Electrophoretic effects

The electrophoretic effect is due to hydrodynamic interactions between the ions (cf fig. 5.1). To the first order approximation one gets  

In this case the MSA pair distribution functions yield a simple extension of Henry s law for electrophoretic mobility [18] 

Where u and Df are the electrophoretic mobility and the diffusion coefficient of an ion i at infinite dilution. 

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L is Avagadro s constant and k is defined above. It can be seen that there are indeed two corrections to the conductivity at infinite dilution tire first corresponds to the relaxation effect, and is correct in (A2.4.72) only under the assumption of a zero ionic radius. For a finite ionic radius, a, the first tenn needs to be modified Falkenliagen [8] originally showed that simply dividing by a temr (1 -t kiTq) gives a first-order correction, and more complex corrections have been reviewed by Pitts etal [14], who show that, to a second order, the relaxation temr in (A2.4.72) should be divided by (1 + KOfiH I + KUn, . The electrophoretic effect should also... 

Removal of Cake by Mass Forces. This method of limiting cake growth employs mass or electrophoretic forces on particles, acting tangentially to or away from the filter medium. Only mass forces are considered here because the electrophoretic effects have been discussed previously. 

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. 

A finite time is required to reestabUsh the ion atmosphere at any new location. Thus the ion atmosphere produces a drag on the ions in motion and restricts their freedom of movement. This is termed a relaxation effect. When a negative ion moves under the influence of an electric field, it travels against the flow of positive ions and solvent moving in the opposite direction. This is termed an electrophoretic effect. The Debye-Huckel theory combines both effects to calculate the behavior of electrolytes. The theory predicts the behavior of dilute (<0.05 molal) solutions but does not portray accurately the behavior of concentrated solutions found in practical batteries. 

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... 

An analysis of Eq. (7.49) shows that the electrophoretic effect accounts for about 60 to 70% of the decrease in solution conductivity, and the relaxation effect for the remaining 40 to 30%. 

The influence of interionic fores on ion mobilities is twofold. The electrophoretic effect (occurring also in the case of the electrophoretic motion of charged colloidal particles in an electric field, cf. p. 242) is caused by the simultaneous movement of the ion in the direction of the applied... 

Fig. 2.6 Electrophoretic effect. The ion moves in the opposite direction to the ionic atmosphere... 

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) ... 

Debye and Falkenhagen predicted that the ionic atmosphere would not be able to adopt an asymmetric configuration corresponding to a moving central ion if the ion were oscillating in response to an applied electrical field and if the frequency of the applied field were comparable to the reciprocal of the relaxation time of the ionic atmosphere. This was found to be the case at frequencies over 5 MHz where the molar conductivity approaches a value somewhat higher than A0. This increase of conductivity is caused by the disappearance of the time-of-relaxation effect, while the electrophoretic effect remains in full force. 

These rules are based on the theory of conductivity of strong electrolytes accounting for the electrophoretic effect only (the relaxation effect terms outbalance each other). 

As soon as the concentration of the solute becomes finite, the coulombic forces between the ions begin to play a role and we obtain both the well-known relaxation effect and an electrophoretic effect in the expression for the conductivity. In Section V, we first briefly recall the semi-phenomenological theory of Debye-Onsager-Falkenhagen, and we then show how a combination of the ideas developed in the previous sections, namely the treatment of long-range forces as given in Section III and the Brownian model of Section IV, allows us to study various microscopic... 

It is well-known that the electrophoretic effect involves the hydrodynamical properties of the solvent in a very crucial way for this reason, the theory of this effect is rather difficult. However, using a Brownian approximation for the ions, we have been able to obtain recently a microscopic description of this effect. This problem, together with the more general question of long-range hydrodynamical correlations, is discussed in Section VI. 

We still have to compute the velocity field term in Eq. (272), which corresponds to the so-called electrophoretic effect. We start from the definition (262) and take for ws (e = a, y) thelowest-order approximation ... 

As was announced at the beginning of this section, both the relaxation and the electrophoretic effects are proportional to V C. More precisely, if we use the definitions (113) and the definition of the current per unit volume ... 

