Ions, absolute mobility

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 absolute ionic mobility or the absolute velocity of an ion represents its velocity in centimeters per second under a potential gradient of one volt per centimeter (potential gradient = applied emf/distance between the electrodes). For example, if the velocity of the ion at infinite dilution is U cm per second when the distance between the electrodes is 25 cm and voltage is 125, the potential gradient is 125/25, i.e., 5 volts per cm and the absolute mobility is U/5 cm s 1. 

Millet determined self-diffusion coefficients for Na and Cs+ ions in hydrated 1200 EW membranes using conductivity measurements and the Einstein equation, D+ = u+kT, where u+ is the absolute mobility of the given cation. u+ can be derived from the equivalent conductivity according to A = 0+IC+ = Fu+, where 0+ is the specific conductivity, C+ is the cation concentration (calculated on the basis of the dry membrane density, EW, and the water content), and F is the Faraday constant. The values of D+ determined via these conductivity measurements... 

In copper there are two conduction electrons per atom and n = 8.5 X 10 electrons per cubic meter. For a wire with a cross section of 1 mm carrying a current of 1 A, a value of v = 25 X 10 m/h is obtained. For the sake of comparison, it is interesting to note that in a molar copper sulfate solution, the absolute mobility (mobility in a potential gradient of 1 V/cm) of copper ions is 2.5 X lO mTh. 

For the sake of comparison, it is interesting to note that in a molar copper sulfate solution the absolute mobility (mobility in a potential gradient of one volt per centimeter) of copper ions is 2.5 X 10 2 m/h. 

In the case of charged species, it is usual to define a charge mobility for the ions, uf, which is related with the absolute mobility by... 

Since the proportionality constant r/m is of considerable importance in discussions of ionic transport, it is useful to refer to it with a special name. It is called the absolute mobility because it is an index of how mobile the ions are. The absolute mobility, designated by the symbol is a measme of the drift velocity acquired... 

Though the two types of mobilities are closely related, it must be stressed that the concept of absolute mobility is more general because it can be used for any force that determines the drift velocity of ions and not only the electric force used in the definition of conventional mobilities. 

Velocity = Absolute mobility x force it is clear that the relaxation component of the drift velocity of an ion can be obtained... 

There are several ways of expressing ionic mobility. According to one of them, the absolute mobility, is the velocity of an ion under an applied force of 1 dyne. The conventional mobility, on the other hand, is the velocity under the force exerted on an ion by its interaction with an electric field of 1 V cm . Deduce the relation between and... 

Three kinds of mobility can be distinguished the absolute mobility, in an infinitely diluted solution, the actual mobility of the fully charged ion at the ionic strength, /, of the solution, and the effective mobility, which depends on the degree of ionization, a. 

Here, is the absolute mobility, that of the ion at infinite dilution, / is the correction factor that takes into account the deviation from ideal behavior. It can be seen that an additional parameter occurs in this equation the mobility of the electro-osmotic flow, /Ueof> which occurs in many cases in the separation systems and leads to an additional velocity vector of the solutes. 

A first approach to take into account the solvent s effect on the absolute mobility of an ion was made by Walden. It is based on the Stokes law of frictional resistance. Walden s rule states that the product of absolute mobility and solvent viscosity is constant. It is clear that the serious limitation of this model is that it does not consider specific solvation effects, because it is based on the sphere-in-continuum model. However, it delivers an appropriate explanation for the fact that, within a given solvent, the mobility depends on temperature to the same extent as the viscosity (in water, for example, the mobility increases by about 2.5% per degree Kelvin). The mobilities do not deviate too... 

The correction factor,/, relates the actual mobility of a fully charged particle at the ionic strength under the experimental conditions to the absolute mobility. It takes ionic interactions into account and is derived for not-too-concentrated solutions by the theory of Debye-Htickel-Onsager using the model of an ionic cloud around a given central ion. It depends, in a com-... 

It is generally held that even though the law of mass action is not obeyed at ordinary concentrations, it must, for thermodynamic reasons hold for the infinitely dilute solution Even in this case, there is no theoretical reason why d-wddfL should be equal to dvu/dCu The calculation increases, then if the mobility of each ion increases by the same fractional amount the transport number /( 4- v) will remain constant although (u + v), which determines the conductivity, may have altered The probability of the increase being the same fractional amount for both ions is perhaps not great, and if this probability be negligible then constancy in transport number would actually mean constancy in absolute mobility... 

