Moving boundary, transport number determination

Fig. 2.7. The moving boundary method for determining transport numbers. AB and CD represent the frontiers between MX and NX at the beginning of the experiment and after time t respectively.

The moving boundary method of determining a transport number (q.v.) depends on observing the movement, under a constant current, of the boundary between the solution under study and a following indicator solution. For accuracy this boundary must remain quite sharp, and the conditions for this are as follows (a) the two electrolytes have a common anion when the movement of a cation is being observed, and vice versa (b) the conductivity of the indicator ion must be lower than that of the leading ion (c) the solution with the lower density must be above the other (d) an initially sharp boundary must be established and (e) the concentrations of the two solutions must be in the correct ratio. 

Moving boundary method for transport number determination condition for sharp boundary... 

For obtaining internal or external mobilities, the corresponding transport numbers are usually measured. There are several methods for determining transport numbers in molten salts that is, the Kleimn method (countercurrent electromigration method or column method), the Hittorf method (disk method), the zone electromigration method (layer method), the emf method, and the moving boundary method. These are described in a comprehensive review. ... 

The transference or transport number of an ion can be determined by (i) the analytical method (ii) the moving boundary method and (iii) the emf method. The first two methods will be dealt with here, but the third will figure in a later section. 

The apparatus used to determine the transport number by the moving boundary method is shown in Figure 6.4. It consists of a long vertical tube of uniform cross-section which is fitted with two electrodes at the two ends. Let the electrolyte, the transport number of whose... 

Figure 6.4 Moving boundary experimental set-up for determining the transport number of E+ ions.

Transport numbers can be measured by several methods. The application of the Hittorf cell (-> Hittorf transport method), that was introduced in 1853, is still the most frequently used technique for the determination of the transport number [iv]. The moving boundary method, analogous to that used by -> Tiselius to measure -> electrophoretic mobilities is also used to measure transport numbers [v]. See also -> Tubandt method. 

Fig. 5.42. Schematic diagrams of methods of determining transport numbers (a) Measure velocity of the bubble (b) measure transfer of the tracer (c) measure the potential difference due to pressure difference (d) measure the change in weight (e) measure the transport of liquid metal electrodes (f) measure the steady-state level (g) measure the change in weight (h) measure the moving boundary.

It may be noted that the values obtained by the moving boundary method, like those given by the Hittorf method, are the so-called apparent transference numbers (p. 114), because the transport of water by the ions will affect the volume through which the boundary moves. It is the practice, however, to record observed transference numbers without applying any correction, since much uncertainty is attached to the determination of the transport of water during the passage of current. Further, in connection with the study of certain types of voltaic cell, it is the apparent" rather than the true" transference number that is involved (cf. p. 202). 

There are two main methods for determining transport numbers, both of which were developed early in the study of conductance. They are the Hittorf method and the moving boundary method. The emf method has been described in Section 9.21. 

Three experimental methods have been employed for the determination of transport numbers. One of them, developed by the German physicist Johann Wilhelm Hittorf (1824-1914) in 1853, involves measuring the changes of concentration in the vicinity of the electrodes. In the second, the moving boundcny method a study is made of the rate of movement, under the influence of a current, of the boundary between two solutions. This method is described on p. 283. A third method, which we will not consider in this book, involves the measurement of the electromotive force of certain electrochemical cells. 

The determination of transport numbers by the moving-boundary method ... 

MB = Moving Boundary, MH = modified Hittorf, PNMR = pulse gradient-field spin echo (PGSE) NMR. Transport numbers at 298 K determined from self-diffusion data provided in the reference. 

Modifications of Hittorf s method of determining transport numbers were used by a large number of experimenters. The moving boundary method was first used by Oliver Lodge, who showed that the hydrogen ion moves with the velocity of 0 0026 cm./sec. under a potential gradient of i volt/cm. It was improved by Whetham. ... 

Essentially there are three methods by means of which transport numbers may be determined, viz. (i) the method due to Hittorf (of which there are several modifications), (ii) the moving boundary method (of which, again, there are several forms) and (iii) methods based on measurements of the e.m.f. s of concentration cells. The principles of methods (i) and (ii) will be considered here, the e.m.f. determination being discussed in a later chapter dealing with the application of e.m.f. measurements. 

The determination of electrophoretic velocities may be carried out experimentally by the use of methods suitable for transport number measurements. Moving boundary techniques have proved useful despite the problem of a difficulty in selecting suitable indicator ions. Reliable estimates of electrophoretic velocities make possible the determination of zeta-potentials. Since colloids migrate at characteristic rates under the influence of an electric field, electrophoresis provides an important means of separation. Coatings, such as rubber or graphite, may be deposited on metal electrodes by this means and additives to these may be co-deposited. 

By electrophoresis (or cataphoresis as it was called formerly) we mean the movement of colloidal particles in an electric field It is in every respect comparable to the mobility of electrolytic ions and can be measured in much the same ways as those by which ionic mobilities are determined. In the methods of electrophoresis we shall recognise the determinations ot the transport number, the moving boundary as well as the analytical method Moreover, the ultramicroscopic visibility of colloidal particles offers the means of studying their electrophoretic mobility directly under the ultra-tpict osccpe These methods are discussed in greater detail in 7 of this chapter ... 

An alternative electrochemical approach to the measurement of fast interfacial kinetics exploits the use of the scanning electrochemical microscope (SECM). A schematic of this device is shown in Fig. 14 the principle of the method rests on the perturbation of the intrinsic diffusive flux to the microelectrode, described by Eq. (34) above. A number of reviews of the technique exist [109,110]. In the case of the L-L interface, the microelectrode probe is moved toward the interface once the probe-interface separation falls within the diffusion layer, a perturbation of the current-distance response is seen, which can be used to determine the rate of interfacial processes, generally by numerical solution of the mass-transport equations with appropriate interfacial boundary conditions. The method has been... 

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