Transport number 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. 

The measurement of transport numbers by the above electrochemical methods entails a significant amount of experimental effort to generate high-quality data. In addition, the methods do not appear applicable to many of the newer non-haloalu-minate ionic liquid systems. An interesting alternative to the above method utilizes the NMR-generated self-diffusion coefficient data discussed above. If both the cation (Dr+) and anion (Dx ) self-diffusion coefficients are measured, then both the cation (tR+) and anion (tx ) transport numbers can be determined by using the following Equations (3.6-6) and (3.6-7) [41, 44] ... 

Manometric and volumetric methods (kinetics) Thermogravimetry (kinetics from very thin films to thick scales stoichiometry) Electrical conductivity of oxides and allied methods (defect structures conduction mechanisms transport numbers) Radioactive tracers and allied methods (kinetics self diffusion markers)... 

We express the altered concentration in terms of the adsorption excess. If all the adsorbed substance were contained to the extent of k gr. per cm.2 on a superficial layer of zero thickness and surface total mass present in the volume Y would be m = V + kto. The layer of altered concentration must, however, have a certain thickness. We will therefore imagine a plate 2 placed in front of the surface and parallel to it, and define the adsorption excess as the concentration in the included layer minus the concentration in the free liquid. That this result is independent of the arbitrarily chosen thickness is easily proved when we remember that the problem is exactly the same as that of finding the change of concentration around an electrode in the determination of the transport number of an ion by Hittorf s method. 

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. ... 

There is difficulty in defining the absolute mobilities of the constituent ions in a molten salt, since it does not contain fixed particles that could serve as a coordinate reference. Experimental means for measuring external transport numbers or external mobilities are scarce, although the zone electromigration method (layer method) and the improved Hittorf method may be used. In addition, external mobilities in molten salts cannot be easily calculated, even from molecular dynamics simulation. 

The internal transport numbers may be measured most accurately and precisely by the Klemm method, which was developed for the purpose of isotope separation. This method has the following merits (1) It is insensitive to a small amount of impurities, such as water. (2) Even in the region of very small concentration of an ion of interest, 12 can be measured accurately. (3) It can be applied to additive ternary systems. An apparatus for the Klemm method of measuring 12 in nitrate mixtures is shown in Fig. I. This cell developed for nitrates by Okada s group has the following advantages compared with other electromigration cells ... 

Various methods are available for determining the solvation number hj and (or) the radius of the primary solvation sheath (1) by comparing the values of the true and apparent ionic transport numbers, (2) by determining the Stokes radii of the ions, or (3) by measuring the compressibility of the solution [the compressibility decreases... 

During electrolysis there is no change in composition of an individual melt close to the electrode surfaces only its quantity (volume) will change. The resulting void space is filled again by flow of the entire liquid melt mass. This flow replaces the diffusional transport of ions customarily associated with aqueous solutions. This has particular consequences for the method used to measure ionic transport numbers ... 

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. 

Based on the general scenario provided above, the analytical method to determine transference or transport numbers has been devised and is carried out in an apparatus which can essentially be regarded as an improvement over the Hittorf apparatus. This consists of two vertical tubes connected together with a U-tube in the middle all three tubes are provided with stop-cocks at the bottom. The U-tube is also provided with stop-cocks at the top by closing these, the solutions in the cathode and anode limbs can be isolated. The silver anode is sealed in a glass tube as shown, and the cathode is a piece of freshly silvered silver foil. The apparatus is filled up with a standard solution of silver nitrate and a steady current of about 0.01 ampere is passed for 2-3 hours. In order to avoid the occurrence of too large a change in concentration it is necessary to pass the current only for a short duration. The... 

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... 

Fig. 2.10 Schematic design of a cell for the determination of transport numbers from measurements of the concentration decrease in electrode compartments (Hittorf s method)...

The methods for determination of transport numbers include the Hittorf method and the concentration cell method (p. 121). 

