Electrophoresis electrophoretic velocity

Electrophoresis. Electrophoresis, the movement of charged particles in response to an electric potential, has become very important in biochemistry and colloid chemistry. In the present study an apparatus similar to that described by Burton( M2-M5) was used. A U-tube with an inlet at the bottom and removable electrodes at the two upper ends was half filled with acetone. The a Au-acetone colloidal solution was carefully introduced from the bottom so that a sharp boundary was maintained between the clear acetone and the dark purple colloid solution. Next, platinum electrodes were placed in the top ends of the U-tube, and a DC potential applied. The movement of the boundary toward the positive pole was measured with time. Several Au-acetone colloids were studied, and electrophoretic velocities determined as 0.76-1.40 cm/h averaging 1.08 cm/h. 

FIG. 12.13 Net charge of egg albumin versus pH. The points were determined by electrophoresis, and the solid line by titration the broken line represents 60% of charge from titration. (Data from L. G. Longsworth, Ann. NY Acad. Sci., 41, 267 (1941). (Redrawn with permission from J. Th. G. Overbeek, Quantitative Interpretation of the Electrophoretic Velocity of Colloids. In Advances in Colloid Science, Vol. 3 (H. Mark and E. J. W. Verwey, Eds.), Wiley, New York 1950.)... 

Fic. 39. Principle of migration in two-dimensional electrophoresis. Each particle migrates according to the resultant vector (Rlf fl2, R3) of the horizontal electrophoretic velocity (Fj, F2, F3 ) and the vertical velocity of the buffer (F). 

In electrophoresis an electric field is applied to a sample causing charged dispersed droplets, bubbles, or particles, and any attached material or liquid to move towards the oppositely charged electrode. Their electrophoretic velocity is measured at a location in the sample cell where the electric field gradient is known. This has to be done at carefully selected planes within the cell because the cell walls become charged as well, causing electro-osmotic flow of the bulk liquid inside the cell. From hydrodynamics it is found that there are planes in the cell where the net flow of bulk liquid is zero, the stationary levels, at which the true electrophoretic velocity of the particles can be measured. 

Good descriptions of practical experimental techniques in conventional electrophoresis can be found in Refs. [81,253,259]. For the most part, these techniques are applied to suspensions and emulsions, rather than foams. Even for foams, an indirect way to obtain information about the potential at foam lamella interfaces is by bubble electrophoresis. In bubble microelectrophoresis the dispersed bubbles are viewed under a microscope and their electrophoretic velocity is measured taking the horizontal component of motion, since bubbles rapidly float upwards in the electrophoresis cells [260,261]. A variation on this technique is the spinning cylinder method, in which a bubble is held in a cylindrical cell that is spinning about its long axis (see [262] and p.163 in Ref. [44]). Other electrokinetic techniques, such as the measurement of sedimentation potential [263] have also been used. 

Analytical expression for the electrophoretic velocity of a sphere can be obtained for a thin but distorted double layer. Dukhin [6] first examined the effect of distortion of thin ion cloud on the electrophoresis of a sphere in a symmetric two-species electrolyte. Dukhin s approach was later simplified and extended by O Brien [7] for the case of a general electrolyte and a particle of arbitrary shape. Since 0(k 1) double layer thickness is much smaller than the characteristic particle size L, the ion cloud can be approximated as a structure composed of a charged plane interface and an adjacent diffuse cloud of ions. Within the double layer, the length scales for variation of quantities along the normal and tangential directions are k ] and L, respectively. 

Keh and Chen [33] employed O Brien s method [7] to examine the polarization effect on the electrophoresis of an infinitely long circular cylinder. They found that neglecting the end effect, the transverse electrophoretic velocity is identical to that for a spherical particle with the same radius. The polarization effects were also investigated for a spheroidal particle [34,35] and an infinitely long elliptical cylinder [36]. An interesting feature discovered from these studies is that the electrophoretic velocity decreases with the reduction of the maximum length of the particle in the direction of the migration. 

Practical applications of electrophoresis usually associate with the migration of particles in the vicinity of solid boundaries subject to an external electric field. Several examples have been mentioned in the Introduction section. The electrostatic and hydrodynamic interactions between the particle and the boundary wall will affect the particle s electrophoretic mobility. In this section, boundary effects on the electrophoretic velocity will be presented and discussed. 

For the electrophoresis of a spherical particle in a circular cylindrical pore, the results obtained from the boundary collocation method show that the presence of the pore wall always reduces the electrophoretic velocity for the entire range of the separation parameter [42]. However, the net wall effect is quite weak, even for the very small gap width between the particle and wall. 

Figure 5 presents the variation of the electrophoretic velocities of the cylinder with X. It is shown that the translational velocity normal to the plane decreases with increasing X, whereas the parallel mobility increases with X. In addition to the translation, the cylinder rotates when the external electric field is applied parallel to the wall. The enhancement of the parallel migration results from the squeezed electric field lines in the small gap between the particle and wall surfaces. This velocity enhancement also occurs for the electrophoresis of a sphere parallel to a plane boundary when the gap width is sufficiently small [40]. The boundary effects on electrophoresis are stronger for a cylinder than for a sphere. 

As mentioned in Sec. I, the system in most applications of electrophoresis contains more than one single particle suspended in the electrolyte solution. The interactions between the particles should be taken into account unless the concentration of particles is very low. In this section, studies on particle interactions in electrophoresis will be reviewed. The results for spherical and nonspherical particles will be presented and discussed separately in two respective subsections. Then, we will show how to obtain the average electrophoretic velocity for a dispersion of particles from the interaction results. 

