Mobilities of ions

Differences in mobilities of ions, molecules, or particles in an electric field can be exploited to perform useful separations. Primary emphasis is placed on electrophoresis and dielec trophoresis. Analogous separation processes involving magnetic and centrifugal force fields are widely apphed in the process industiy (see Secs. 18 and 19). 

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. 

The Contact between Solvent and Solute Particles Molecules and Molecular Ions in Solution. Incomplete Dissociation into Free Ions. Proton Transfers in Solution. Stokes s Law. The Variation of Electrical Conductivity with Temperature. Correlation between Mobility and Its Temperature Coefficient. Electrical Conductivity in Non-aqueous Solvents. Electrical Conduction by Proton Jumps. Mobility of Ions in D20. 

The application of Stokes s law to mobilities is a case in point. In Sec. 35 we shall show that, if we compare mobilities of ions in methanol, ethanol, and water, a crude application of Stokes s law yields values that do not even lie in the right order. Nevertheless, when we discuss ionic... 

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. 

The ion mobility coefficients pj are calculated similarly. First, the ion mobility of ion j in background neutral i is calculated using the low- -field Langevin mobility expression [219]. Then Blanc s law is used to calculate the ion mobility in... 

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. 

Mohnen, V.A., Formation, Nature, and Mobility of Ions of Atmospheric Importance, in Electrical Processes in Atmospheres (H. Dolezalek and R. Reiter, eds.) pp. 1-17, Steinkopff, Darmstadt, Federal Republic of Germany (1977). 

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

Electrophoresis is the term given to the migration of charged particles under the influence of a direct electric current. It is a single-phase system and depends upon the relative mobilities of ions under identical electrical conditions. 

The value for k will normally decrease as the concentration of the solution decreases but the value for A will increase because of the increased dissociation of molecules in dilute solutions. A value for the molar conductance at infinite dilution (A,)) can be determined by plotting the calculated values for A against the molar concentration of the solution used and determining the plateau value for A. From such investigations it is possible to determine the ionic mobilities of ions (Table 4.3) and calculate the molar conductance of an... 

The ion hopping rate is an apparently simple parameter with a clear physical significance. It is the number of hops per second that an ion makes, on average. As an example of the use of hopping rates, measurements on Na )3-alumina indicate that many, if not all the Na" ions can move and at rates that vary enormously with temperature, from, for example, 10 jumps per second at liquid nitrogen temperatures to 10 ° jumps per second at room temperature. Mobilities of ions may be calculated from Eqn (2.1) provided the number of carriers is known, but it is not possible to measure ion mobilities directly. 

However, when the concentration or mobility of ion pairs is significant compared with the individual ions then the measured diffusion coefficients for both constituents approach that of the ion pairs and not the free ions and as a consequence the apparent t+, and hence t, approach 0.5. In fact it is no longer valid to apply the above equation in order to determine transport numbers. Generally, in the presence of mobile ion pairs or more complex mobile ion clusters, diffusion coefficients and t+ measurements... 

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. 

Capillary isotachophoresis is usually performed in constant current mode, which implies the invariable ratio between concentration and electrophoretic mobility of ions. Therefore, bands that are less concentrated than the LE are sharpened, whereas those that are more concentrated than the LE are broadened to adapt their concentration to the requested constant value between concentration and electrophoretic mobility. The consequence of this unique property of CITP is that each sample component can be concentrated to an extent that depends on its initial concentration and the concentration of the leading electrolyte. Therefore, the opportune selection of composition and concentration of the leading electrolyte allows the enrichment of diluted analytes. 

Low viscosity and small molar volume to ensure high mobilities of ions... 

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. 

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