Electrophoretic retardation

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 °°)... 

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 ions in the mobile part of the double layer show a net movement in a direction opposite to that of the particle under the influence of the applied electric field. This creates a local movement of liquid which opposes the motion of the particle, and is known as electrophoretic retardation. It is allowed for in the Henry equation. 

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,... 

Equations (4.8) and (4.9) differ by a factor of 1.5 in the denominator because the Hiickel theory assumes that the charged particle has no influence on the local applied field, while Smoluchowski theory assumes that the applied field is uniform and parallel to the particle surface. Henry theory covers the transition from Ka < 1 (Hiickel theory) to Ka > 100 (Smoluchowski theory) by taking account of both frictional force and electrophoretic retardation,... 

Induction forces in the double layer caused by the electric field electrophoretic retardation)... 

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. 

Improved theories showed that [4.3.5] remained valid under less restrictive conditions. Onsager ) gave a derivation In which the electrophoretic retardation Is accounted for. This derivation is very similar to his treatment of the electrophoretic correction in the ionic mobilities but contains a number of incorrect steps. 

For V we substitute Stokes law v = 2a Apg/9rj (see (1.6.4.331) where a is the particle radius, Ap the density difference between particle and solution and g the standard acceleration of free fall or the corresponding acceleration caused by centrifugation. Electrophoretic retardation Is Ignored and Q = 4ne ea., as for the Coulomb case. We obtain... 

The problem may be stated as finding the function f In (4.3.6]. For reasons discussed earlier we shall only consider dielectric particles. Figure 4.4 gave Henry s solution. In which electrophoretic retardation was accounted for. but not yet double layer polarization. If polarization Is properly included, surface conduction beyond the slip plane Is automatically taken Into account, with Du = Du , given by [4.3.65, 66 or 67]. However, Du s 0 for "rigid particles". 

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). 

This is the value given by the potential solution used in the electrophoretic retardation analysis (Eq. 7.2.7). 

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... 

Bulged bases may occur with one or more extra bases that are unopposed on the complementary strand of duplex. Base bulges introduce a pronounced kinking of the helix axis, which can readily be observed as an electrophoretic retardation of the bulged molecule (Bhattacharyya and Lilley, 1989 Rice and Crothers, 1989). 

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. ... 

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). 

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... 

The resistance of lipoplexes formed from compounds LI and L2 and plasmid DNA was studied by electrophoretic retardation assays. Initial complexation experiments showed that all compounds were able to form full lipid/DNA complexes despite the presence of fluorinated regions near the headgroup. Fluorinated lipoplexes were formed with an excess of pure compounds LI and L2 and their integrity was tested with anionic, cationic, or neutral surfactants. When lipoplexes were analyzed by agarose... 

Alkaline Phosphatases.—Various degrees of specific interaction between concanavalin A and human alkaline phosphatases, extracted by n-butanol from various sources, have been demonstrated by a simple electrophoretic retardation technique and affinity chromatography. The lectin-binding abilities of the enzymes demonstrated the glycoproteinaceous characters of the latter. 

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