Background Theory and Principles of Capillary Electrophoresis

1 Introduction

This chapter describes the basic theoretical concepts and principles of capillary electrophoresis (CE). The depth of discussion should provide enough background to understand the basic operation of CE instruments and the principles by which CE separates analytes. This is complemented in the next chapter by a discussion of the most common modes of separation operated by CE. For a more comprehensive explanation of the theoretical aspects of CE, please refer to one or more of the reference books listed in the Bibliography. In addition, a list of definitions for terms and abbreviations is given in the Glossary.

2 What is Capillary Electrophoresis?

The process of electrophoresis is defined as 'the differential movement or migration of ions by attraction or repulsion in an electric field'. In practical terms, a positive (anode) and negative (cathode) electrode are placed in a solution containing ions. Then, when a voltage is applied across the electrodes, solute ions of different charge, i.e., anions (negative) and cations (positive), will move through the solution towards the electrode of opposite charge. Capillary electrophoresis, then, is the technique of performing electrophoresis in buffer-filled, narrow-bore capillaries, normally from 25 to 100 µm in internal diameter (ID).

3 Instrumentation

The instrumentation required for CE is remarkably simple in design, as Figure 1.1 illustrates. The ends of a capillary are placed in separate buffer reservoirs, each containing an electrode connected to a high-voltage power supply capable of delivering up to 30 kV. The sample is injected onto the capillary by temporarily replacing one of the buffer reservoirs (normally at the anode) with a sample reservoir and applying either an electric potential or external pressure for a few seconds. After replacing the buffer reservoir, an electric potential is applied across the capillary and the separation is performed. Optical (UV-visible or fluorometric) detection of separated analytes can be achieved directly through the capillary wall near the opposite end (normally near the cathode).

CE is very suited to automation, and the arrangement of commercial CE instruments will seem familiar to those with knowledge of modern HPLC. Basic features of a CE instrument include an autosampler, a detection module, a high-voltage power supply, the capillary and, of course, a computer to control everything. So, if we consider that the power supply is equivalent to an HPLC pump and the capillary is equivalent to a column, the instrumentation is completely analogous. This is especially so as the software packages used to control most commercial CE instruments are based heavily on existing HPLC software.

4 Electrophoresis Theory

The theory that governs electrophoresis is directly applicable to CE and can be dealt with very briefly, with reference to a few equations. As mentioned earlier, electrophoresis is the movement or migration of ions or solutes under the influence of an electric field. Therefore, separation by electrophoresis relies on differences in the speed of migration (migration velocity) of ions or solutes. Now, ion migration velocity can be expressed as:

v = μeE (1.1)

where v is ion migration velocity (m s-1, μe is electrophoretic mobility (m2 V-1 s-1 and E is electric field strength (Vm-1.

The electric field strength is a function of the applied voltage divided by the total capillary length. Electrophoretic mobility is a factor that indicates how fast a given ion or solute may move through a given medium (such as a buffer solution). It is an expression of the balance of forces acting on each individual ion; the electrical force acts in favour of motion and the frictional force acts against motion. Since these forces are in a steady state during electrophoresis, electrophoretic mobility is a constant (for a given ion under a given set of conditions). The equation describing electrophoretic mobility is:

μe = q/6πνr (1.2)

where q is the charge on the ion, ν is the solution viscosity and r is the ion radius. The charge on the ion (q) is fixed for fully dissociated ions, such as strong acids or small ions, but can be affected by pH changes in the case of weak acids or bases. The ion radius (r) can be affected by the counter-ion present or by any complexing agents used. From equation (1.2) we can see that differences in electrophoretic mobility will be caused by differences in the charge-to-size ratio of analyte ions. Higher charge and smaller size confer greater mobility, whereas lower charge and larger size confer lower mobility.

Electrophoretic mobility is probably the most important concept to understand in electrophoresis. This is because electrophoretic mobility is a characteristic property for any given ion or solute and will always be a constant. What is more, it is the defining factor that decides migration velocities. This is important, because different ions and solutes have different electrophoretic mobilities, so they also have different migration velocities at the same electric field strength. It follows that, because of differences in electrophoretic mobility, it is possible to separate mixtures of different ions and solutes by using electrophoresis.

5 Electroosmotic Flow (EOF)

A vitally important feature of CE is the bulk flow of liquid through the capillary. This is called the electroosmotic flow and is caused as follows.

An uncoated fused-silica capillary tube is typically used for CE. The surface of the inside of the tube has ionisable silanol groups, which are in contact with the buffer during CE. These silanol groups readily dissociate, giving the capillary wall a negative charge. Therefore, when the capillary is filled with buffer, the negatively charged capillary wall attracts positively charged ions from the buffer solution, creating an electrical double layer and a potential difference (zeta potential) close to the capillary wall, as described according to Stern's model in Figure 1.2. Stern's model for an electrical double layer includes a...