Relaxation effect, 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 °°)... 

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. 

The influence of the interionic forces is due to two phenomena, namely, the electrophoretic effect and the time-of-relaxation effect. The net ionic atmosphere around a given ion carries the opposite charge and therefore moves in a direction opposite to the central ion. The final result is an increase in the local viscosity, and retardation of the central ion. This is called the electrophoretic effect. The time-of-relaxation effect is also related to the fact that the ionic atmosphere around a given ion is moving and therefore disrupted from its equilibrium configuration. It follows that the ionic atmosphere must constantly be re-formed from new counter ions as the ion under observation moves through the solution. The net effect is that the electrical force on each ion is reduced so that the net forward velocity is smaller. 

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 equivalent conductance of salts or ions increases as the concentration decreases. This phenomenon is directly related to the interionic forces present in solution a given cation, for example, will have more anions in its vicinity than expected from a purely random distribution. This ionic atmosphere has two effects, electrophoretic and time of relaxation, both of which tend to decrease the ion s mobility. In the former effect, the solvent molecules associated with the ionic atmosphere are moving in a direction opposite to that of the central ion. In the latter, the ionic atmosphere moves slower than the central ion, causing a charge separation (electrostatic retarding force) on the central ion. 

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). 

We have already discussed qualitatively the relaxation and electrophoretic effects which retard the motion of ions, surrounded by their ion atmospheres, through a solution. Such effects will show themselves at the experimental level in conductivity measurements. For the ion conductivity Xj of an ion species i in a very dilute solution of a strong electrolyte, Onsager derived the expression... 

Under the influence of such high field strengths, the ions move very rapidly indeed (up to metres s ). Since the rearrangement time of the atmosphere about an ion is slow by comparison, the retardation of the ion s motion by the electrophoretic and relaxation effects becomes progressively smaller as the field strength becomes larger. This effect is only observed for strong electrolytes. 

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. 

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. 

The first effect arises because the ion atmosphere is greatly modified at high fields. The ion velocity is very large and the ion traverses distances comparable to that of the radius of the ion atmosphere in times so short that the atmosphere cannot reform. As a consequence the relaxation field is destroyed and the electrophoretic field significantly altered. There is less retardation X increases, approaching a high field limit. 

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