Potentiometry is used in the determination of various physicochemical quantities and for quantitative analysis based on measurements of the EMF of galvanic cells. By means of the potentiometric method it is possible to determine activity coefficients, pH values, dissociation constants and solubility products, the standard affinities of chemical reactions, in simple cases transport numbers, etc. In analytical chemistry, potentiometry is used for titrations or for direct determination of ion activities. 

Radiotracer techniques involving lsO in the anodization process are used with subsequent neutron activation analysis84 or SIMS.85 Another method involves implantation of inert ion markers into the surface layer of the sample prior to anodization and examination of the position of the markers after the oxide film has grown to a certain thickness.86 Assuming immobility of the inert species, the ratio of the cation to the anion transport number, t+/, should be equal to the ratio of the outer to the inner layer thickness. Numerous experimental determinations72,87 suggest t+ and f to be 0.4 and 0.6, respectively. 

Using a salt bridge. Following directly from the calculation above, the first method of minimizing the junction potential is to choose an electrolyte characterized by similar transport numbers and activites for its anions and cations. However, such experimental conditions are usually impracticable. 

As described in Section 5.8, the conductivity of electrolyte solutions is a result of the transport of ions. Thus, conductimetry is the most straightforward method for studying the behavior of ions and electrolytes in solutions. The problems of electrolytic conductivity and ionic transport number in non-aqueous solutions have been dealt with in several books [1-7]. However, even now, our knowledge of ionic conductivity is increasing, especially in relation to the role of dynamical solvent properties. In this chapter, fundamental aspects of conductimetry in non-aqueous solutions are outlined. 

Transport numbers can be measured by different methods. The small mono- and divalent inorganic ions have been used to demonstrate skin permselectivity, and have been determined from membrane potential measurements, or by the Hittorf method [10,25,77,79]. The latter method has been frequently used for drugs alternatively, the transport number can be estimated from the slope of a plot of drug flux as a function of current intensity (Figure 14.4) [18,66]. 

The steady-state result (Eq. (77)) can be directly used to separate ionic and electronic conductivities the disadvantage of the technique is that it presupposes gas-separation. If not special measures are taken, it becomes unreliable for the ionic transport number less than 1%. Thus, this method well complements the Wagner-Hebb method which is very sensitive to small transference numbers. The partial conductivities of PbO shown in Figure 48 have been de-convoluted by the emf technique just described.3... 

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. 2.6. The Hittorf method for determining transport numbers. In the diagram the passage of a current I for time t is shown. It is assumed that t+ +1 = 1. The electrolytic cell is divided into three compartments.

This method is used to determine the transport number of M in salt MX. A solution of higher density than MX, NX (where uN > wM), is put in a... 

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 methods of measuring the velocity of electrokinetic motion are fully described in some of the reviews mentioned above. They include (for cataphoresis) various forms of U-tube in which the motion of the boundary of the suspension is observed, transference methods similar to Hittorf s transport number measurements in electrochemistry, and microscopic cells in which the motion of individual particles is watched, due allowance being made for the motion of the suspending fluid in the opposite direction to the particles. Sumner and Henry s device1 of fixing a sphere on a fibre and observing its deflexion in a horizontal electric field is very ingenious, and not so frequently mentioned as other methods. 

See also - Tubandt method for the determination of transport numbers in - solid electrolytes. 

Hittorf transport method — Only at infinite dilution can the molar conductivity of a solution be split into the two limiting molar conductivities associated with the individual ions, which are independent of each other. This is because only at infinite dilution can we completely neglect interionic interactions. However, in order to determine the values of the individual ionic conductivities, an additional measurement is necessary in order to partition Ao into AJ and Ag we must determine the so-called -> transport numbers of the individual ions. The total current i, can be written as the sum of partial currents i+ and i, corresponding to the currents carried by the cations and anions. We define the transport number of the cations, t+, as t+ = -fi— = and simi-... 

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