The mobility of ions

Ion transport through membranes is central to the operation of many biological processes, particularly signal transduction in neurons, and we need to be equipped to describe ion migration quantitatively. 

An ion in solution responds to the presence of an electric field, migrates through the solution, and carries charge from one location to another. The study of the motion of ions down a potential gradient gives an indication of their size, the effect of solvation, and details of the type of motion they undergo. 

When an ion is subjected to an electric field E, it accelerates. However, the faster it travels through the solution, the greater the retarding force it experiences from the viscosity of the medium. As a result, as we show in the following Justification, the ion settles down into a limiting velocity called its drift velocity, s, which is proportional to the strength of the applied field  

When the particle has reached its drift speed, the accelerating and viscous retarding forces are equal, so we can write 

At this point we can compare this expression for the drift speed with eqn 8.22 and hence find the expression for mobility given in eqn 8.23. 

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The mobilities of ions in molten salts, as reflected in their electrical conductivities, are an order of magnitude larger than Arose in Are conesponding solids. A typical value for diffusion coefficient of cations in molten salts is about 5 X lO cm s which is about one hundred times higher Aran in the solid near the melting point. The diffusion coefficients of cation and anion appear to be about the same in Are alkali halides, wiAr the cation being about 30% higher tlrair Are anion in the carbonates and nitrates. 

Mobility of Ions in D20. The viscosity of liquid D20 at room temperature has a value 1,232 times the viscosity of H20. Since the D2O and HaO molecules are so similar in other respects, we should expect the mobility of ions dissolved in D20 to be smaller than in H20. The conductivity of potassium chloride and potassium acetate was measured in mixtures of D20 and H20 up to a composition containing 97 per cent of D20.1 The values for ions in D2O, given in Table 7, were obtained by extrapolation from values obtained in the mixed solvent containing a few per cent of H20. As was expected, the conductivity in D20 was found to be smaller than in H20. But the change was not quite so great as the change in the viscosity, as is shown by the ratios in the last column of Table 7. We must conclude that, for some or all of the ions, the... 

One attraction of MD simulation is the possibility of computer animation. The mobility of ions inside a charged cylindrical pore can be visualized. Some movie clips of EMD and NEMD are downloadable at http //chem.hku.hk/ kyc/movies/. mpg. Some features that escape statistical averages can be learned in watching the animation. While the coions are present mainly in the center of the pore, occasional collisions with the wall do occur, as observed in the movie. The time scale of a coion staying near the wall is of the order of 1 ps, compared to 10 ps for the counterion. While the averaged equilibrium distributions indicate an infinitesimal concentration of coion at the wall, reaction of coion with the wall can occur within a time scale of 1 ps. From the video, it can also be observed that the radial mobility of the counterion is more significant compared to the coion s and compared to the axial mobility. It is consistent with the statistical results. 

Diffusion of ions can be observed in multicomponent systems where concentration gradients can arise. In individnal melts, self-diffnsion of ions can be studied with the aid of radiotracers. Whereas the mobilities of ions are lower in melts, the diffusion coefficients are of the same order of magnitude as in aqueous solutions (i.e., about 10 cmVs). Thus, for melts the Nemst relation (4.6) is not applicable. This can be explained in terms of an appreciable contribntion of ion pairs to diffusional transport since these pairs are nncharged, they do not carry cnrrent, so that values of ionic mobility calculated from diffusion coefficients will be high. 

Another method for obtaining these values is to determine the mobilities of ions, from which the ratio A+ /A" can be calculated. This is based on the measurement of the absolute velocities of the cations and anions under the influence of a potential gradient, as originally suggested by Lodge (1886) and applied later by Masson and many others. For instance, Masson (1899)1 carried out experiments with 10% KC1 solution in gelatine gel, the principle of which is illustrated in Fig. 2.2. 

The mobility of ions in melts (ionic liquids) has not been clearly elucidated. A very strong, constant electric field results in the ionic motion being affected primarily by short-range forces between ions. It would seem that the ionic motion is affected most strongly either by fluctuations in the liquid density (on a molecular level) as a result of the thermal motion of ions or directly by the formation of cavities in the liquid. Both of these possibilities would allow ion transport in a melt. 

Nolan, J.J. The Mobilities of Ions Produced by Spraying Distilled H20, Proc. Roy Irish Acad. 23A 9-23 (1916). 

