Electrophoretic retardation effect

When in motion, the diffnse electrical donble-layer aronnd the particle is no longer symmetrical and this canses a rednction in the speed of the particle compared with that of an imaginary charged particle with no donble-layer. This rednction in speed is cansed by both the electric dipole field set np which acts in opposition to the applied field (the relaxation effect) and an increased viscons drag dne to the motion of the ions in the donble-layer which drag liqnid with them (the electrophoretic retardation effect). The resnlting combination of electrostatic and hydrodynamic forces leads to rather complicated eqnations which, nntil recently, conld only be solved approximately. In 1978, White and O Brien developed a clever method of nnmerical solntion and obtained detailed cnrves over the fnll range of Ka valnes (0 °°)... 

In the presence of the applied electric field, the EDL ions move in opposition to the motion of the dispersed species. This produces an opposing local flow of liquid, which causes an electrophoretic retardation effect (accounted for by the Henry equation earlier). Also, the movement of the dispersed species distorts the EDL and some time is needed to restore symmetry, a relaxation time. The asymmetrical mobile part of the EDL contributes a retarding force. The reduction in electrophoretic mobility that results is called the electrophoretic relaxation effect (note that this is different from the electrophoretic retardation that is accounted for by the Henry equation). 

This effect is called the relaxation effect. Second, in the presence of the ionic atmosphere, a viscous drag is enhanced than in its absence because the atmosphere moves in an opposite direction to the moving ion. This retarding effect is called the electrophoretic effect. In Eq. (7.1), the Ah°°-term corresponds to the relaxation effect, while the E-term corresponds to the electrophoretic effect. For details, see textbooks of physical chemistry or electrochemistry. 

Until now we have ignored an important factor. The electric field affects not only the surface charges of the particle, but also the ions in the electrical double layer. The counterions in the double layer move in a direction opposite to the motion of the particle. The liquid transported by them inhibits the particle motion. This effect is called electrophoretic retardation. Therefore the equation is only valid for D [Pg.77]

The Effect of NaCl on the Electrophoretic Mobility of PS Latex Particle. The em of the Dow 357 nm latex in the H-form and Na-form, along with two other Dow monodisperse latexes in the H-form with diameters of 795 and 1100 nm, was measured as a function of NaCl concentration. The results in Figure 1 show that the em for all three latexes increased with increasing concentration of NaCl to a maximum at about 1 x 10 "2 M NaCl followed by a rapid decrease. Converting the electrophoretic mobility to zeta potential, using tables derived by Ottewill and Shaw (6) from the results of Wiersma et al. in order to account for relaxation and retardation effects, led to the same dependency as shown in Figure 2. 

For large particles with thin electric double layers, meaning particles for which Ka> 100. This theory takes account of the opposite effect of the applied electric field on the ions in the electric double layer, an effect called electrophoretic retardation which acts to reduce particle velocity,... 

The numerical results show that the polarization effect of the double layer impedes particle s migration because an opposite electric field is induced in the distorted ion cloud, which acts against the motion of the particle. For a given ica, the electrophoretic mobility increases first, reaches a maximum value and then decreases as the absolute zeta potential is increased. This maximum mobility arises because the electrophoretic retarding forces increase at a faster rate with zeta potential than does the driving force. 

Figure 3 illustrates the effect of two different agarose concentrations on electrophoretic mobility (2). Aside from the mobility retardation effect, qualitatively there is no dramatic effect upon resolution in this concentration range. However, it is preferable to use a lower gel concentration since it shortens r in times. 

With a finite-thickness double layer we may distinguish three effects that will alter the electrophoretic velocity from that given by the Helmholtz-Smoluchowski or Huckel relations. These effects, which in general are not mutually exclusive, are termed electrophoretic retardation, surface conductance, and relaxation (Shaw 1969). 

The electrophoretic effect arises from the motion of the atmosphere in the direction opposite to that of the ion. Both the atmosphere and the ion pull solvent with them and each is, in effect, swimming upstream against the solvent pulled along by the motion of the other. This retardation is less in very viscous solvents because the motion of both the atmosphere and the ion is slowed down. The expression for the electrophoretic retardation has the form,foruni-univalentelectroIytes,Ac whereA. = 8.249 x where>jisthe... 

FIGURE 20.2 Forces acting on a charged particle. The particle is negatively charged and surrounded by a positively charged ionic atmosphere, indicated by the dashed circle. Fi is the electrical force, F2 is Stokes frictional drag, F3 is electrophoretic retardation, and F4 is the relaxation effect. 

Equation 20.7 can be applied when any of the following conditions are met (i) ca > 1, (ii) /cfl < 1, or (iii) f 25 mV. In these cases, the relaxation effect is negligible. More accurate theories that take into account the relaxation effect and electrophoretic retardation have been developed by Booth, Overbeek, " and O Brien. ... 

By way of example, the influence of the viscoelectric effect on the relation between electrophoretic mobility and (for ka 1, i.e., when the electrophoretic retardation is negligibly small) is elaborated as follows. Based on Equation 10.5, with Q = 0, the relation between v f and is given by... 

This expression does not include the effect of a nonuniform electrical field (see (3.1.12)) and the electrophoretic retardation. Note that buoyancy forces do not appear in F as such. Lee et al. (1977a) have tabulated the magnitudes of each of these forces, i.e. gradients, which can create a value of Vlnai r,p equal to 1 cm ... 

This expression was derived by correcting Stokes" equation (25) for the so-called electrophoretic retardation caused by the action of the external field on the double layer. Under the influence of the external field the counter ions are driven in a direction opposite to that of the particle. They impart their movement to the liquid surrounding them and in this way cause a flow of liquid in the wrong direction. Thus it is as if the particle does not move in a stationary liquid but in a moving liquid the electrophoretic velocity is decreased. The exact calculation of this effect results in eq. (28). 

B In Huckel s and Henry s treatment of electrophoresis the reader who is familiar with the theory of the conductivity of strong electrolytes will have missed the so-cailed time-of-relaxation effect This effect, originating in the deformation of the double layer also has a retarding influence on the electrophoresis. In the applied field the charge of the double layer is displaced in a direction opposite to the movement of the particle Not only does this charge retard the electrophoresis by its movement (electrophoretic retardation see 6a), but also by the dissymmetry of the double layer resulting from this displacement a retarding potential difference is set up. 

So Schmidt and Erkkila experimenting on congo-sols and casein-sols found a rise in conductance of 6-30% for a frequency of about 10. In fields of very high tensions (100,000 V/cm) the velocity of the particles may be so large, that the particle is drawn out of its ionic atmosphere, so that both the time-of-relaxation effect and the electrophoretic retardation disappear. An example of this effect is found in Hartley s work on paraffin-chain salts. 

The Dehye-Hbckel theory of electrolytes based on the electric field surrounding each ion forms the basis for modern concepts of electrolyte behavior (16,17). The two components of the theory are the relaxation and the electrophoretic effect. Each ion has an ion atmosphere of equal opposite charge surrounding it. During movement the ion may not be exacdy in the center of its ion atmosphere, thereby producing a retarding electrical force on the ion. 

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