# Capillary electrophoresis

Acronym CE Electrophoresis BiomoleculesChiral molecules gel electrophoresisTwo-dimensional gel electrophoresis Capillary electrophoresis mass spectrometry

Acronym CE Electrophoresis BiomoleculesChiral molecules gel electrophoresisTwo-dimensional gel electrophoresis Capillary electrophoresis mass spectrometry

Capillary electrophoresis (CE) is a family of electrokinetic separation methods performed in submillimeter capillaries and in micro- and nanofluidic channels. Very often, CE refers to capillary zone electrophoresis (CZE), but other electrophoretic techniques including capillary gel electrophoresis (CGE), capillary isoelectric focusing (CIEF), capillary isotachophoresis and micellar electrokinetic capillary chromatography (MECC) belong also to this class of methods.[1] In CE methods, analytes migrate through electrolyte solutions under the influence of an electric field. Analytes can be separated according to ionic mobility, additionally they may be concentrated by means of gradients in conductivity and pH.

## Instrumentation

The instrumentation needed to perform capillary electrophoresis is relatively simple. A basic schematic of a capillary electrophoresis system is shown in figure 1. The system's main components are a sample vial, source and destination vials, a capillary, electrodes, a high-voltage power supply, a detector, and a data output and handling device. The source vial, destination vial and capillary are filled with an electrolyte such as an aqueous buffer solution. To introduce the sample, the capillary inlet is placed into a vial containing the sample and then returned to the source vial (sample is introduced into the capillary via capillary action, pressure, or siphoning). The migration of the analytes is then initiated by an electric field that is applied between the source and destination vials and is supplied to the electrodes by the high-voltage power supply. It is important to note that all ions, positive or negative, are pulled through the capillary in the same direction by electroosmotic flow, as will be explained. The analytes separate as they migrate due to their electrophoretic mobility, as will be explained, and are detected near the outlet end of the capillary. The output of the detector is sent to a data output and handling device such as an integrator or computer. The data is then displayed as an electropherogram, which reports detector response as a function of time. Separated chemical compounds appear as peaks with different retention times in an electropherogram.[2] Capillary electrophoresis was first combined with mass spectrometry by Richard D. Smith and coworkers, and provides extremely high sensitivity for the analysis of very small sample sizes.

Figure 1: Diagram of capillary electrophoresis system

## Detection

Separation by capillary electrophoresis can be detected by several detection devices. The majority of commercial systems use UV or UV-Vis absorbance as their primary mode of detection. In these systems, a section of the capillary itself is used as the detection cell. The use of on-tube detection enables detection of separated analytes with no loss of resolution. In general, capillaries used in capillary electrophoresis are coated with a polymer for increased stability. The portion of the capillary used for UV detection, however, must be optically transparent. Bare capillaries can break relatively easily and, as a result, capillaries with transparent coatings are available to increase the stability of the cell window. The path length of the detection cell in capillary electrophoresis (~ 50 micrometers) is far less than that of a traditional UV cell (~ 1 cm). According to the Beer-Lambert law, the sensitivity of the detector is proportional to the path length of the cell. To improve the sensitivity, the path length can be increased, though this results in a loss of resolution. The capillary tube itself can be expanded at the detection point, creating a "bubble cell" with a longer path length or additional tubing can be added at the detection point as shown in figure 2. Both of these methods, however, will decrease the resolution of the separation.[3]

Figure 2: Techniques for increasing the pathlength of the capillary: a.) a bubble cell and b.) a z-cell (additional tubing).[2]

Fluorescence detection can also be used in capillary electrophoresis for samples that naturally fluoresce or are chemically modified to contain fluorescent tags. This mode of detection offers high sensitivity and improved selectivity for these samples, but cannot be utilized for samples that do not fluoresce. The set-up for fluorescence detection in a capillary electrophoresis system can be complicated. The method requires that the light beam be focused on the capillary, which can be difficult for many light sources.[3] Laser-induced fluorescence has been used in CE systems with detection limits as low as 10−18 to 10−21 mol. The sensitivity of the technique is attributed to the high intensity of the incident light and the ability to accurately focus the light on the capillary.[2]

In order to obtain the identity of sample components, capillary electrophoresis can be directly coupled with mass spectrometers or Surface Enhanced Raman Spectroscopy (SERS). In most systems, the capillary outlet is introduced into an ion source that utilizes electrospray ionization (ESI). The resulting ions are then analyzed by the mass spectrometer. This set-up requires volatile buffer solutions, which will affect the range of separation modes that can be employed and the degree of resolution that can be achieved.[3] The measurement and analysis are mostly done with a specialized gel analysis software.

For CE-SERS, capillary electrophoresis eluants can be deposited onto a SERS-active substrate. Analyte retention times can be translated into spatial distance by moving the SERS-active substrate at a constant rate during capillary electrophoresis. This allows the subsequent spectroscopic technique to be applied to specific eluants for identification with high sensitivity. SERS-active substrates can be chosen that do not interfere with the spectrum of the analytes.[4]

## Modes of separation

The separation of compounds by capillary electrophoresis is dependent on the differential migration of analytes in an applied electric field. The electrophoretic migration velocity ($u_{p}$) of an analyte toward the electrode of opposite charge is:

$u_{p}=\mu _{p}E\,$

The electrophoretic mobility can be determined experimentally from the migration time and the field strength:

$\mu _{p}=\left({\frac {L}{t_{r}}}\right)\left({\frac {L_{t}}{V}}\right)$

where $L$ is the distance from the inlet to the detection point, $t_{r}$ is the time required for the analyte to reach the detection point (migration time), $V$ is the applied voltage (field strength), and $L_{t}$ is the total length of the capillary.[3] Since only charged ions are affected by the electric field, neutral analytes are poorly separated by capillary electrophoresis.

