Moving boundary, transport number

Transport numbers are intended to measure the fraction of the total ionic current carried by an ion in an electrolyte as it migrates under the influence of an applied electric field. In essence, transport numbers are an indication of the relative ability of an ion to carry charge. The classical way to measure transport numbers is to pass a current between two electrodes contained in separate compartments of a two-compartment cell These two compartments are separated by a barrier that only allows the passage of ions. After a known amount of charge has passed, the composition and/or mass of the electrolytes in the two compartments are analyzed. Erom these data the fraction of the charge transported by the cation and the anion can be calculated. Transport numbers obtained by this method are measured with respect to an external reference point (i.e., the separator), and, therefore, are often referred to as external transport numbers. Two variations of the above method, the Moving Boundary method [66] and the Eiittorff method [66-69], have been used to measure cation (tR+) and anion (tx ) transport numbers in ionic liquids, and these data are listed in Table 3.6-7. 

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.

The transport number of an ion varies with the ionic constitution of the solution, and is another way of expressing conductivities or mobilities. There are two important methods for measuring transport numbers the Hittorf method and the moving boundary method5. 

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.

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. 

This is an important point in electroanalytical chemistry, where the general procedure is to arrange for the ions that are being analyzed to move to the electrodeelectrolyte interface by diffusion only. Then if the experimental conditions correspond to clearly defined boundary conditions (e.g., constant flux), the partial differential equation (Pick s second law) can be solved exactly to give a theoretical expression for the bulk concentration of the substance to be analyzed. In other words, the transport number of the substance being analyzed must be made to tend to zero if the solution of Pick s second law is to be applicable. This is ensured by adding some other electrolyte in such excess that it takes on virtually the entire burden of the conduction current. The added electrolyte is known as the indifferent electrolyte. It is indifferent only to the electrodic reaction at the interface it is far from indifferent to the conduction current. 

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). 

By measuring the conductance of several picrates in di-wopropyl ketone at different concentrations, it was shown by the method of Fuoss and Kraus 6 that up to concentration of 01 M there is no detectable triple ion formation. Thus concentrations high enough to satisfy condition (ii) are attainable without the formation of multiple ions. The results of semi-quantitative preliminary experiments indicated that tetraethylammonium and picrate ions had nearly the same mobility in di-wopropyl ketone. This was confirmed by measuring the transport number of the picrate ion by the moving-boimdary method. The conditions for the successful use of the moving-boundary method have been fully examined by Longsworth and Maclnnes.7 A simplified apparatus was used and is shown in fig. 3 camphor-sulphonate was found to be a suitable indicator ion. 

Comparison of the Transport Numbers of the Cation in KCl at 25° C-, obtained by the E ME, Hittorf and Moving Boundary Methods... 

Concentrations of KCl Ej/E ratio Transport Number of K+ EM Hittorf Moving Boundary... 

There are three main techniques for measuring transport numbers emf methods and the Hittorf and moving boundary methods described in Sections 11.19.1 and 11.19.2 to 11.9.4. 

Ionic mobilities are important quantities when considering the moving boundary method of measuring transport numbers (see Section 11.19.2) and in the theory of conductance (see Chapter 12 and Appendix 12.1). 

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 moving boundary method was developed in 1886 by the British physicist Sir Oliver Joseph Lodge (185I-I940) and in 1893 by the British physicist Sir William Cecil Dampier (formerly Whetham) (1867-1952). The method is illustrated in Figure 6.10. Suppose that it is necessary to measure the transport numbers of the ions in the electrolyte MA. Two other electrolytes M A and MA are selected as indicators each has an ion in common with MA, and the electrolytes are such that moves more slowly than M, and A " moves more slowly than A". The solution of MA is placed in the electrolysis tube with the solution of M A on one side of it and that of MA on the other the electrode in M A is the anode, that in MA is the cathode. 

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

In addition, at the boundary of the two solutions a fraction of the charge is carried by H and a fraction t is carried by Cl". The fractions t + and t are the transf erence numbers, or transport numbers, of the ions. One mole of positive charge passing through the boundary requires that t+ moles of ion are moved upward from the solution to the solution a2,... 

To calculate the transport numbers of sodium chloride from moving boundary measurements. 

Moving Boundary method [68] and the Hittorff method [68-71] have been used to measure cation (tR+) and anion (tx ) transport numbers in ionic liquids, and these data are listed in Table 3.6-10. 

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. ... 

The Ag+ ions move to the cathode, while the electrons move to the anode. Therefore in the Agl phase all the current is carried by Ag+ ions, and the transport number measured by deposition of silver at the cathode is unity. The excess sulphur liberated at the phase boundary AggS/AgI eventually reacts... 

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. 

Such methods represent direct applications of Equations (4.31) and (4.32) whereby transport numbers are related to the speeds with which ions move. Moving boundary techniques are based upon the observed rate of movement, under the influence of an applied e.m.f., of a sharp boundary between solutions of two different electrolytes having an anion or cation in common. Measurement of the rate of movement of a sharp boundary presents few problems, since, even if the solutions do not differ in colour, the difference in their refractive indices makes the boundary between them easily distinguishable. A schematic diagram of the relation between two such solutions is shown... 

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. 

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