Transport number.

The fraction of current carried by the cations is clearly 7 /(7 + 7 ) tliis fraction is tenned the transport number of the cations, and evidently... 

Table A2.4.1. Typical transport numbers for aqueous solutions.

Commercially available membranes are usually reinforced with woven, synthetic fabrics to improve the mechanical properties. Several hundred thousand square meters of IX membranes are now produced aimuaHy, and the mechanical and electrochemical properties are varied by the manufacturers to suit the proposed appHcations. The electrochemical properties of most importance for ED are (/) the electrical resistance per unit area of membrane (2) the ion transport number, related to current efficiency (2) the electrical water transport, related to process efficiency and (4) the back-diffusion, also related to process efficiency. 

The ion transport number is defined as the fraction of current carried through the membrane by counterions. If the concentration of fixed charges in the membrane is high compared to the concentration of the ambient solution, then the mobile ions in the IX membrane are mosdy counterions, co-ions are effectively excluded, and the ion transport number then approaches 1. Commercial membranes have ion transport numbers in dilute solutions of ca 0.85—0.95. The relationship between ion transport number and current efficiency is shown in Figure 3 where is the fraction of current carried by the counterions (anions) through the AX membrane and is the fraction of current carried by the counterions (cations) through the CX membrane. The remainder of the current (1 — in the case of the AX membranes and (1 — in the case of the CX membranes is carried by co-ions and... 

Fig. 3. Relationship between current efficiency and ion transport number.

In sodium chloride solutions the ion transport number for Na+ is about 0.4 compared to about 0.6 for CU. Thus a CX membrane would be expected to polarize at lower current densities than an AX membrane. Careful measurements show that CX membranes do polarize at lower current densities however, the effects on pH are not as significant as those found when AX membranes polarize. Such differences ia behavior have beea satisfactorily explaiaed as resultiag from catalysis of water dissociatioa by weaMy basic groups ia the AX membrane surfaces and/or by weaMy acidic organic compounds absorbed on such surfaces (5). 

The transport number is a measure of the permselec tivity of a membrane. If, for example, a membrane is devoid of coions, then all current through the membrane is carried by the counterion, and the transport number = 1. The transport numbers for the membrane and the solution are different in practical ED applications. 

The relative contributions of ions, electrons and positive holes to the conductivity is described drrough the transport number which is related to a partial conductivity defined by... 

The oxidation rate is decreased by a factor of four in a composite of TiC and Cr. This is because the formation of Ci 203 covers the composite with an oxide which oxidizes slowly because of the low transport number of electrons tlu ough the oxide. 

Wandenings-geschwindigkeit, /. migration velocity. -sinn, m. direction of migration (of ions), -zahl,/. transport number. 

The behavior of ionic liquids as electrolytes is strongly influenced by the transport properties of their ionic constituents. These transport properties relate to the rate of ion movement and to the manner in which the ions move (as individual ions, ion-pairs, or ion aggregates). Conductivity, for example, depends on the number and mobility of charge carriers. If an ionic liquid is dominated by highly mobile but neutral ion-pairs it will have a small number of available charge carriers and thus a low conductivity. The two quantities often used to evaluate the transport properties of electrolytes are the ion-diffusion coefficients and the ion-transport numbers. The diffusion coefficient is a measure of the rate of movement of an ion in a solution, and the transport number is a measure of the fraction of charge carried by that ion in the presence of an electric field. 

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] ... 

Transport numbers for several non-haloaluminate ionic liquids generated from ionic liquid self-diffusion coefficients are listed in Table 3.6-7. The interesting, and still open, question is whether the NMR-generated transport numbers provide the same measure of the fraction of current carried by an ion as the electrochemically... 

It is unclear at this time whether this difference is due to the different anions present in the non-haloaluminate ionic liquids or due to differences in the two types of transport number measurements. The apparent greater importance of the cation to the movement of charge demonstrated by the transport numbers (Table 3.6-7) is consistent with the observations made from the diffusion and conductivity data above. Indeed, these data taken in total may indicate that the cation tends to be the majority charge carrier for all ionic liquids, especially the allcylimidazoliums. However, a greater quantity of transport number measurements, performed on a wider variety of ionic liquids, will be needed to ascertain whether this is indeed the case. 

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)... 

When paint films are immersed in water or solutions of electrolytes they acquire a charge. The existence of this charge is based on the following evidence. In a junction between two solutions of potassium chloride, 0 -1 N and 0 01 N, there will be no diffusion potential, because the transport numbers of both the and the Cl" ions are almost 0-5. If the solutions are separated by a membrane equally permeable to both ions, there will still be no diffusion potential, but if the membrane is more permeable to one ion than to the other a diffusion potential will arise it can be calculated from the Nernst equation that when the membrane is permeable to only one ion, the potential will have the value of 56 mV. 

For a fully dissociated salt, all techniques should give the same values of transport number, t. Transference number measurements are appropriate for electrolytes containing associated species and any technique within one of the three groups will give a similar response, but values of 7] across the groups may vary. 

For DC polarization studies, the ratio of steady-state to initial current is not the transport number but determines the limiting current fraction , the maximum fraction of the initial current which may be maintained at steady-state (in the absence of interfractional resistances). Variations... 

The vesicular acetylcholine transport can be inhibited by vesamicol and several related compounds. Vesami-col competitively inhibits transport by binding to a cytoplasmic domain on VAChT with a Kd of 5 nM. Vesamicol binding can be used to estimate transporter number, but neither vesamicol nor its analogues are currently used clinically. 

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. 

The rate of product formation can be predicted from a knowledge of the conductivity and transport numbers of cations in the product barrier phase and appropriate thermodynamic data. This interpretation is based on the Wagner model (Sect. 2.3). 

Swelling water uptake, electric conductivity, and transport number of the membranes are measured as a function of the ion-exchange capacity (lEC). lEC has been estimated in terms of... 

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