The velocity of migration of an analyte in capillary electrophoresis will also depend upon the rate of electroosmotic flow (EOF) of the buffer solution. In a typical system, the electroosmotic flow is directed toward the negatively charged cathode so that the buffer flows through the capillary from the source vial to the destination vial. Separated by differing electrophoretic mobilities, analytes migrate toward the electrode of opposite charge.[2] As a result, negatively charged analytes are attracted to the positively charged anode, counter to the EOF, while positively charged analytes are attracted to the cathode, in agreement with the EOF as depicted in figure 3.

Figure 3: Diagram of the separation of charged and neutral analytes (A) according to their respective electrophoretic and electroosmotic flow mobilities

The velocity of the electroosmotic flow, $u_{o}$ can be written as:

$u_{o}=\mu _{o}E$

where $\mu _{o}$ is the electroosmotic mobility, which is defined as:

$\mu _{o}={\frac {\epsilon \zeta }{\eta }}$

where $\zeta$ is the zeta potential of the capillary wall, and $\epsilon$ is the relative permittivity of the buffer solution. Experimentally, the electroosmotic mobility can be determined by measuring the retention time of a neutral analyte.[3] The velocity ($u$) of an analyte in an electric field can then be defined as:

$u_{p}+u_{o}=(\mu _{p}+\mu _{o})E$

Since the electroosmotic flow of the buffer solution is generally greater than that of the electrophoretic flow of the analytes, all analytes are carried along with the buffer solution toward the cathode. Even small, triply charged anions can be redirected to the cathode by the relatively powerful EOF of the buffer solution. Negatively charged analytes are retained longer in the capilliary due to their conflicting electrophoretic mobilities.[2] The order of migration seen by the detector is shown in figure 3: small multiply charged cations migrate quickly and small multiply charged anions are retained strongly.[3]

Electroosmotic flow is observed when an electric field is applied to a solution in a capillary that has fixed charges on its interior wall. Charge is accumulated on the inner surface of a capillary when a buffer solution is placed inside the capillary. In a fused-silica capillary, silanol (Si-OH) groups attached to the interior wall of the capillary are ionized to negatively charged silanoate (Si-O-) groups at pH values greater than three. The ionization of the capillary wall can be enhanced by first running a basic solution, such as NaOH or KOH through the capillary prior to introducing the buffer solution. Attracted to the negatively charged silanoate groups, the positively charged cations of the buffer solution will form two inner layers of cations (called the diffuse double layer or the electrical double layer) on the capillary wall as shown in figure 4. The first layer is referred to as the fixed layer because it is held tightly to the silanoate groups. The outer layer, called the mobile layer, is farther from the silanoate groups. The mobile cation layer is pulled in the direction of the negatively charged cathode when an electric field is applied. Since these cations are solvated, the bulk buffer solution migrates with the mobile layer, causing the electroosmotic flow of the buffer solution. Other capillaries including Teflon capillaries also exhibit electroosmotic flow. The EOF of these capillaries is probably the result of adsorption of the electrically charged ions of the buffer onto the capillary walls.[2] The rate of EOF is dependent on the field strength and the charge density of the capillary wall. The wall's charge density is proportional to the pH of the buffer solution. The electroosmotic flow will increase with pH until all of the available silanols lining the wall of the capillary are fully ionized.[3]

Figure 4: Depiction of the interior of a fused-silica gel capillary in the presence of a buffer solution.

## Efficiency and resolution

The number of theoretical plates, or separation efficiency, in capillary electrophoresis is given by:

$N={\frac {\mu V}{2D_{m}}}$

where $N$ is the number of theoretical plates, $\mu$ is the apparent mobility in the separation medium and $D_{m}$ is the diffusion coefficient of the analyte. According to this equation, the efficiency of separation is only limited by diffusion and is proportional to the strength of the electric field. The efficiency of capillary electrophoresis separations is typically much higher than the efficiency of other separation techniques like HPLC. Unlike HPLC, in capillary electrophoresis there is no mass transfer between phases.[3] In addition, the flow profile in EOF-driven systems is flat, rather than the rounded laminar flow profile characteristic of the pressure-driven flow in chromatography columns as shown in figure 5. As a result, EOF does not significantly contribute to band broadening as in pressure-driven chromatography. Capillary electrophoresis separations can have several hundred thousand theoretical plates.[5]

Figure 5: Flow profiles of laminar and electroosmotic flow.

The resolution ($R_{s}$) of capillary electrophoresis separations can be written as:

$R_{s}={\frac {1}{4}}\left({\frac {\triangle \mu _{p}{\sqrt {N}}}{\mu _{p}+\mu _{o}}}\right)$

According to this equation, maximum resolution is reached when the electrophoretic and electroosmotic mobilities are similar in magnitude and opposite in sign. In addition, it can be seen that high resolution requires lower velocity and, correspondingly, increased analysis time.[3]

## References

1. ^ Graham Kemp, Capillary electrophoresis: a versatile family of analytical techniques Biotechnology and Applied Biochemistry (1998) 27, (9–17)
2. Skoog, D.A.; Holler, F.J.; Crouch, S.R "Principles of Instrumental Analysis" 6th ed. Thomson Brooks/Cole Publishing: Belmont, CA 2007.
3. Skoog, D.A.; Holler, F.J.; Crouch, S.R "Principles of Instrumental Analysis" 6th ed. Chapter 30 Thomson Brooks/Cole Publishing: Belmont, CA 2007.
4. ^ Lin H.; Natan, M.; Keating, C. Anal. Chem. 2000, 72, 5348-5355.
5. ^ Skoog, D.A.; Holler, F.J.; Nieman, T.A. "Principles of Instrumental Analysis, 5th ed." Saunders college Publishing: Philadelphia, 1998.

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