# Background

### Fundamentals

In Learning Module I we discussed the two mechanisms of separative transport in free zone capillary electrophoresis: electrophoresis and electroosmosis. In evaluating the order of migration we noted that neutral analyte comigrate in a band. It turns out that free zone capillary electrophoresis can be modified with certain additives that impart an additional selectivity based on hydrophobic partitioning. MEKC is a popular mode of capillary electrophoresis first reported in 1984 by Shigeru Terabe et. al. [1] and requires the addition of a micellar pseudo-stationary phase in capillary electrophoresis. A micelle is formed when amphiphilic molecules that contain distinct hydrophilic and hydrophobic regions self-assemble to form liquid crystal aggregates. A common surfactant used in MEKC is sodium dodecyl sulfate, SDS, which is comprised of a 12-carbon hydrophobic chain and charged sulfate head group. The hydrophobic alkyl chains collect or assemble in the core of the aggregate to reduce the contact of alkyl and water. The sulfated head groups are presented on the portions of the aggregate with greatest exposure to the aqueous running buffer. These aggregates are classically represented as rigid spheres with a well-defined core region and a well-defined outer region, although, the surfactant molecules are constantly undergoing exchange.

An SDS micelle has a net negative charge, since SDS itself is anionic. As a result, an SDS micelle has a characteristic electrophoretic mobility when it is a component of the running buffer. Additionally, an SDS micelle contains a hydrophobic region, into which analyte molecules may partition. A highly hydrophobic analyte, such as n-decanophenone, or Sudan III, may partition completely into an SDS micelle, in which case, the migration time of this analyte is identical to the migration time of the SDS micelle. A neutral analyte with an intermediate hydrophobicity will exchange between micelle and aqueous running buffer. During the time the neutral analyte associates with the micelle, it will assume the velocity of the micelle. When the neutral analyte is not associated with the micelle, it will assume a velocity dictated by electroosmotic flow. The migration time of the analyte will be a function of the amount of time it assumes the electroosmotic velocity and the amount of time it assumes the micelle velocity. Thus a series of neutral analyte with varying hydrophobicity will have different migration time. This is demonstrated pictorially in Figures 3.1A, B.

Figure 3.1a is a pictoral representatiion of the separative transport in MEKC.
Figure 3.1b describes the components of the resulting hypothetical electropherogram.

### MEKC Figure of Merit

Retention factor, sometimes called capacity factor, is used to evaluate the relative hydrophobicity of the analyte. The term for retention factor is written k’, and is the ratio of moles analyte in the micelle phase-to-moles of analyte in the aqueous component of running buffer (see equation 3.1). Recall that when neutral analyte associates with micelle it assumes the micelle velocity and when neutral analyte is not associated with micelle it has a velocity equal to that of the bulk electroosmotic flow. Therefore, the velocity of neutral analyte in MEKC, υapparent, is the sum of the mole fraction of neutral analyte in the aqueous phase times the velocity of electroosmotic flow, υeof, and the mole fraction of neutral analyte in the micelle phase times the velocity of the micelle, υmicelle, (see equation 3.2). Equation 3.2 can be rearranged in order that capacity factor may be expressed in terms of parameters that are easily measured in an MEKC experiment, shown in equation 3.14. Thus capacity factor of a neutral molecule may be determined by measuring the time of the electroosmotic flow, teof, the retention time of the hydrophobic/neutral analyte, tR, and the time of an analyte that serves as a micelle marker, tmicelle.

$k' = \dfrac{moles_{micelle}}{moles_{aqueous}} \tag{equation 3.1}$

$υ_{apparent} = υ_{eof} \dfrac{η_{aqueous}}{η_{micelle} + η_{aqueous}} + υ_{micelle} \dfrac{η_{micelle}}{η_{micelle} + η_{aqueous}} \tag{equation 3.2}$

Click here to see the derivation of k’ for neutral compounds in Appendix A

$k' = \dfrac{t_R - t_{eof}}{t_{eof} ( 1 - \dfrac{t_R}{t_{micelle}} )} \tag{equation 3.14}$

### Application of MEKC to charged analyte

MEKC may also be applied to separate charged analyte of similar charge-to-size ratio. When charged analyte associates with micelle it assumes the micelle velocity and when charged analyte is not associated with micelle it has a velocity comprised of both bulk electroosmotic flow and electrophoretic mobility. Retention factor is also determined from measurable parameters for charged compounds subject to MEKC. However, the calculation includes contributions from electrophoretic mobility. In the case of MEKC separation of negatively charged analyte, the apparent velocity of the compound in aqueous component of the running buffer is the difference of the bulk electroosmotic flow to ward the detection window, and the electrophoretic velocity away from the detection window (towards the injection end of the capillary). The velocity components for an anionic compound separated using MEKC is described by equation 3.15. Using a derivation similar to that for neutral analytes the equation for capacity factor is expressed by equation 3.31. In this case mobility, μ, is related to velocity by electric field, where electric field is applied voltage divided by total capillary length. See equations 3.28a-c in the derivation of k’ for anions.

$υ_{apparent} = υ_{eof} \dfrac{η_{aqueous}}{η_{micelle} + η_{aqueous}} + υ_{eph\_analyte} \dfrac{η_{aqueous}}{η_{micelle} + η_{aqueous}} + υ_{micelle} \dfrac{η_{micelle}}{η_{micelle} + η_{aqueous}} \tag{equation 3.15}$

Click here to see the derivation of k’ for anions in Appendix B

$k' = \dfrac{t_{anion\_MEKC} \left(1 + \dfrac{μ_{eph\_anion}} {μ_{eof\_MEKC}}\right) − t_{eof\_MEKC}}{t_{eof\_MEKC} \left(1 − \dfrac{t_{anion\_MEKC}}{t_{n−dec\_MEKC}}\right)} \tag{equation 3.31}$

There are a variety of other conditions that may be used for MEKC to facilitate the separation of anions, neutral compounds, or cations. Micelles may have a net negative charge, as in the case of SDS. They may also have a net neutral charge, or net positive charge. In the later case, the user needs to consider the interaction of cationic surfactant with anionic capillary surface, since the introduction of cationic surfactant often reverses electroosmotic flow. Other, more sophisticated micelles have been used in MEKC, including, mixed micelles, polymeric micelles, polyelectrolyte micelle complexes and bicelles. Depending on the transport mechanisms for analyte and micelle, the derivation for retention factor may be different from what is outlined in Appendices A and B. The discussion of these other systems in further detail is beyond the scope of this Learning Module. Instead, the reader is referred to other sources that provide an in depth discussion of the derivation of expressions for retention factor [2-4].