A comparison of the absolute mobilities during electrophoresis in these two electrolytes, respectively, shows that, in all cases except those of epf-inositol and, probably, methyl a-n-mannofuranoside, the values are appreciably smaller in the solutions containing sulfonated benzeneboronic acid. The extent of the decrease is probably too great to be due solely to the difference in ionic radii of pairs of the migrating substances. Although different degrees of ionization of such pairs will contribute to this effect, it also seems that sulfonated benzeneboronic acid has, in general, a lower affinity for diols than has the borate ion.. ... 

Electrophoresis in sodium stannate solution has shown that polyhydroxy compounds form anionic complexes with the stannate ion. Only two hydroxyl groups are required for their formation and, from the 0-0 distance in the Sn(OH)e ion, it was to be expected that complexes would be formed from acyclic 1,2-diols. It is interesting that the mobility of cfs-2,3-butanediol is about half that of the trans isomer. This result is in contrast to that for other electrolytes discussed in this review, particularly for sulfonated benzeneboronic acid, although the absolute mobilities of these isomers are much lower in stannate solution. The 0-0 distance in Sn(OH)e is probably great enough to allow the formation of a non-planar 5-membered ring. In this event also, the complex of as-2,3-bu-tanediol should be relatively stable. 

Arsenious acid, As(OH)s, behaves as a weak acid with a dissociation constant of about 8X10 at 25°. As is the case with boric acid, the addition of n-mannitol to aqueous solutions of arsenious acid increases the acidity of the solution. The formation constants for complexes between polyhydroxy compounds and the arsenite ion have been found to be considerably smaller than those for the corresponding borate complexes. This is also reflected in the absolute mobilities of such compounds during electrophoresis in arsenite solution. 

When we describe the mobility of ions we often use the absolute mobility, B ... 

The acceleration of a particular ion between braking events is proportional to E by Equation 1.5 and their frequency is proportional to N. Hence v is proportional to E/N (Figure 1.3d and e) and, by Equation 1.8, ITis proportional to 1 /N. The absolute mobility scale enabling comparisons between IMS data at different N is established by introducing the reduced mobility, Kq—the value for standard temperature and pressure, STP (To = 273.16 K and Pq = 760 Torr or Aq = 2.687 x 10 m ), the Loschmidt constant. Assuming an ideal buffer gas, the mobility under any conditions may be converted to Kq using ... 

FIGURE 1.11 2D IMS/MS spectra of (1+) tryptic peptide ions from rabbit muscle aldolase generated using matrix-assisted laser desorption ionization (MALDI). (From Ruotolo, B.T., McLean, J.A., Gillig, K.J., Russell, D.H., J. Mass Spectrom., 39, 361, 2004.) Except for the systematic shift of absolute mobility, the separations in four gases are broadly similar. 

By Equation 3.48, the speed of ion elimination from the gap is proportional to both K and AEp . As the absolute mobilities of precursor and product ions generally differ, their v values are unequal despite fixed... 

FIGURE 5.9 Pairwise correlations between ion mass (or m/z), absolute mobility, and coefficients Oi and 02 for amino acid cations ( ) and anions (o). (From Shvartsburg, A.A., Mashkevich, S.V., Smith, R.D., J. Phys. Chem. A, 110, 2663, 2006.) The transport properties (in N2 gas) are from IMS and FAIMS experiments. No values of K for anions have been... 

The basis of ionic conduction is the mobility of ions [3]. In liquid electrolytes it is the consequence of a three-dimensional random movement of ions. The characteristic of the random walk is that the mean distance traveled by the ion is zero, but the mean square distance is proportional to time. Because of this movement, the concentration of ions is uniform throughout the volume of the electrolyte in the absence of an electric field. Under the influence of a certain force, e.g., in an electric field, the ions acquire a nonrandom component of velocity in the direction of the force. The velocity developed under unit applied force is called the absolute mobility of the ion. The conventional, or electrochemical, mobility is the velocity of ions in a unit electric field. The relationship between the absolute and conventional mobility is... 

Discussing the situation in which the influence of the concentration gradient of ions is balanced by the electric field acting in the opposite direction of the gradient, Einstein found that the diffusion coefficient is proportional to the absolute mobility of the ion ... 

---