Transference numbers moving-boundary method

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. 

Another way of determining the transference numbers is moving boundary methode, whereby the movement of a visible boundary between two solutions of different electrolytes in an electrical field is followed by observing the colour or light refraction. If for instance a solution of potassium permanganate is in contact with a solution of potassium nitrate the displacement of colored... 

Three methods have been generally employed for the experimental determination of transference numbers the first, based on the procedure originally proposed by Hittorf (1853), involves measurement of changes of concentration in the vicinity of the electrodes in the second, known as the moving boundary method, the rate of motion of the boundary between two solutions under the influence of current is studied (cf. p. 116) the third method, which will be considered in Chap. VI, is based on electromotive force measurements of suitable cells. 

Although the Hittorf method is simple in principle, accurate results are difficult to obtain it is almost impossible to avoid a certain amount of mixing as the result of diffusion, convection and vibration. Further, the concentration changes are relatively small and any attempt to increase them, by prolonged electrolysis or large currents, results in an enhancement of the sources of error just mentioned. In recent years, therefore, the Hittorf method for the determination of transference numbers has been largely displaced by the moving boundary method, to be described later. 

The Moving Boundary Method.—The moving boundary method for measuring transference numbers involves a modification and improvement of the idea employed by Lodge and by Whetham (cf. p. 60) for the study of the speeds of ions. On account of its relative simplicity and the accuracy of which it is capable, the method has been used in recent years for precision measurements. ... 

If it is required to determine the transference numbers of the ions constituting the electrolyte MA, e.g., potassium chloride, by the moving boundary method, it may be supposed that two other electrolytes, designated by M A and MA, e.g., lithium chloride and potassium acetate, each having an ion in common with the experimental solute MA, arc available to act as indicators.Imagine the solution of MA to be placed between the indicator solutions so as to form sharp boundaries at a and 5, as shown in Fig. 41 the anode is inserted in the. solution of M A and the cathode in that of MA. In order that the boundaries... 

When carrying out a transference number measurement by the moving boundary method the bulk concentration of the indicator solution is chosen so as to comply with equation (15), as far as possible, using approximate transference numbers for the purpose of evaluating c. The experiment is then repeated with a somewhat different concentration of indicator solution until a constant value for the transference number is obtained this value is found to be independent of the applied potential and hence of the current strength. 

Experimental Methods.—One of the difficulties experienced in performing transference number measurements by the moving boundary method was the establishment of sharp boundaries recent work, chiefly by Macinnes and his collaborators, has resulted in such improvements of technique as to make this the most accurate method for the determination of transference numbers. Since the earlier types of apparatus... 

Results of Transference Number Measurements.—Provided the measurements are made with great precision, the results obtained by the Hittorf and moving boundary methods agree within the limits of experimental error this is shown by the most accurate values for various solutions of potassium chloride at 25° as recorded in Table XXVIII. 

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). 

Some of the most recent data of the transference numbers of the cations of various salts at a number of concentrations at 25°, mainly obtained by the moving boundary method, are given in Table XXIX ... 

Transference Numbers in Mixtures.—Relatively little work has been done on the transference numbers of ions in mixtures, although both Hittorf and moving boundary methods have been employed. In the former case, it follows from equation (3) that the transference number of any ion in a mixture is equal to the number of equivalents of that ion migrating from the appropriate compartment divided by the total number of equivalents deposited in a coulometer. It is possible, therefore, to derive the required transference numbers by analysis of the anode and cathode compartments before and after electrolysis. 

Much use of transference numbers has been made in the development of electrochemistry. The chief methods for their determination are (a) the Hittorf method, (6) die moving boundary method and (c) the electromotive force method. Of these the first two will be considered in this chapter. 

The Moving Boundary Method for Determining Transference Humbers. A means of obtaining transference numbers which has proved, in recent years, to be of greater precision than the Hittorf procedure is the method of moving boundaries. The phenomenon which makes the measurements possible is as follows. If a potassium chloride solution is placed in a tube above a cadmium chloride solution, as is shown in Fig. 4a, and electric current is passed in the direction indi-... 

The Hittorf transference number may be defined as the number of equivalents of a given ion constituent which, on passage of one faraday of electricity, cross a plane fixed with respect to the solvent, usually, of course, water. In a determination by the moving boundary method the position of a boundary is fixed with respect to the graduations of the tube. Hence, in order to obtain a value of a transference number comparable with that found by the Hittorf method, the motion of the water with respect to the tube must be computed. 

Table IV. Cation Transference Numbers at 25° for Aqueous Solutions of Electrolytes Determined by the Moving Boundary Method...

The Transference Numbers of Ion Constituents in Mixtures of Electrolytes. The moving boundary method can in certain cases be used to determine the transference numbers of the ion constituents in mixtures of electrolytes. The method used by Longsworth 32 for determining the transference numbers in mixtures of hydrochloric acid and potassium chloride is as follows. 

