Effective ionic mobility

The effective ionic mobility is a measure of rate of electromigration or electrophoresis of a charged particle under a unit electric gradient. Higher the charge and smaller the size of the particle or ion will result in higher mobilities. The values of uj have been estimated for ions by multiplying the... 

These constitute the basic elements of the fibers and are responsible for its rigidity. The cellulose microfibrils, however, are not totally crystalline but rather contain amorphous regions which are accessible to water molecules. Water does not penetrate the crystalline region. The total water content of a whole fiber and its distribution within the fiber is a function of the relative amount of amorphous material, the presence of lignins, which are hydrophobic, and the presence of hemicelluloses which are hydrophilic. The total water content of a whole fiber will affect the conductivity by allowing an increased effective ionic mobility. 

The concepts of ionic mobility ui, m /s-V) and effective ionic mobility ( f, m /s-V) are introduced as representative parameters of electromigration (ionic migration). The effective ionic mobility defines the velocity of the ionic species under the effect of a unit electric field, which can be theoretically estimated using the Nemst-Townsend-Einstein relation (Holmes, 1962). Ionic mobility is related to the ionic valence (z,) and molecular diffusion coefficient (Z) m /s) of species as follows ... 

TABLE 14.1. Diffusion Coeflident, Ionic Mobility at Infinite Dilntion and Effective Ionic Mobility in Soil... 

The movement of ions toward the oppositely charged electrode is called electromigration, which is quantified by the effective ionic mobility. The effective ionic mobility (f/f) is defined as the velocity of ion within the pore space under the influence of a unit electrical potential gradient. The Nernst-Einstein equation is used to relate the ionic mobility to the diffusion coefficient of the ion in a dilute solution (Koryta, 1982) as follows ... 

Figure 3 Effective electrophoretic ionic mobilities q of different drugs influenced by bile acid concentration (buffer 0-30 ttiM glycodeoxychoUc acid, Na), 20mM phosphate, pH 7.4, detection 220nm). Note, hwe and in the foUowing applications q means the effective ionic mobility with consideration of the EOF.

Different di- and trihydroxy bile salts and drugs that differ in lipophilicity, basicity, and structure have been compared in order to examine solvatochromic equilibria. The principle exploited in the determination of thermodynamic equilibrium constants is the indirect measurement of the capacity factor affected by the tenside concentration (in this case, the bile acid concentration). A pronounced shift in the migration times and thus effective ionic mobility... 

Figure 4 Effective ionic mobility of drugs D1 and D2 in dependence on the concentration of the bile acid taurodeoxychoUc acid (TDCA), 10mM sample sigmoid fit. In the presence of Ca +, the ionic mobility is shifted to higha- negative values.

With increased peptide concentrations in the running buffer, the effective ionic mobility of the analyte molecule is shifted to lower values. This reflects the change of the net receptor charge due to counterion binding by the positively charged peptide molecule. The starting point of effective ionic mobility that is identical to the intrinsic effective ionic mobility of the receptor is different for the two receptors. 

Electrokinetic Transport in Soil Remediation, Table 1 Diffusion, ionic mobility, and effective ionic mobility for selected cationic and anionic species. Effective mobility was calculated for porosity n = 0.6 and tortuosity t = 0.35 [1]... 

A more general relation between the effective ionic mobility of a substance A and all other species i which are derived from A is (Karger and Foret, 1993)... 

Thus in the case of ions, measurements of this type are generally used to obtain values of the mobility and, through Stoke s law or related equations, an estimate of the effective ionic size. 

Fully hydrated potassium ion coordinates about 10-11 molecules of water, whereas sodium coordinates about 16-17 molecules [115]. The ionic mobility of potassium is about 50% greater than that of sodium. In simple terms, this means that more of the water in a potassium-catalyzed resin will be available as free water for viscosity reduction and that movement of water from a glue line into the wood will have less effect in moving the adhesive off of the glue line with it. 

Intrinsic viscosity measurements were done with a large number of solvents varying in pH, ionic strength, etc., using Cannon-Ubbelohde semimicro dilution viscometers. This was done to provide information on the effect of mobile phase composition on the size of a polymer molecule in solution and thus to facilitate the interpretation of GPC behavior. 

Ideas concerning the ionic atmosphere can be used for a theoretical interpretation of these phenomena. There are at least two effects associated with the ionic atmosphere, the electrophoretic effect and the relaxation effect, both lowering the ionic mobilities. Formally, this can be written as... 

