Electrophoretic velocities

Electrophoretic Mobility The velocity with which a solute moves in response to the applied electric field is called its electrophoretic velocity, Vepi it is defined as... 

Total Mobility A solute s net, or total velocity, Vtot, is the sum of its electrophoretic velocity and the electroosmotic flow velocity thus. 

The 2eta potential (Fig. 8) is essentially the potential that can be measured at the surface of shear that forms if the sohd was to be moved relative to the surrounding ionic medium. Techniques for the measurement of the 2eta potentials of particles of various si2es are collectively known as electrokinetic potential measurement methods and include microelectrophoresis, streaming potential, sedimentation potential, and electro osmosis (19). A numerical value for 2eta potential from microelectrophoresis can be obtained to a first approximation from equation 2, where Tf = viscosity of the liquid, e = dielectric constant of the medium within the electrical double layer, = electrophoretic velocity, and E = electric field. 

Migration velocity The electrophoretic velocity of a charged particle in an electric field. 

Overbeek, JTG, Quantitative Interpretation of the Electrophoretic Velocity of Colloids. In Advances in Colloid Science Mark, H Verwey, EJW, eds. Interscience New York, 1950 Vol. 3, p 97. 

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. 

The ratio of the two virtual lengths defines a parameter called the electrophoretic velocity factor k, which is analogous to the chromatographic retention factor and it is expressed as [140] ... 

The movement of the charged analyte in the electric field can be described in the simplest way by balancing two forces fhaf influence fhe ion movement. Ions are accelerated by the force of the electric field equal to F = zE, where 2 is the charge of the analyte and E is the electric field sfrengfh. This acceleration is balanced by the frictional resistance Fj of fhe environment for which a spherical particle equals Ff = 6nqrv, where tj is the viscosity of fhe medium, r is fhe radius of the analyte and v is the velocity of fhe analyte. If fhe two forces are equal, the analyte moves at the constant electrophoretic velocity proportional to the strength of fhe elecfric field as follows ... 

If one compares Eqs. (6.317) and (6.314) everything is fine, except that this Stokes law approach gives a numerical factor / =, whereas the electro-osmotic approach gives/= f. It turns out that each is right for a particular set of conditions. This conclusion comes out of an accurate mathematical treatment that results in the following expression for the electrophoretic velocity ... 

FIG. 12.4 The domain within which most investigations of aqueous colloidal systems lie in terms of particle radii and 1 1 electrolyte concentration. The diagonal lines indicate the limits of the Hiickel and the Helmholtz-Smoluchowski equations. (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.)... 

Even in the absence of a colloid, an electrolyte solution will display electroosmotic flow through a chamber of small dimensions. Therefore the observed particle velocity is the sum of two superimposed effects, namely, the true electrophoretic velocity relative to the stationary liquid and the velocity of the liquid relative to the stationary chamber. Figure 12.10a shows the results of this superpositioning for particles tracked at different depths in the cell. The particles used in this study are cells of the bacterium Klebsiella aerogenes in phosphate buffer. Rather than calculated velocities or mobilities, Figure 12.10a shows the reciprocal of the time... 

Electrophoretic measurements by the microscope method are complicated by the simultaneous occurrence of electro-osmosis. The internal glass surfaces of the cell are usually charged, which causes an electro-osmotic flow of liquid near to the tube walls together with (since the cell is closed) a compensating return flow of liquid with maximum velocity at the centre of the tube. This results in a parabolic distribution of liquid speeds with depth, and the true electrophoretic velocity is only observed at locations in the tube where the electro-osmotic flow and return flow of the liquid cancel. For a cylindrical cell the stationary level is located at 0.146 of the internal diameter from... 

Fig. 3. The experimental velocity Ve is the resultant of the electrophoretic velocity V and the velocity of the hydrodynamic flow Vf in each point of the strip. There is a point N where Ve — 0. The migrating particle is unable to leave this point (A8).

If evaporation velocity is equal to the electrophoretic velocity but opposite in direction, the result of the interaction is the immobilization of the migrating ion on a definite point of the strip. If we consider the diagram, it is easy to understand why a particle must find its restpoint N independent of the actual spot of the paper where it was originally applied. This phenomenon explains the experiment of Fig. 4. 

During the run the paper is heated above room temperature, and buffer solvent must evaporate in proportion to the size of the chamber and the quantity of condensate. This evaporation is greatest at the beginning of the run, but in a smaller chamber it may become so slight that rheophoresis falls to nil and the fraction travels into the buffer vessel (Fig. 23). Most commercial forms of apparatus are not vapor saturated before the run begins and evaporation remains throughout the experiment at a sufficiently high level to cause immobilization of the fractions at the place where buffer flow and electrophoretic velocity neutralize each other. 

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. 

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