The moving boundary method

This method for determining transport numbers is the preferred method since it is inherently more accurate than the Hittorf method. Even more important is the fact that the transport numbers can be found over a range of concentrations. This, in turn, means that ionic mobilities and individual ionic molar conductivities can also be found over a range of concentrations. 

In this time, all of the K (aq) at x will have moved to x and all of the other K (aq) in between will have moved beyond x . All of the K (aq) which started in the volume of the solution of KCl(aq) between x and x will have moved downward. 

The current and time will give an experimental value of the total charge passed  

All the quantities in this equation are known and so the transport number for K (aq) can be found for the given [KCl]. 

Varying the concentration of the KCl solution will allow determination of the transport numbers for both ions over a range of concentrations. From these the individual molar ionic conductivities for KCl(aq) over a range of concentrations can be found. 

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In the case of small ions, Hittorf transference cell measurements may be combined with conductivity data to give the mobility of the ion, that is, the velocity per unit potential gradient in solution, or its equivalent conductance. Alternatively, these may be measured more directly by the moving boundary method. 

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 second method, namely the moving boundary method, is based on the direct observation of migration of ions under the influence of an applied potential - unlike Hittorf s method in which the changes in concentration at the electrodes are measured. 

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... 

Tiselius, A. W. K., The moving-boundary method of studying the electrophoresis of proteins, Ph.D. thesis. University of Uppsala, Sweden, 1930. 

The electrophoretic mobility of sodium dodecyl sulfate micelles was determined by the moving-boundary method after the micelles were made visible by solubilizing dye in them. This quantity was measured at the critical micelle concentration (CMC) in the presence of various concentrations of NaCl. The radius of the micelles was determined by light scatteringj... 

AktivKemiMineralGeol A22, No 10(1946) (Electrophoresis by the moving boundary method) 5) A. Weissberger, Physicochemical Methods of Organic Analysis , VanNostrand, NY, Vol 1(1949), pp 1685—1712 6) R.E. Kirk D.F. Othmer, Edits, Encyclopedia of Chemical Technology", Interscience,... 

The sedimentation constant s has been determined by applying the moving boundary method (46)... 

Zone electrophoresis is normally carried out horizontally in a suitable medium such as paper, polyacrylamide gel, starch gel or cellulose acetate. The sample components can be completely separated and quantitatively and qualitatively identified in much lower quantities than by the moving-boundary method. The procedure consists of saturating the support material with a buffer solution. The ends of the strip of support are immersed in separate reservoirs of buffer solution to maintain the saturation. The sample is then applied as a narrow band near one end of the support strip. A voltage potential is created down the length of the strip causing the sample components to ionize and then migrate at a rate dependent on their charge, molecular size and interactions with the support medium. When the process is complete, the strip is removed and developed for examination of the separated components. Densitometry is normally used for quantitation of the bands after suitable color development. 

The moving boundary method is usually complicated by small differences between the ascending and descending boundaries in the two arms of the U-tube. These boundary anomalies result from differences in the conductivity (and, therefore, the potential gradient) at each boundary. They can be minimised by working with low protein concentrations. 

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.

Today electrophoresis is most often performed on a supporting medium rather than by the moving boundary method. The medium may be paper, a... 

Aug. 10,1902, Stockholm, Sweden - Oct. 29,1971, Uppsala, Sweden) Tiselius studied chemistry in Uppsala and joined the laboratory of -> Svedberg in 1925. In 1930 he received the Ph.D. for his thesis entitled The moving-boundary method of studying the electrophoresis of proteins . In 1937, a research professorship was established for Tiselius. His fundamental work in developing -> electrophoresis was encouraged and supported by Svedberg. In 1948 he was awarded the Nobel Prize in Chemistry for his achievements in electrophoresis and adsorption analysis. 

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. 

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... 

In the practical application of the moving boundary method one boundary only is observed, and so the necessity of finding two indicator solutions is obviated the method of calculation is as follows. If one faraday of electricity passes through the system, equiv. of the cation must pass any given point in one direction if c equiv. per unit volume is the concentration of the solution in the vicinity of the boundary formed by the M ions, this boundary must sweep through a volume t /c while one faraday is passing. The volume swept out by the cations for the pa.ssage of Q coulombs is thus... 

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... 

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 ... 

II) Mooing boundary electrophoresis. The moving boundary method to measure electrophoretic mobilities differs from the previous one in that no attempt Is made to observe Individual particles. Rather the collective motion of all the colloids In a sol Is studied. If the sol adjoins an equilibrium colloid-free solution the boundary between sol and solution will move under the influence of a field applied across this border, hence the name. The rate at which this boundary is displaced gives the electrophoretic mobility. 

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. 

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-... 

In the development of the moving boundary method it was pointed out by early workers that the electrochemical reactions which occur at the electrodes on the passage of current are accompanied by volume changes which may affect the observed displacement of the boundary. Denison and Steele considered the effect to be negligible, though their conclusion was subsequently shown to be incorrect by Lewis20 whose discussion of the matter is essentially that given below. 

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. 

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