However, the present formulation has the advantage of furnishing a mathematically rigorous foundation to the classical theory and is readily extended to other physical situations, like plasmas32 and semiconductors. Also, it allows us to give a microscopic foundation to the theory of the electrophoretic effect, which is much more delicate because it involves the difficult question of long-range hydrodynamical correlations this point will be the object of Section VI. 

Our discussion of Section V has indicated that the electrophoretic effect has to be found in the Ta term defined in Eq. (301) (see also Eq. (312)) moreover we have already found a diagram (Fig. 14a) in which the solvent is transmitting the wave number —k from ion /S to ion a, as we expect to find from the classical theory. This term was not calculated in Section V because it gives a contribution of order ei to while the relaxation term is of order e6 it will be considered presently. 

In order to calculate the contribution of the electrophoretic effect to the limiting law, as given by the graph of Fig. 22, the simplest way is to use the above-mentioned analogy between... 

An additional problem with some supporting media is the phenomenon of electroendosmosis, in which the buffer itself moves due to an electrophoretic effect and hence masks the movement of the solute to some extent. However, this feature is exploited in some situations to aid separation. Electroendosmosis is caused by the presence of negatively charged groups on... 

Because of the nature of electroporation, virtually any molecule can be introduced into cells. For transfer of DNA, the electroporation forces are important. An electrophoretic effect of the field causes the polyanion DNA to travel toward the positive electrode. Fluorescence studies have shown that DNA enters the cell through the pole facing the negative electrode, where the membrane is more destabilized and where the field will drive the DNA towards the center of the cell (245). Membrane resealing occurs after pore formation. Whereas pore formation happens in the microsecond time frame, membrane resealing happens over a range of minutes with variations depending on electrical parameters and temperature (246). 

Equation (6.313) indicates that electrophoretic mobility is independent of the shape of the particles. Suppose, however, that the particle is spherical. Then one could arrive at the electrophoretic mobility in a completely different way and in a maimer used to calculate the electrophoretic effect in conduction (see Section 4.6.4). One starts with Stokes law (see Section 4.4.8)... 

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. 

In any case, in sulphuric acid the electrophoretic term is very small because of the high viscosity of sulphuric acid (ij = 24 5 centipoise at 25°). Thus the electrophoretic effect could only decrease the conductivity by 0 3%, even at c = 1. Substituting, e = 100, T — 298°K and — 10 [4, 5] we have... 

Recently another electrically assisted drug delivery technology, electroporation, was proposed as an alternative or adjuvant to iontophoresis. Electroporation comprises the use of electric pulses to induce transient changes in the cell membrane architecture that turn it into more permeable barrier. Beside the permeabilization effect on cell membrane, it was postulated that this technique induces electrophoretic effect on charged macromolecules and drives them to move across the destabilized membrane [205]. 

The electronic ink is supplied by E ink corporation (Comiskey 1998). The film consists of electrophoretic microcapsules in a polymer binder, coated on to a 25 pm polyester/indium tin oxide sheet (Fig. 14.10). Optical contrast is achieved by moving black and white sub-micron particles with opposite charge in a transparent fluid within a microcapsule. Depending on which sub-micron particles are closest to the viewer, light is scattered back (white state) or absorbed (black state). The electrophoretic effect is multi-stable - without any electric field the microcapsules keep their switching state. This greatly reduces the power consumption of the display (Ritter 2001). 

Depending on s, /i"1 may vary from 3-1000 A, or beyond. For example, in 10 2 M NaCl, A"1 = 30 A. The important point is that double layer thickness h 1 varies as 1/ 1/2 and thus also with overall electrolyte concentration c as l/c1/2. Consequently, retardation by the electrophoretic effect, which we indicated to be greatest for thin double layers (small A 1), increases with electrolyte concentration. 

An electrophoretic effect. Ion movement causes motion of solvent molecules associated with ions of the opposite sign. The result is a net flux of solvent molecules in the direction contrary to that of the ion considered. 

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