This rale follows immediately from Stokes s law for the motion of spherical bodies in viscous fluids when assuming constant radii. It is applicable in particular for the change in ionic mobility that occurs in a particular solvent when the temperature is varied. Between solvents it remains valid when the electrolytes have poorly solvated ions, such as N(C2H5)4l. For other electrolytes we find rather significant departures from this rale. These are due in particular to the different degrees of solvation found for the ions in different solvents, and hence their different effective radii. 

The electrical conduction in a solution, which is expressed in terms of the electric charge passing across a certain section of the solution per second, depends on (i) the number of ions in the solution (ii) the charge on each ion (which is a multiple of the electronic charge) and (iii) the velocity of the ions under the applied field. When equivalent conductances are considered at infinite dilution, the effects of the first and second factors become equal for all solutions. However, the velocities of the ions, which depend on their size and the viscosity of the solution, may be different. For each ion, the ionic conductance has a constant value at a fixed temperature and is the same no matter of which electrolytes it constitutes a part. It is expressed in ohnT1 cm-2 and is directly proportional to the mobilities or speeds of the ions. If for a uni-univalent electrolyte the ionic mobilities of the cations and anions are denoted, respectively, by U+ and U, the following relationships hold ... 

In the ideal case, the ionic conductivity is given by the product z,Ft/ . Because of the electrophoretic effect, the real ionic mobility differs from the ideal by A[/, and equals U° + At/,. Further, in real systems the electric field is not given by the external field E alone, but also by the relaxation field AE, and thus equals E + AE. Thus the conductivity (related to the unit external field E) is increased by the factor E + AE)/E. Consideration of both these effects leads to the following expressions for the equivalent ionic conductivity (cf. Eq. 2.4.9) ... 

It follows from Eqs. (2.6.6), (2.6.8) and (2.6.10) that the presence of the solvent has two effects on the ionic mobility the effect of changing viscosity and that of changing the ionic radius as a result of various degrees of solvation of the diffusing particles. If the effective ionic radius does not change in a number of solutions with various viscosities and if ion association does not occur, then the Walden rule is valid for these solutions ... 

Table VII should be 1.939 for the ratio k = 0.5. Part of the 17% discrepancy between the results of Lin et al. (L9) and Eq. (27) may be ascribed to the use of incorrect diffusivities. An estimate of the errors is possible for part of their experiments. The value of the product nD/T of K3Fe(CN)6 based on the electric mobility at infinite dilution as used by Lin et al. is 11% too high, according to more recent measurements of the effective ionic diffusivity of Fe(CN)(% by Gordon et al. (G5). Similarly, the mobility product of K4Fe(CN)6 is 16% too high, and that of 02 no less than 26% too high, compared with data of Davis et al. (D7) (see Table III). According to Eq. (27) the value of D would have to be 27% too high to account fully for a coefficient that is 17% too high consequently, the discrepancy cannot be attributed entirely to incorrect diffusivities.

The first work on pKa determination by zone electrophoresis using paper strips was described by Waldron-Edward in 1965 (15). Also, Kiso et al. in 1968 showed the relationship between pH, mobility, and p/C, using a hyperbolic tangent function (16). Unfortunately, these methods had not been widely accepted because of the manual operation and lower reproducibility of the paper electrophoresis format. The automated capillary electrophoresis (CE) instrument allows rapid and accurate pKa determination. Beckers et al. showed that thermodynamic pATt, (pATf) and absolute ionic mobility values of several monovalent weak acids were determined accurately using effective mobility and activity at two pH points (17). Cai et al. reported pKa values of two monovalent weak bases and p-aminobenzoic acid (18). Cleveland et al. established the thermodynamic pKa determination method using nonlinear regression analysis for monovalent compounds (19). We derived the general equation and applied it to multivalent compounds (20). Until then, there were many reports on pKa determination by CE for cephalosporins (21), sulfonated azo-dyes (22), ropinirole and its impurities (23), cyto-kinins (24), and so on. 

At high field strengths a conductance Increase Is observed both In solution of strong and weak electrolytes. The phenomena were discovered by M. Wien (6- ) and are known as the first and the second Wien effect, respectively. The first Wien effect Is completely explained as an Increase In Ionic mobility which Is a consequency of the Inability of the fast moving Ions to build up an Ionic atmosphere (8). This mobility Increase may also be observed In solution of weak electrolytes but since the second Wien effect Is a much more pronounced effect we must Invoke another explanation, l.e. an Increase In free charge-carriers. The second Wien effect Is therefore a shift in Ionic equilibrium towards free ions upon the application of an electric field and is therefore also known as the Field Dissociation Effect (FDE). Only the smallness of the field dissociation effect safeguards the use of conductance techniques for the study of Ionization equilibria. 

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