where q is the charge on the ion and E is the applied electric field, i.e. the greater the charge on an ion the more rapidly it migrates in a particular electric field.

For a spherical ion:

where η is the viscosity of the medium used for electrophoresis, r is the ion radius and ν is the ion velocity.

When the frictional drag and the electric field experienced by the ion are equal:

substituting this expression into Equation 1:

[Equation 2]

If the applied electric field is increased beyond the point where the drag and electric field are equal, the ion will begin to migrate. From Equation 2 it can be seen that:

(i) The greater the charge on the ion, the higher its mobility.

(ii) The smaller the ion, the greater its mobility. Linked to this, since Equation 2 applies to a spherical ion, the more closely an ion approximates to a sphere, i.e. the smaller its surface area, the greater its mobility. This effect is consistent with other types of chromatography.

Thus the mobility of an ion can be influenced by its pKa value – the more it is ionised the greater its mobility – and its molecular shape in solution. Since its degree of ionisation may have a bearing on its shape in solution, it can be seen that the behaviour of analytes in solution has the potential to be complex. For many drugs the manipulation of the pH of the electrophoresis medium should have a marked effect on their relative mobilities. Thus one would predict that the electrophoretic separation of the two bases (morphine and codeine), which are of a similar shape and size but have different pKa values, would increase with pH. If we assume that morphine and codeine possess the same mobilities at full charge, then Figure 14.1 indicates how their mobilities vary with pH. As can be seen in Figure 14.1, the biggest numerical difference in mobility is when the pH = pKa of the weaker base, although the ratio of the mobilities goes on increasing with pH, e.g. at pH 8.9 the ion mobility of codeine is ca two times that of morphine.

Fig. 14.1 Variation of the ionic mobility of morphine and codeine, assuming identical ionic mobilities at full charge, with pH.

Variation of ion mobility with pH is only part of the story with regard to separation by capillary electrophoresis – the other major factor is electro-osmotic flow (EOF).

EOF

The wall of the fused-silica capillary can be viewed as being similar to the surface of silica gel, and at all but very low values the silanol groups on the wall will bear a negative charge. The pKa of the acidic silanol groups ranges from 4.0 to 9.0 and the amount of negative charge on the wall will increase as pH rises. Cations in the running buffer are attracted to the negative charge on the wall, resulting in an increase in positive potential as the wall is approached. The effect of the increased positive potential is that more water molecules are drawn into the region next to the wall (Fig. 14.2). When a potential is applied across the capillary, the cations in solution migrate towards the cathode. The cations in a concentrated layer near to the capillary wall exhibit a relatively high mobility (conductivity) compared to the rest of the running buffer and drag their solvating water molecules with them towards the cathode, creating EOF. The rate of EOF is pH dependent since the negative charge on the silanol groups increases with pH, and between a pH of 3 and 8 the EOF increases about 10 times. The EOF decreases with buffer strength since a larger concentration of anions in the running buffer will reduce the positive potential at the capillary wall and thus reduce the interaction of the water in the buffer with the cations at the wall.

Fig. 14.2 Electro-osmotic flow.

The flow profile obtained from EOF is shown in Figure 14.3 in comparison with the type of laminar flow shown in HPLC. The flat flow profile produces narrower peaks than are obtained in HPLC separations and is a component in the high separation efficiencies obtained in capillary electrophoresis (CE).

Fig. 14.3 Flow profiles obtained in CE and HPLC.

Migration in CE

The existence of EOF means that all species, regardless of charge, will move towards the cathode. In free solution, cations move at a rate determined by their ion mobility + the EOF. Neutral compounds move at the same rate as the EOF and anions move at the rate of the EOF – their ion mobility; the rate of EOF towards the cathode exceeds the rate at which anions move towards the anode, by approximately ten times. A typical separation could be viewed as shown in Figure 14.4. The cations in solution migrate most quickly, with the smaller cations reaching the cathode first; the neutral species move at the same rate as the EOF; and the anions migrate most slowly, with the smallest anions reaching the cathode last. The EOF is useful in that it allows the analysis of all species but it adds complexity to the method in that it needs to be carefully balanced against ion mobility. Table 14.1 shows how EOF can be controlled using different variables and illustrates some of the complexity of CE relative to HPLC.

Fig. 14.4 Migration of ionic and neutral species in CE.

Table 14.1 Variables affecting EOF

Variable	Effects on EOF	Comments
Buffer pH	EOF increases with pH	Most convenient method for controlling EOF but has to be balanced against effects on the charge on the analyte
Buffer strength	EOF decreases with increasing buffer strength	(i)Increased ionic strength means increased electric current flow through the capillary, which can cause heating
		(ii)At low ionic strength more sample absorption onto the capillary walls occurs
		(iii)Low buffer concentrations reduce sample stacking following injection
Electric field	Increased electric field increases EOF	Lowering the applied electric field may reduce separation efficiency and raising the field strength may cause heating
Temperature	Increased temperature decreases viscosity and thus increases flow	Easy to control
Organic modifier	Changes potential at capillary wall – the dielectric constant of the running buffer and the viscosity. Usually decreases EOF	Complex effects – can be useful but best determined experimentally
Surfactant	Absorbs onto the surface of the capillary wall	(i)Cationic surfactants have a high affinity for the silanol groups and thus block access by the smaller cations in solution, reducing EOF. At high concentration they form a double layer, giving the capillary wall an effective positive charge and causing EOF to reverse flow towards the anode
		(ii)Anionic surfactants reduce the access of the smaller ions in the running buffer to the positive potential at the wall thus increasing the zeta potential and thus EOF
Covalent wall coating	Can raise or lower EOF depending on the coating	(i)Neutral coatings reduce negative charge of the capillary wall thus reducing EOF
		(ii)Ionic coatings will have marked effects on EOF