pinch valves. 

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