Net electrophoretic velocity

Using Eqs.(79a) and (83), we find that during a complete cycle of duration (t + t ), the net electrophoretic velocity is, for XBack ... 

This result indicates that the net electrophoretic velocity is, in fact, V o P lse durations t smaller than the tube-renewal time... 

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

The separation mechanism is based on stereoselective ion-pair formation of oppositely charged cationic selector and anionic solutes, which leads to a difference of net migration velocities of the both enantiomers in the electric field. Thus, the basic cinchona alkaloid derivative is added as chiral counterion to the BGE. Under the chosen acidic conditions of the BGE, the positively charged counterion associates with the acidic chiral analytes usually with 1 1 stoichiometry to form electrically neutral ion-pairs, which do not show self-electrophoretic mobility but... 

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.)... 

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. 

A smooth curve is obtained which indicates a reasonable migration velocity whose value is relatively independent of pH near pH 8. Although the pH 5 value is missing as noted above, the interpolated curve crosses the velocity axis at about pH 5.25, essentially identical to the accepted pi value of 5.2 where the electrophoretic velocity is expected to be zero. (However, the net velocity at all pH values is towards the detector due to the presence of electro-osmotic flow.)... 

Fig. 6.4. Diagram illustrating the principle for counterflow (a) and normal-flow (b) gradients (Reprinted with permission from [31]. Copyright 1999 American Chemical Society). The direction of electroosmotic flow is opposite to that of the electrophoretic movement in both methods and is opposite to the net migration velocity, vmigr (= ve0 - ve ph), in (a) and coincides with the net migration direction in (b). veo is not constant along the capillary, and velph is higher in the direction of the electrophoretic migration.

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. 

The second method of exploitation occurs when the electric field is of a polarity such that the charged-particle migration occurs away from the filter medium. The contribution to the net-particle velocity of the electrophoretically induced flow away from the filter medium is generally orders of magnitude less than the contribution to the net-... 

The next step is to evaluate the electrophoretic and relaxation components of the net drift velocity of an ion. 

Identification of sample components based solely on migration time in capillary electrophoresis (CE) requires reproducibilities not normally obtained. These are caused, mainly, by two effects temperature effects and electro-osmotic affects. Migration times in CE are determined by the electro-osmotic velocity Ueof and effective electrophoretic migration velocity Ueef the net migration velocity Vt is the vector sum of both velocities ... 

For a charged species i carried by elutant flow and under the influence of an electric field, the net species velocity, , is the sum of the convective and electrophoretic migration velocities,... 

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. 

The electrophoretic velocity with which the particle moves with respect to its suspending medium is proportional to the strength of the applied electric field, the proportionality factor being called the electrophoretic mobility. The electrophoretic mobility pe is proportiOTial to the magnitude of the net charge on the particle and is inversely proportional to the size of the particle ... 

Minor et al. [32] have analyzed the time dependence of both the electroosmotic flow and electrophoretic mobility in an electrophoresis cell. They concluded that, for most experimental conditions, the colloidal particle reaches its steady motion after the application of an external field in a much shorter time than electroosmotic flow does. Hence, if electrophoresis measurements are performed in an alternating field with a frequency much larger than the reciprocal of the characteristic time for steady electroosmosis (t 10° sec), but smaller than that of steady electrophoresis (t 10 sec), the electroosmotic flow cannot develop. In such conditions, electroosmosis is suppressed, and the velocity of the particle is independent of the position in the cell. Figure 3.6 is an example we measured the velocity of polystyrene particles in the center of a cylindrical cell using a pulsed field with the frequency indicated when the frequency is above 10 Hz, the velocity (average between the field-on and field-off values) tends to the true electrophoretic velocity measured at the stationary level. Another way to overcome the electroosmosis problem is to place both electrodes providing the external field, inside the cell, completely surrounded by electroneutral solution as no net external field acts on the charged layer close to the cell walls, the associated electroosmotic flow wiU not exist [33]. 

The movement of charged analytes is now considered as a consequence of the combination of their own individual electrophoretic mobilities (Equation [3.61]) and their participation in the bulk electro-osmotic flow (EOF). The net speed of motion of an analyte ion in the field direction (along the length of the capillary) is the vector sum of its electrophoretic velocity (Equation [3.61])... 

E. (a) Capillary electrophoresis was conducted at pH 9, at which electroosmotic velocity is greater than electrophoretic velocity for a particular anion. Draw a picture of the capillary, showing the anode, cathode, injector, and detector. Show the directions of electroosmotic and electrophoretic flow of a cation and an anion. Show the direction of net flow for each ion. 

---