Electrophoretic mobility and electro-osmotic flow

Under the effects of various phenomena or simultaneous actions such as temperature, viscosity, voltage, these particles will have migration velocities that will be faster, the smaller they are and the greater their charge. The separation depends upon the charge-to-size ratio of the hydrated analyte ions. 

For each ion the limiting migration velocity results from the equilibrium between the electric force F, which is exerted in the electric field E acting on the particle of charge q, and the forces resulting from the solution viscosity 17. Neutral 

Hiickel proposed an equation taking account of the influence of these factors upon the electrophoretic velocity of an ion considered as a sphere of radius r. 

The charged species present in the sample are submitted to two principal effects, which are their individual electrophoretic mobility and the more global electro-osmotic flow. 

A compound bearing an electric charge move within the electrolyte assumed to be immobile at a velocity Upp (m/s) which depends upon the conditions of the experiment and of its own electrophoretic mobility fi p. For a given ion and medium, p,pp is a constant which is characteristic of that ion. This parameter is defined from the electrophoretic migration velocity of the compound and the exerted electric field E, using expression 8.1  

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In capillary electrophoresis, components of a mixture are separated according to two main factors electrophoretic mobility and electro-osmotic flow. These terms apply to ions, molecules or micelles. 

The velocity of a solute in the capillary is determined by its electrophoretic mobility and electro-osmotic flow (EOF), which are affected by temperature, and which is influenced by the diameter and length of the capillary, its contents, concentration, and pH of running buffer, applied voltage, current, viscosity, and zeta-potential. The subtle variation of EOF is also a main factor in maintaining high reproducibility if CE is automated by the constant temperature of the capillary and running buffer with proper buffering capacity. However, it is difficult to keep the temperature constant, as EOF depends on the condition of the fused silica. 

Using SI units, the velocity of the electro-osmotic flow is expressed in meters per second (m/s) and the electric field in volts per meter (V/m). Consequently, in analogy to the electrophoretic mobility, the electro-osmotic mobility has the dimension square meters per volt per second. Because electro-osmotic and electrophoretic mobilities are converse manifestations of the same underlying phenomenon, the Hehnholtz-von Smoluchowski equation applies to electro-osmosis as well as to electrophoresis. In fact, when an electric field is applied to an ion, this moves relative to the electrolyte solution, whereas in the case of electro-osmosis, it is the mobile diffuse layer that moves under an appUed electric field, carrying the electrolyte solution with it. 

In MEKC, mainly anionic surface-active compounds, in particular SDS, are used. SDS and all other anionic surfactants have a net negative charge over a wide range of pH values, and therefore the micelles have a corresponding electrophoretic mobility toward the anode (opposite the direction of electro-osmotic flow). Anionic species do not interact with the negatively charged surface of the capillary, which is favorable in common CZE but especially in ACE. Therefore, SDS is the best-studied tenside in MEKC. Long-chain cationic ammonium species have also been employed for mainly anionic and neutral solutes (16). Bile salts as representatives of anionic surfactants have been used for the analysis of ionic and nonionic compounds and also for the separation of optical isomers (17-19). 

By combining the apparent mobility and the electro-osmotic flow, which is responsible for the migration of the bulk electrolyte, it is possible to calculate the migration velocity or the electrophoretic mobility of charged species. Using equation (8.3), equation (8.5) can be written as ... 

Electrodriven separations, such as capillary electrophoresis (CE) and capillary electrochromatography (CEC), are based on the different electrophoretic mobilities in an electric field of the molecules to be separated. They provide a higher separation efficiency then conventional HPLC since the electrophoretic flow (EOF) has a plug-flow profile. Whereas the mobile phase in CE is driven only by the electro-osmotic flow, it is generated in CEC by a combination of EOF and pressure. CEC has a high sample capacity which favours its hyphenation with NMR. 

Capillary electrophoresis separations are dependent on the relative mobilities of analytes under the influence of an electric field and do not depend on mobile phase/stationary phase interactions. A fused silica capillary is filled with a buffer and both ends submerged into two reservoirs of the buffer. A platinum electrode is immersed in each reservoir and a potential difference (5-30 kV) is applied across the electrode. An aliquot of sample of a few nanoliters is injected onto the capillary by either hydrostatic or electrokinetic injection, and the components migrate to the negative electrode. Separations of analytes arise from differences in the electrophoretic mobilities, which are dependent on the mass-to-charge ratio of the components, physical size of the analyte, and buffer/analyte interactions. An electro-osmotic flow (EOF) of the buffer occurs in the capillary and arises as a result of interactions of the buffer with dissociated functional groups on the surface of the capillary. Positive ions from the buffer solution are attracted to negative ions... 

The results of measurements by the microscopic method show that the electrophoretic mobility of the particles varies with the distance from the wall of the cell particles close to the wall move in a direction opposite to that in which those in the center migrate. In any event, the results show an increase in velocity from the walls to the center of the cell. The explanation of this fact lies in the electro-osmotic movement of the liquid a double layer is set up between the liquid and the walls of the cell and under the influence of the applied field the former exhibits electro-osmotic flow. For the purpose of obtaining the true electrophoretic velocity of the suspended particles it is neceasary to observe particles at about one-fifth the distance from one wall to the other. A more accurate procedure is to make a series of measurements at different distances from the side of the cell and to apply a correction for the electro-osmotic flow. The algebraic difference of the corrected electrophoretic velocity and the speed of the particles near the walls gives the electro-osmotic mobility of the liquid in the particular cell. If the solution contains a protein which is adsorbed on the surface of the walls of the vessel and on the particles, it is possible to compare the electrophoretic and electro-osmotic mobilities in one experiment reference to the significance of such a comparison was made on page 532. 

As the mobile phase moves through the capillary containing the sorbent under the effect of this electro-osmotic flow (EOF), sample components partition between the two phases in sorption and diffusive mechanisms characteristic of liquid chromatography. Ions in the sample move both under the influence of EOF and by their added attraction toward the oppositely charged electrode (electrophoresis). Uncharged components, on the other hand, move only under the influence of EOF. Thus, sample components, in general, separate by chromatographic and, sometimes, electrophoretic processes. 

As previously mentioned, electrophoretic separations using open-tube capillaries are based on solute differential mobility, which is a function of charge and molecular size. A different approach is required for separating neutral or uncharged compounds. Because charge is absent, electrophoretic mobility is zero. Electro-osmotic flow would allow them to migrate, but their velocities would be equal. Separation would not be possible with the above method. 

By combining the electro-osmotic flow and the apparent mobility it is possible to calculate the true electrophoretic mobility of the species carrying charges. From relation 8.3 it can be written ... 

Two electrically dependent phenomena contribute to the net mobility of an analyte, i.e., the intrinsic electrophoretic mobility and the electro-osmotic flow (EOF) [154], The mobility can be evaluated from the electropherogram using the migration time, t, of the analyte migrating a distance from the injection point to... 

The electrophoretic process begins when the source buffer vial is removed and replaced with a sample vial. The sample is injected onto the top of the capillary. Separation of components occurs as the analytes and buffer migrate through the capillary under then-own electrophoretic mobility and under the influence of electro-osmotic flow (EOF), which moves from anode to cathode. Eventually, each component migrates from the capillary as a narrow band (or peak). 

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