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common nowadays. The microscale nature of the capillary used, where only micro-

litres of reagent are consumed by analysis and only nanolitres of sample needed for

analysis, together with the ability for on-line detection down to femtomole (10^15

moles) sensitivity in some cases has for many years made capillary electrophoresis the

method of choice for many biomedical and clinical analyses. Capillary electrophoresis

can be used to separate a wide spectrum of biological molecules including amino

acids, peptides, proteins, DNA fragments (e.g. synthetic oligonucleotides) and nucleic

acids, as well as any number of small organic molecules such as drugs or even metal

ions (see below). The method has also been applied successfully to the problem of

chiral separations (Section 11.5.5).

As the name suggests, capillary electrophoresis involves electrophoresis of samples

in very narrow-bore tubes (typically 50mm internal diameter, 300mm external diam-

eter). One advantage of using capillaries is that they reduce problems resulting from

heating effects. Because of the small diameter of the tubing there is a large surface-to-

volume ratio, which gives enhanced heat dissipation. This helps to eliminate both

convection currents and zone broadening owing to increased diffusion caused by

heating. It is therefore not necessary to include a stabilising medium in the tube and

allows free-flow electrophoresis.

Theoretical considerations of CE generate two important equations:

t¼

L^2

V

ð 10 : 4 Þ

wheretis the migration time for a solute,Lis the tube length,mis the electrophoretic

mobility of the solute, andVis the applied voltage.

The separation efficiency, in terms of the total number of theoretical plates,N,is

given by

N¼V

2 D

ð 10 : 5 Þ

whereDis the solute’s diffusion coefficient.

From these equations it can be seen, first, that the column length plays no role in

separation efficiency, but that it has an important influence on migration time and

hence analysis time, and, secondly, high separation efficiencies are best achieved

through the use of high voltages (mandDare dictated by the solute and are not easily

manipulated).

It therefore appears that the ideal situation is to apply as high a voltage as possible

to as short a capillary as possible. However, there are practical limits to this approach.

As the capillary length is reduced, the amount of heat that must be dissipated

increases owing to the decreasing electrical resistance of the capillary. At the same

time the surface area available for heat dissipation is decreasing. Therefore at some

point a significant thermal effect will occur, placing a practical limit on how short a

tube can be used. Also the higher the voltage that is applied, the greater the current,

and therefore the heat generated. In practical terms a compromise between voltage

used and capillary length is required. Voltages of 1050 kV with capillaries of

50 100 cm are commonly used.

428 Electrophoretic techniques