In practical applications of electrophoresis, collections of colloidal particles in bounded systems are usually encountered and the experimentally measured electrophoretic mobility is actually the average value for the entire suspension. It is therefore necessary to determine the average electrophoretic velocity for a suspension of colloidal particles. For dilute dispersions, the first order correction to the mobility of an isolated particle can be determined from the... 

Electrophoresis of nonconducting colloidal particles has been reviewed in this chapter. One important parameter determining the electrophoretic velocity of a particle is the ratio of the double layer thickness to the particle dimension. This leads to Smoluchowski s equation and Huckel s prediction for the particle mobility at the two extrema of the ratio when deformation of the double layer is negligible. Distortion of the ion cloud arising from application of the external electric field becomes significant for high zeta potential. An opposite electric field is therefore induced in the deformed double layer so as to retard the particle s migration. 

Electrophoretic velocity, i/ep, or rate of migration (in electrophoresis) — The velocity of a charged analyte under the influence of an electric field relative to the -> background (supporting) electrolyte. 

The overall migration velocity in electrophoresis, is the sum of the electrophoretic velocity of the charged separand, uep, and the electrosmotic velocity measured by a neutral tracer, u, as both migration processes take place simultaneously. Thus... 

The characterization and control of electrostatic forces are of particular interest. Electrostatic forces depend on the electric charge and potential at the particle surfaces. When subjected to a uniform, unidirectional electric field E. charged colloidal particles accelerate until the electric body force balances the hydrodynamic drag force, so that the particles move at a constant average velocity v. This motion is known as electrophoresis, and v is the electrophoretic velocity. 

The application of laser Doppler velocimetry (LDV) to measure the electrophoretic mobility n of charged colloidal particles is known as laser Doppler electrophoresis (LDE). In a typical LDE experiment, an applied electric field drives the collective motion of charged colloidal particles. The particles pass through an interference pattern created by a dual-beam experimental setup (Section III.A.2). The collective electrophoretic velocity of the particles is then determined via intensity- or spectrum-based analysis of the scattered light, and the electrophoretic mobility n is calculated by dividing the velocity by the applied electric field strength. 

There has been much controversy concerning the applicability of equation (22) to particles of different shapes according to Smoluchowski s treatment (1903) the equation for the electrophoretic velocity should be independent of the shape of the moving particle. On the other hand, Debye and Hiickel find that if the thickness of the double layer, i.e., 1/ic, is large in comparison with the radius of the particle, i.e., for small spherical particles, the velocity of electrophoresis is given by... 

Electrophoresis The motion of colloidal species caused by an imposed electric field. The species move with an electrophoretic velocity that depends on their electric charge and the electric field gradient. The electrophoretic mobility is the electrophoretic velocity per unit electric field gradient and is used to characterize specific systems. 

The movement of a charged colloidal particle in an external electrical field is called electrophoretic motion and the respective phenomenon is electrophoresis. The electrophoretic velocity in the two limiting cases, of a thin and thick EDL around a spherical particle, can be calculated by von Smoluchowski 3 and HiickeF formulas ... 

A charged particle will move relatively to the surrounding stationary liquid under the influence of applied electric field this is generally referred to as electrophoresis. The particle s electrophoretic velocity ... 

The action of external electric field on the free disperse system results in particle motion (electrophoresis). The electrophoretic velocity, vE, is not a function of ( -potential only, but also depends on the particle radius, r, and the type of electrolyte present in the system. However, it turns out (see fine print further down) that all of these factors can be simultaneously accounted for by the numerical coefficient, kt, introduced into the Helmholtz-Smoluchowski equation (V.26). If the particles are spherical, k, changes from 2/3 for particles smaller compared to the ionic atmosphere thickness (kt 1) to 1 for large particles ( kt 1). Consequently, the particle flux due to the applied electric... 

A number of methods for the determination of electrophoretic velocity and electrokinetic potential of particles have been developed. These methods include the moving boundary method (a direct study of motion of the boundary between the disperse system and the free dispersion medium due to the applied potential difference), microelectrophoresis (a direct observation of moving particles using a microscope or ultramicroscope), electrophoresis in gels, paper electrophoresis, etc [ 13]. These methods are broadly used to study disperse systems formed with low molecular weight substances, as well as polymers, especially those of natural origin. Electrophoretic methods allow one to separate and analyze mixtures of proteins, and thus are effectively used in scientific research and medical diagnostic applications. 

An indirect way to obtain information about the potential at foam lamella interfaces is by bubble electrophoresis, in which an electric field is applied to a sample causing charged bubbles to move toward an oppositely charged electrode. The electrophoretic mobility is the measured electrophoretic velocity divided by the electric field gradient at the location where the velocity was measured. These results can be interpreted in terms of the electric potential at the plane of shear, also known as the zeta potential, using well-known equations available in the literature (29—31). Because the exact location of the shear plane is generally not known, the zeta potential is usually taken to be approximately equal to the potential at the Stem plane (Figure 11) ... 

Electrophoresis The motion of colloidal species caused by an imposed electric field. The term replaces the older term cataphoresis. The species move with an electrophoretic velocity that depends on their electric charge and the electric field gradient. The electrophoretic mobility is the electrophoretic velocity per unit electric field gradient and is used to characterize specific systems. An older synonym, no longer in use, is kataphoresis. The term microelectrophoresis is sometimes used to indicate electrophoretic motion of a collection of particles on a small scale. Previously, microelectrophoresis was used to describe the measurement techniques in which electrophoretic mobilities are determined by observation through a microscope. The recommended term for these latter techniques is now microscopic electrophoresis (see reference 1). 

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