Inspection of Eq. (13.6) shows that the selectivity behavior of a liquid membrane is specified completely by the membrane selectivity constant, Ky, which in turn is dependent on the equilibrium constant of Eq. (13.5) and on the mobility of ions i and j within the membrane. For the case in which the membrane consists of a neutral carrier [129], the exchange reaction can be presented as ... 

The contactless conductivity microchip detection system, developed in our laboratory [31], has been particularly useful for this task. Its popularity has grown rapidly in recent years. Conductivity is a universal detection technique for CE microchips, as it relies on the same property of the analyte as the separation itself, namely the mobility of ions under the influence of an electrical field. Such a detector can thus sense all ionic species having conductivity different from the background electrolyte. 

Electrophoresis is another separation process that, however, is based on the mobility of ions in an electric field. The different modes of modern capillary electrophoresis with its different separation mechanisms have paid more and more attention during the last decade. 

The fat globules of milk reduce the conductivity by occupying volume and by impeding the mobility of ions. Thus the conductivity of whole milk is less than that of skim milk by about 10%, and that of cream varies with the fat content (Gerber 1927 Muller 1931 Prentice 1962). Homogenization of milk does not measurably influence conductivity (Prentice 1962). The conductivity of whey and ultrafiltrate is slightly greater than that of skim milk (Schulz 1956 Schulz and Sydow 1957). A possible relationship between the electrical conductivity and physical stability of evaporated milk and concentrated infant milk products has been reported (Hansson 1957). Samples of poor physical stability tended to have relatively low conductivity values compared to those of the more stable products. 

As we shall see, the solution conductivity depends on the ion concentration and the characteristic mobility of the ions present. Therefore, conductivity measurements of simple, one-solute solutions can be interpreted to indicate the concentration of ions (as in the determination of solubility or the degree of dissociation) or the mobility of ions (as in the investigations of the degree of solvation, complexation, or association of ions). In multiple-solute solutions, the contribution of a single ionic solute to the total solution conductivity cannot be determined by conductance measurements alone. This lack of specificity or selectivity of the conductance parameter combined with the degree of tedium usually associated with electrolytic conductivity measurements has, in the past, discouraged the development of conductometry as a widespread electroanalyti-cal technique. Today, there is a substantial reawakening of interest in the practical applications of conductometry. Recent electronic developments have resulted in automated precision conductometric instrumentation and applications... 

C. A. Maekay gave 11-1 volts for the ionizing potential of the gas R. A. Morton and R. W. Riding, 11-7 volts and A. T. Waldie, 11 volts. H. Henstock discussed the electronic structure and L. B. Loeb, L. B. Loeb and M. F. Ashley, and H. R. Hasse, the mobilities of ions in gaseous mixtures of air and ammonia. H. M. Goodwin and M. de K. Thompson10 found the dielectric constant of commercial liquid ammonia at —34° to be 21 ammonia prepared from ammonium chloride and lime, 23 and commercial liquid ammonia after dehydration, 22. C. T. Zahn found the dielectric constant, e, to be ... 

The specific conductivity (y) is a measure of the mobility of ions in an electrolyte or electrons in a metallic conductor. Thus, y is about 1 or 107 S/m for a 0.1 kmol/m3 aqueous salt solution or for a metal such as iron, respectively. Such a difference in charge mobility makes the temperature dependence of % [i-e.,(l/x)3x/97k] positive for ions of about 2.5% per K, but negative for metals and alloys of approximately an order of magnitude lower (Prentice, 1991). 

Figure 3.21 Properties measured during electrochemical detection. Amperometry measures the current or charge transferred between neutral or ionic analytes and the electrode. Conductivity measures the mobility of ions in an electric field. (Reprinted from Ref. 49 with permission.)...

GHz. A detailed study of the internal conductivity of erythrocytes revealed the intracellular ionic mobility to be identical with that of ions in dilute electrolyte solutions if appropriate allowance is made for internal friction with suspended macromolecules (5). Tissue conductivities near 100 or 200 MHz, sufficiently high that cell membranes do not affect tissue electrical properties, are comparable to the conductivity of blood and to somewhat similar protein suspensions in electrolytes of physiological strength. Hence, it appears that the mobility of ions in the tissue fluids is not noticeably different from their mobility in water. 

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