Spheres, electrophoretic mobility

Lumpkin, O, Electrophoretic Mobility of a Porous Sphere Through Gel-Like Obstacles Hy-drodnamic Interactions, Journal of Chemical Physics 81, 5201, 1984. 

Outer-sphere adsorption of Pb(ll)EDTA on goethite. Geochim. Cosmochim. Acta 63(19/20) 2957-2969 Bargar, J.R. Reitmeyer, R. Davis, J.A. (1999) Spectroscopic confirmation of uranium(Vl)-carbonato adsorption complexes on hematite. Environ. Sci. Techn. 33 2481-2483 Bargar, J.R. Reitmeyer, R. Lenhart, J.J. Davis, J.A. (2000) Characterization of U(Vl)-car-bonato ternary complexes on hematite EX-AFS and electrophoretic mobility measurements. Geochim. Cosmochim. Acta 64 ... 

It is apparent from the above sections that the understanding of electrophoretic mobility involves both the phenomena of fluid flow as discussed in Chapter 4 and the double-layer potential as discussed in Chapter 11. In both places we see that theoretical results are dependent on the geometry chosen to describe the boundary conditions of the system under consideration. This continues to be true in discussing electrophoresis, for which these two topics are combined. As was the case in Chapters 4 and 11, solutions to the various differential equations that arise are possible only for rather simple geometries, of which the sphere is preeminent. 

According to Booth and Henry188, the equation relating electrophoretic mobility with zeta potential for non-conducting spheres with large kq when corrected for surface conductance takes the form... 

O Brien s method was extended to study the electrophoresis of a nonuniformly charged sphere with thin but polarized ion cloud in a symmetric electrolyte [32]. The electrophoretic mobility depends on the charge distribution at the particle surface. It is found that the polarization effect of the ion could leads to different electrophoretic mobilities for particles with different zeta potential distributions but having an identical velocity for the limit of infinite Ka. This intriguing result is due to the fact that the theory for undistorted ion cloud is linear in the distribution of zeta potential, whereas the polarization effects are nonlinear. 

Figure 3 presents the variation of the electrophoretic mobility with the dimensionless distance X when a sphere moves perpendicularly towards a conducting plane. The solid line represents the results from the bipolar coordinate method and the dash curve is the approximate results from the reflection method. A good agreement between the results from the both methods is attained. The electrophoretic velocity of the sphere decreases monotonically with increasing X and is expected to vanish as the particle... 

Here, kd is the inverse of the Debye length. Even though the -potentials for latex spheres may exceed 25 mV and, therefore, require a more complex equation to relate to mobility (as per O Brien and White [265]), the low ionic strength (small kd) of El-FFF measurements should still ensure a proportionality between pe and . From the retention data, it is possible to obtain quantitative information regarding either the -potential of samples with known particle size eluting from the channel or the particle size, if the electrophoretic mobility is known. 

Henry [3] derived the mobility equations for spheres of radius a and an infinitely long cylinder of radius a, which are applicable for low ( and any value of Ka. Henry s equation for the electrophoretic mobility p of a spherical colloidal particle of radius a with a zeta potential C is expressed as ... 

Electrokinetic equations describing the electrical conductivity of a suspension of colloidal particles are the same as those for the electrophoretic mobility of colloidal particles and thus conductivity measurements can provide us with essentially the same information as that from electrophoretic mobihty measurements. Several theoretical studies have been made on dilute suspensions of hard particles [1-3], mercury drops [4], and spherical polyelectrolytes (charged porous spheres) [5], and on concentrated suspensions of hard spherical particles [6] and mercury drops [7] on the basis of Kuwabara s cell model [8], which was originally applied to electrophoresis problem [9,10]. In this chapter, we develop a theory of conductivity of a concentrated suspension of soft particles [11]. The results cover those for the dilute case in the limit of very low particle volume fractions. We confine ourselves to the case where the overlapping of the electrical double layers of adjacent particles is negligible. 

The theoretical basis of the transport of solute ions during iontophoresis can be compared to electrophoresis through a gel network. When the ionized solute has a mean Stokes radius smaller than the average mesh size (hole in the network), the solute is considered as a rigid sphere undergoing Brownian movement, with a mobility dependent on the frequency of solute interaction with the porous network. The sphere mobility is assumed to be proportional to the fractional volume of the pore that is accessible to the sphere [92]. The electrophoretic mobility, u, of such a solute sphere has been shown to be directly related to the molecular weight of the solute [93] ... 

Figure 4.32. Effect of space filling on the electrophoretic mobility of spheres, xa = 50. the volume fraction p is indicated. HS = Helmholtz-Smoluchowski (Redrawn from Kozak and Davis, loc. cit).

Spheres. Semilogarithmic plots of the electrophoretic mobility, p ( velocity/voltage gradient), as a function of gel concentration have been found to be linear for monoraolecular proteins in starch... 

Suarez et al. (36) use a combination of FTIR spectroscopy, electrophoretic mobility and pH titration data to deduce the specific nature of anionic surface species sorbed to aluminum and silicon oxide minerals. Phosphate, carbonate, borate, selenate, selenite and molybdate data are reviewed and new data on arsenate and arsenite sorption are presented. In all cases the surface species formed are inner-sphere complexes, both monodentate and bidentate. Two step kinetics is typical with monodentate species forming during the initial, rapid sorption step. Subsequent slow sorption is presumed due to the formation of a bidentate surface complex, or in some cases to diffusion controlled sorption to internal sites on poorly crystalline solids. 

The values of the functions i(x) and 02(x) calculated numerically using Eqs. 17 and 19 are given in Tables 1 and 2, respectively. The effect of the polarization (or relaxation) of the diffuse ions in the electric double layer surrounding the particle is not included in Eq. 16 up to the order C. Note that the results of i(icfl) given by Eqs. 17a and 19a are the same as those derived by Henry for the electrophoretic mobilities of a dielectric sphere [6] and circular cylinder in the direction normal to its axis [7], respectively. All results of the above investigations show that the diffusiophoretic mobility of a particle in... 

In the 1970s, S. S. Dukhin s group was perhaps the first to recognize that the electrophoretic mobility of polarizable particles must generally depend on the electric field [9]. In a series of Russian papers, which have yet to gain widespread attention, they predicted perturbations of the mobility as AZ oc and thus nonlinear electrokinetic motion At/ oc, which they have come to call the Stotz-Wien effect. For the case of a steady weak field applied to an ideally polarizable sphere of radius a, A. S. Dukhin derived an expansion for the mobility ... 

Key contributions to the understanding and evaluation of the electrophoretic mobility, and, in general, of the physical basis of electrokinetic phenomena is due to Overbeek [26], and also to Booth [27], who produced theories that followed similar lines, for spheres in both cases. These... 

FIGURE 3.5 Full calculation of the electrophoretic mobility of spheres as a function of the zeta potential for the Ka values indicated, compared with the Helmholtz-Smoluchowski formula. 

FIGURE 3.18 Frequency dependence of the relative dielectric increment of 265-nm radius polystyrene spheres in 0.1 nunol/1 KCl solution. Symbols experimental data soUd line classical calculation dashed line DSL calculation. In both calculations, the zeta potential used was the one best-fitting simultaneously electrophoretic mobility and dielectric dispersion data. 

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