Moving-boundary cell

Several designs have gained popularity, and they are named after their inventors Abramson (flat cell), Briggs, Briggs-Mattson, Hamilton-Stevens, Mattson [252,253], Riddick, and van Gils. A moving-boundary cell is shown and described in [7,47]. 

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. 

Differential ultracentrifugation methods may also be applied to analysis of the purity of macromolecular samples. If one sharp moving boundary is observed in a rotating centrifuge cell, it indicates that the sample has one component and therefore is pure. In an impure sample, each com ponent would be expected to form a separate moving boundary upon sedimentation. 

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. 

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). 

Early experiments in the development of isoelectric focusing, a high-resolution steady-state electrophoresis method, occurred in 1912, with an electrolytic cell that was used to isolate glutamic acid from a mixture of its salts.1 A simple U-shaped cell, such as that used for moving-boundary electrophoresis (Chapter 9), with two ion-permeable membranes equidistant from the center, created a central compartment that separated anodic and cathodic chambers, as shown in Figure 11.1. Redox reactions occurring in the anodic (Eq. 11.1) and cathodic (Eq. 11.2) electrolyte compartments generated H+ and OH ions in the respective chambers ... 

Figure 13.11. Results for a moving-boundary ultracentrifuge experiment using different optical detection systems and a double-sector cell. Part (a) is a graphical representation, (b) is the result of an uv photograph, (c) is a plot of absorbance versus distance (from b), id) is a photograph obtained with Schlieren optics, (e) is an interference diagram obtained using Rayleigh optics, and (f) is another interference diagram, obtained with Lebedev optics.

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. 

The cell in the rotor is sector shaped (Fig. 35.17). As the rotor spins, the macromolecule moves outward leaving the pure solvent behind. A moving boundary is established between the solution and the solvent. The position of the boundary can be detected by the difference in refractive index between the two parts of the cell. Using measurements of the positions and V2 at times and 2 we can calculate the value of 5 from Eq. (35.80). Alternatively, if In r is plotted against t, we can obtain the value of s from the slope. 

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. 

Eulerian methods perform weU for a variety of moving boundary problems. However, in these problems, particularly when surface forces are to be included in the flow calculations, the interface is diffused and occupies a few grid cells in practical calculations. This is undesirable in many problems both from an accuracy and physical realizability/modeling standpoint. 

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