The moving-boundary method for the measurement of transference numbers has been brought to a high state of perfection. A schematic diagram of the apparatus is shown in Fig. 31.6. A tube has two electrodes fixed at the ends and contains two solutions having an... 

The moving-boundary method yields more accurate data on transference numbers than does the Hittorf method. Experimentally it is easier to handle. The difficulties lie in the establishment of a sharp boundary, the necessity of avoiding convection currents, and excessive heating by the current. However, once the boundary is established, the flow of current sharpens the boundary, making this a minor difficulty. The relative concentrations of the two solutes are important in maintaining a sharp boundary. The faster moving ion, M in this example, does not lead by more than a few atomic diameters, since a potential difference develops in such a sense as to slow it down in the steady state the two ions move with the same velocity, but M is always a little bit ahead of M. 

Among the experimental methods for determining transference numbers, the moving boundary method (cf. 82,190,194,211) allows their determination with a precision close to that of conductances. Fi ne 5 gives an example... 

Some empirical assumptions have been made to avoid the difficult and time-consuming experiments (Hittorf or moving boundary method) to determine transference numbers. 

Macinnes DA, Cowperthwaite lA, Blanchard KC (1926) The moving-boundary method for determining transference numbers. V. A constant current apparatus. J Am Chem Soc 48 1909-1912... 

Macinnes DA, Longswoith L (1932) Transference numbers by the method of moving boundaries. Chem Rev 11 171-230... 

Figure 20.6 Example ceU for calculation of transference number by tbe moving boundary method.

As mentioned earlier, electrolytes used in lithium batteries are usually concentrated, binary electrolytes that exhibit nonideal behavior. In addition, polymer and gel electrolytes are opaque, highly resistive, and sticky, and therefore their transference numbers are not easily measurable using traditional techniques such as the Hittorf or moving boundary methods. Recent theoretical studies have described the substantial error involved in measuring transference numbers with techniques that assume ideal behavior [14, 15], and have described how experimental data can be interpreted rigorously using concentrated-solution theory to obtain transference numbers. One method is the galvanostatic polarization technique [120,121,122] ... 

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.

An alternative, somewhat simple but less accurate, procedure for measuring transference numbers by the moving boundary principle, utilizes the air-lock method of establishing the boundary. The apparatus for a rising boundary is shown in Fig. 44 the graduated measuring tube A has a bore of about 7 mm., whereas E and F are fine capillaries the top of the latter is closed by rubber tubing with two pinchcocks. The electrodes are placed in the vessels B and C. 

A more rigid but laborious method, for deriving transference numbers from E.M.p. data, makes use of the fact that the activity coefficient of an electrolyte can be expressed, by means of an extended form of the Debye-Hiickel equation, as a function of the concentration and of two empirical constants.When applied to the same data, however, this procedure gives results which are somewhat different from those obtained by the method just described. Since the values are in better agreement with the transference data derived frorq moving boundary and other measurements, they are probably more reliable. 

In spite of its simplicity accurate results are very difficult to get with the Hittorf method. The main difficulties are, first, the necessity for avoiding mixing of the electrode and middle portions during an electrolysis, which may take from sixteen to twenty-four hours, and secondly, the need for extremely accurate analyses of the solutions, since the method depends essentially on small differences between large quantities. For these reasons the more recent accurate data on transference numbers have been obtained, in greatest part, by means of the more complicated, but more speedily and accurately carried out, method of moving boundaries, which will be next described. 

The results of moving boundary determinations of transference numbers in which the modern developments of the method have been employed are given in Table IV, and are mainly due to the investigations of Longsworth. The figures in this table will be referred to a number of times in following chapters. The transference numbers are of use in interpreting the results of determinations of the potentials of concentration cells as activity coefficients which, in turn, may be used to test the validity of the thermodynamic aspects of the interionic attraction theory of electrolytes. In addition the transference numbers, alone, and with conductance measurements, are of utility in connection with tests of the interionic attraction theory of electrolytic conductance. 

Although we have assumed that the moving boundary and the Hittorf methods, when correctly used, yield the same values of transference numbers, there has been no adequate test of this assumption until recently. The only measurements of transference numbers by the Hittorf method available for this comparison, in which modern technique has... 

A basic feature which differentiates isotachophoresis from the other electrophoretical techniques is that zones migrate at the same velocity from the moment the equilibrium has established. By this the name iso-tachos is explained. Its simplest version is the moving boundary technique applied to the measurement of transference numbers (known since Nemst ° Whetham and Kohlrausch ). Theoretical, experimental and instrumental elaboration of this technique was described in detail by Macinnes and Longsworth Based on the example of this simple method, basic features and characteristics of isotachophoretical migration and its terminology can be described and explained. 

The detailed theory and mode of operation of the main experimental methods of obtaining transference numbers—Hittorf, direct and indirect moving boundary, analytical boundary, e.m.f. of cells with transference or of cells in centrifugal fields— have been published elsewhere. Only the features particularly pertinent to work with electrolytes in organic solvents will be dealt with here. 

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