New Looks at Capillary Zone Electrophoresis (CZE) and Micellar Electrokinetic Capillary Chromatography (MECC) and Optimization of MECC

© 2012 Ghowsi and Ghowsi, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. New Looks at Capillary Zone Electrophoresis (CZE) and Micellar Electrokinetic Capillary Chromatography (MECC) and Optimization of MECC


Introduction
The origin of theoretical plates for electrophoresis in general sense has been obtained from the work of Giddings¹. Giddings has derived the following equation for the number of theoretical plates.
For an ideal process, in which Ө=1 and T=298K,this equation reduces where we have used the Faraday constant F=96500 coulombs/mol. This voltage drops V in the range of 100-10000 v with charge number Z=1 capable of yielding 2000-200000 theoretical plates, a range comparable to that found in chromatographic system. Jorgenson and Lukacs², also in their land mark paper provided a theory for capillary zone electrophoresis (CZE) in which they proposed two fundamental equations for resolution and migration time. Resolution and number of theoretical plates are the focus of this work. This is how number of theoretical plates are derived for capillary zone electrophoresis and used in resolution equation by Jorgenson There is mistake occurs in Jorgenson and Lukacs work², t in eqn. (7) is replaced by eqn. (8), this is the case when electroomosis is absent.
By making this mistake substitution eqn (8) , what has been obtained by Jorgenson and Lukacs for N , eqn. (2) is

Theory
According to Gidding's theory¹ the evaluation of the ultimate capabilities of zone electrophoresis is possible. To calculate the number of theoretical plates and separable zone achieveable in ideal zone electrophoresis, the electrostatic force exerted on a mole of charged particles on electric field of strength E is where z=net charge of a single particle in proton units and F=Faraday constant the negative chemical potential drop across the separation path.
In which X´ is the distance where f, force applied in capillary eletrophoresis. For conventional mode of capillary zone electrophoresis, electroosmotic and electrophoretic velocities are in opposite direction. This conventional mode is similar to tread mill and electric stairs where the moveing object has two movements one walking and the other one movement of the stairs.
There X´ in eqn. (17) is not the length of capillary, it is effective distance where the electric force which is applied is greater than the length of capillary is called Replacing the electrophoretic velocity variable with the product of electrophoretic mobility and electric field ep ep v E   yields the following expression: In order to observe the dependence, efficiency has on capillary length and electroosmosis, a substitution for the time variable in eqn.(21) is made. Net displaccment of the analyte or capillary length, X, is related to the retention time, t as shown substituting eqn.(25) into eqn.(20) yields the expression, By making additional substitution for electrophoretic and electroosmotic velocity produced, ( ) plate height is the ratio of effective length X´ to efficiency N is Substituting equation into eqn.(28) yields an expression for plate height.
This interesting result shows that the theoretical plate height is independent of electroosmotic flow when it is based on the effective distance the analyte travels rather than the capillary length. Instead, plate height has a simple inverse relation with the electric field strength. Equation for resolution: Based width resolution is the quantitative measure of ability to separate two analytes. For two adjacent peaks with similar elution times, peak showed be nearly identical: Assuming eqn.(30) is true, resolution for species A and B expressed in terms of their retention times and the peak base width for either species².
The conventional expression for separation can be written with parameters related to either species A or B, shown here using the retention time and peak base width for species B². ( ) The resolution time variable R t and the efficiency N are eliminated by inserting eqns.(25) and (26) into eqn.(33) for the analyte B:

Micellar electrokinetic capillary chromatography (MECC)
By converting figure of Merits in MECC to electrochemical parameters 5 and pursuing similar procedure we applied to capillary electrophoresis and using effective length³ solute travels rather than length of capillary and then converting the resolution equation in terms of chromatography parameters new equation for resolution could be found which is published in another paper 7 .

Optimization of micellar electrokinetic capillary chromatography (MECC) as a nano separation technique using three dimensional and two dimensional plottings of characteristic equations
Feyman with the lecture of plenty of room at the bottom at an American Physical Society at Caltech on December 29, 1959 considered the possibility of direct manipulation of individual atoms as a more powerful forms of synthetic chemistry than those used at the time . In conventional chromatography there are two phases involved one is the stationary phase and one is the mobile phase 6 . Terabe et al proposed Micellar Electrokinetic Capillary Chromatography 8 , MECC, which has the smallest pseudo stationary phase within nano range called micelle.
The very high strength of separation comes from these nano sized materials. That is why we call this technique MECC.

Nano separation technique
There are several work which have been done to final the optimum conditions of this Nano Separation Technique 5,[8][9][10] .
In all optimization characteristic equation is the focus.
What is the characteristic equation?
In column chromatography the resolution equation is given as 6 1/2 Where k´ is the capacity factor, α is the selectivity and N is the number of theoretical plates.
Variables of this equations were defined in the previous work 7 . The characteristic equation of s R for equation (43) is the last two terms.
In a comparison between the characteristic equation (42)

Two dimensional and tree dimensional plots of characteristic equations
In present work by the help of modern technology of computer and three dimensional software of Dplot direct access to the plot of characteristic equations (42) and (44) are possible.

Conclusion
The fundamental eqn.12 for the number of theoretical plates has been used to obtain resolution equation by Jorgenson eqn.14. The number of theoretical plates equation in previous work by Jorgenson is wrong, automatically makes the resolution equation wrong.
With the consideration that length X in eqn. 17 is the distance where force is applied in capillary electrophoresis, number of theoretical plates which depends on eqn.17 is discussed. Another