Mobility, absolute

Thus when an electric field is appHed to a soHd material the mobile charge carriers are accelerated to an average drift velocity v, which, under steady-state conditions, is proportional to the field strength. The proportionality factor is defined as the mobility, = v/E. An absolute mobility defined as the velocity pet unit driving force acting on the particle, is given as ... 

Butterman, M Tietz, D Orban, L Chrambach, A, Ferguson Plots Based on Absolute Mobilities in Polyarcylamide Gel Electrophoresis Dependence of Linearity of Polymerization Conditions and Application on the Determination of Free Mobility, Electrophoresis 9, 293, 1988. Caglio, S Chiari, M Righetti, PG, Gel Polymerization in Detergents Conversion Efficiency of Methylene Blue vs. Persulfate Catalysis, as Investigated by Capillary Zone Electrophoresis, Electrophoresis 15, 209, 1994. 

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. 

To emphasize the difference between the results in different kinds of rock, it is helpful to consider the relative mobility, Ar, which is the ratio of the measured absolute mobility to the rock permeability. The dimension of relative mobility is reciprocal centipoise, whereas absolute mobility is measured in (md/cp). 

Experimental mobility values, 1.2 X 10-2 cm2/v.s. for eam and 1.9 x 10-3 cm2/v.s. for eh, indicate a localized electron with a low-density first solvation layer. This, together with the temperature coefficient, is consistent with the semicontinuum models. Considering an effective radius given by the ground state wave-function, the absolute mobility calculated in a brownian motion model comes close to the experimental value. The activation energy for mobility, attributed to that of viscosity in this model, also is in fair agreement with experiment, although a little lower. 

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. 

JL Beckers, FM Everaerts, MT Ackermans. Determination of absolute mobilities, pK values, and separation numbers by capillary electrophoresis. Effective mobility as a parameter for screening. J. Chromatogr. 537 407-428 (1991). 

The constant of proportionality of Equation 6.14 is defined the absolute mobility or mobility at infinite dilution (p°) ... 

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... 

The shorter migration distance on paper than in free solution has been explained on the basis of a longer migration path along the tortuous capillaries of the paper (A8, D15, K22), with a field actually smaller than that calculated from the potential measured at the ends of the strip. It seems impossible to make absolute mobility measurements on paper, although relative mobilities may be obtained for clinical use (M22). 

If the ionic strength is lowered, mobility increases (Fig. 15), but there is a limit to this favorable effect, as fractionation becomes less sharp and some proteins may even lose their solubility. The practical range of u for electrophoretic work on proteins is about 0.05-0.075. It is easy to calculate x for a given buffer, but there is no means for determining the actual ionic strength of the buffer inside the strip and consequently no means of measuring absolute mobilities. One reason is that... 

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... 

Thus, the conventional and absolute mobilities are proportional to each other, the proportionality constant being an integral multiple z,- of the electronic charge. In the example cited earlier. 

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. 

The Einstein Relation between the Absolute Mobility and the Diffusion Coefficient... 

Thus, one has provided a fundamental basis for the phenomenological coefficient B it is the absolute mobility divided by the Avogadro number. 

One can therefore define the absolute mobility u bs for diffusing particles by dividing the drift velocity by either the diffusional driving force or the equal and opposite Stokes viscous force... 

The fundamental expression (4.172) relating the diffusion eoeffieient and the absolute mobility ean be written thus ... 

By using the relation between the conventional and absolute mobilities, Eq. (4.163) can be written... 

To avoid cumbersome notation, the symbol for the conventional mobilities has been contracted to u. The absence of a bar above the u stresses that it is not the absolute mobility... 

Though the subscript abs has been dropped, it is clear from the presence of a bar over the us that one is referring to absolute mobilities. 

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

The ionic mobihties given in tables are around 10 cm V s . What would be the corresponding order of magnitude for the absolute mobility (the velocity under an accelerating force of 1 dyn s" ). 

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... 

Because and may change, the hydrodynamic radius and, therefore, the absolute mobility change as well. 

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-... 

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