Term transport number

In the literature, several different notations for tj and Tj have been used. Today, the terms transport number and transference number are used for q side by side Staverman introduced the terms reduced electrical transport number for Ti and electrical transport number for tj. Scatchard called Ti a transference number and ti a transport number, while Agar " introduced the notation Washburn number if Ti is referred to one of the uncharged components. The solvent transference number A, which was introduced by C. Wagner is a reduced transference number with the reference system fixed to the sum of moles of all solvent components. Elektrische Losungsmitteliiberfuhrung , (electrolytic solvent transport) originates in the proposal of Nernst to discriminate between solvent molecules in the solvation shell of the ions and the free solvent. is a reduced transference number referred to the motion of the free solvent. Inspection of Eqs. (54) and (57) shows that Ti depends on the reference system used. This will be shown in the following section in more detail. 

A discussion of the chemical drive of solvation and hydration processes, respectively, leads to the introduction of the basic concept of electrolytic dissociation, the disintegration of a substance in solution into mobile ions. Subsequently, we learn about the migration of these ions along an electric potential gradient as a special case of spreading of substances in space. The ionic mobilities provide a link to conductance and the related quantities conductivity as well as molar and ionic conductivity. For determining the conductivity of ions experimentally, the introduction of the term transport number which indicates the different contribution of ions to the electric current in electrolytes is very useful. In the last section, the technique for measuring conductivities is presented as well as its application in analytical chemistry where conductometric titration is a routine method. 

The term transport number, t, is reserved for the contribution of an individual species. 

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. 

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... 

It should be noted that when a mobility ratio is expressed in terms of the transport number, an experimental error, say, of 0.01, is not small enough at small concentrations, as seen from Eq. (8). For example, at Xi = 0.05, this error amounts to as much as 20% for m,. It is thus preferable to express the ratio in terms of ,2 rather than f. 

In aqueous electrolyte solutions the molar conductivities of the electrolyte. A, and of individual ions, Xj, always increase with decreasing solute concentration [cf. Eq. (7.11) for solutions of weak electrolytes, and Eq. (7.14) for solutions of strong electrolytes]. In nonaqueous solutions even this rule fails, and in some cases maxima and minima appear in the plots of A vs. c (Eig. 8.1). This tendency becomes stronger in solvents with low permittivity. This anomalons behavior of the nonaqueous solutions can be explained in terms of the various equilibria for ionic association (ion pairs or triplets) and complex formation. It is for the same reason that concentration changes often cause a drastic change in transport numbers of individual ions, which in some cases even assume values less than zero or more than unity. 

The defect population in the doped solid under moist conditions then consists of V%, OHo, h, and Y /x. The domains over which each species is dominant for conductivity can be represented diagrammatically when data concerning the conductivity of the solid has been measured (Fig. 8.20). In this representation, the conductivity fields are bounded by lines tracing the locus where the transport number for a pair of defects is equal to 0.5. (The diagram could equally well be drawn in terms of domains delineating the defect species that predominate.)... 

Look up why KCl or KNO3 are the most common choices of swamping electrolytes. (Hint think in terms of transport numbers, t, and conductivities, A.)... 

Separators are characterized by structural and functional properties the former describes what they are and the latter how they perform. The structural properties include chemical (molecular) and microcrystalline nature, thickness, pore size, pore size distribution, porosity, and various chemical and physical properties such as chemical stability, and electrolyte uptake. The functional properties of interest are electrical resistivity, permeability, and transport number. It is useful to characterize separator materials in terms of their structural and functional properties and to establish a correlation of these properties with their performance in batteries. A variety of techniques are used to evaluate separators. Some of these techniques are discussed in this section. 

When the correction terms of formula (48) can indeed be neglected, the transport ratios obtained from B.I.P. measurements must be the same as those from transport number measurements, the membrane being placed in a solution of both ions. This is found to be so as long as ions of the same kind are concerned, e.g. for Na+ and K+. For a larger... 

The transport number can also be expressed in terms of the fraction of the concentration, Cj, the charge, zj7 and ionic mobility, uj7 of each ion in the electrolyte,... 

Electrolytic domain — describes the range of external conditions (- activity of components, temperature or pressure), where the ion transport number of a material is equal to or higher than 0.99 and the material is considered as -> solid electrolyte. Usually this term is related to thermodynamic - equilibrium. 

Solid electrolyte — is a class of solid materials, where the predominant charge carriers are -> ions. This term is commonly used for -> conducting solids with ion -> transport number equal to or higher than 0.99 (see also -> electrolytic domain). Such a requirement can only be satisfied if the -> concentration and -> mobility of ionic -> charge carriers (usually -> vacancies or interstitials) both are relatively high, whilst the content of -> electronic defects is low. See also -> superionics, -> defects in solids, - diffusion, and -> Nernst-Einstein equation. 

The mobility method (Section 2.10.1) has the advantage of yielding individual solvation numbers directly (as long as the transport numbers are known). However, this positive point is offset by the fact that the viscosity term used should be the local viscosity near the ion, which will be less than the viscosity of the solvent, which is... 

This discussion then follows on to give rise to the idea of a transport number. This is a term that describes the fact that when we talk about the drift velocity, cations and anions of equal but opposite charge do not have the same speed although the applied field is the same. On the whole, cations tend to be smaller than anions and we show that the drift velocity is inversely proportional to the radius of the solvated ion, so that transport numbers tend to be larger for the cation and smaller for the anion in an electrolyte. 

The iontophoretic flux of an ion /, can also be defined in terms of the transport number of the solute, by... 

Electroosmotic effects also influence current efficiency, not only in terms of coupling effects on the fluxes of various species but also in terms of their impact on steady-state membrane water levels and polymer structure. The effects of electroosmosis on membrane permselectivity have recently been treated through the classical Nernst-Planck flux equations, and water transport numbers in chlor-alkali cell environments have been reported by several workers.Even with classical approaches, the relationship between electroosmosis and permselectivity is seen to be quite complicated. Treatments which include molecular transport of water can also affect membrane permselectivity, as seen in Fig. 17. The different results for the two types of experiments here can be attributed largely to the effects of osmosis. A slight improvement in current efficiency results when osmosis occurs from anolyte to catholyte. Another frequently observed consequence of water transport is higher membrane conductance, " " which is an important factor in the overall energy efficiency of an operating cell. 

A MEPAS application uses two sources of data user input and constituent database. The user inputs site and regional data to define the nature of the issue, source term, transport pathway, and exposure scenarios. To help ensure consistency for a large number of applications, a constituent database was developed that contains chemical, physical, environmental, exposure, and toxicity data for each constituent. The constituent database used for the Environmental Survey is documented by Strenge and Peterson (16). This database currently has entries for 397 constituents new constituents are added as needed. 

What vehicles of transportation do not need a fuel derived from oil How important are they in terms of numbers of people or tons of goods they can carry Approximately what percentage of the U.S. energy requirement is needed for transportation ... 

Pritzker and Fahidy [6] considered the solution of Equation 15.9 under galvanostatic conditions as an unknown function of (x,y, 8). In this case, we are going to simplify Equations 15.26 through 15.28 by considering transport number, f in the addition term of the diffusion and migration current density,... 

The transport number has been defined in Section 9.1 as the fraction of the total current carried by a given ion. This is the definition most useful to the determination of transport numbers from emfs. In Chapter 11 the transport number is defined in terms of ionic mobilities, and/or individual molar ionic conductances (see Section 11.17), which are more directly linked to the methods described in that chapter. 

Transport numbers are a very important property of ions both in terms of their intrinsic interest, and also in giving a bridge between consideration of emf s and conductances. They are also very important when electrolytes where one of the ions is large are being studied, such as polyelectrolyte solutions. 

The total conductivity is sometimes expressed in terms of the transference or transport number, defined as... 

Although the transport of solvents, such as water, which usually occurs in a direction opposite the solute, could be formulated in similar terms, it is more common to report the so-called water-transport number, which is the ratio of the water flux to the solute flux. A negative value of the water-transport number indicates transport of solvent in the same direction as the solute. Ideally, the absolute value of the water transport number should be less than 1.0. 

The fraction of current carried by the cations is clearly 1 /(1 + / ) this fraction is termed the transport number of the cations, t" ", and evidently... 

Equation (13-91) applies to a cell in which the only neutral component is the solvent. If neutral components other than the solvent are present, it is necessary to consider the changes in free energy due to the mass transport of these components in terms of the mass-transport numbers t,. In fact, as an alternative to the procedure outlined above. 

The evaluation of Eq. (13-107) is most readily accomplished when it is rewritten in terms of the equivalent conductances of the various ions involved. The transport number of component i is given by... 

An alternative development of the three-phase model, in terms of nondimen-sional parameters, is very good for those who like to think in terms of numbers. We define the reaction-transport parameters using the corresponding Damkohler numbers. 

Divide the entire mass transfer equation by the scahng factor for diffusion (i.e ,mixCAo/i )- This is an arbitrary but convenient choice. Any of the r + 2 dimensional scaling factors can be chosen for this purpose. When the scaling factor for the diffusion term in the dimensional mass transfer equation is divided by ,mixCAo/T, the Laplacian of the molar density contains a coefficient of unity. When the remaining r - -1 scaling factors in the dimensional mass transfer equation are divided by i,mixCAo/T, the dimensionless mass transfer equation is obtained. Most important, r -h 1 dimensionless transport numbers appear in this equation as coefficients of each of the dimensionless mass transfer rate processes, except diffusion. Remember that the same dimensionless number appears as a coefficient for the accumulation and convective mass transfer rate processes on the left-hand side of the equation. 

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