## Theory

The ability to drive a liquid through a packed capillary under the inSuence of an electric Reld was Rrst described by Pretorius in 1974, but a lack of the necessary hardware at the time meant that his suggestion was not followed up. Pretorius showed that the linear velocity of a liquid (u) under electrical flow conditions was given by the equation:

e EC 4ny

where E is the applied electrical field in V cm-1; e is the dielectric constant (dimensionless); C is the zeta potential in volts; and y is the viscosity of the liquid in kg m"1 s"1.

Pretorius estimated from eqn [1] that, with voltages up to 1500 V cm"1, it should be possible to generate linear velocities of 0.1 to 1cms_1, which are similar to those used in modern HPLC. He also noted that eqn [1] is independent of particle diameter, which means that the Sow rate could be maintained in a column packed with very Rne material. When the various contributions to column plate height are summed and plotted against linear velocity, it can be seen that the overall dispersion in an electrically driven system is approximately half that of a corresponding pressure-driven system. This is almost entirely due to a dramatic decrease in the contribution of the eddy diffusion term in the electrically driven system, as illustrated in Figure 1.

The driving force in electrochromatography results from the electrical double layer that exists at any liquid-solid interface. The electrical double layer inside a fused silica capillary Rlled with an electrolyte is shown in Figure 2.

Under alkaline conditions, the surface silanol groups of the fused silica become ionized, leading to a negatively charged surface. This surface will have a layer of positively charged ions in close proximity that is relatively immobile. This surface layer of ions is called the Stern layer. The remainder of the excess charge, constituting the Goiiy layer, is solvated and has the characteristics of a typical solvated ion. This layer extends into the bulk of the liquid and is the so-called double layer. The concentration of ions in the double layer is relatively small compared to the total ion concentration and falls off exponentially from the capillary surface, as does the electrical potential, which is proportional to the charge density. The potential at the boundary between the Stern layer and the diffused Goiiy double layer is known as the zeta potential, C, and ranges from 0 to 100 mV. As the charge density drops off with distance from the surface, so does the zeta potential. The distance from the immobile layer to a point in the bulk liquid at which the potential is 0.37 of that at the interface between the Stern layer and the diffuse layer is deRned as the thickness of the double layer, denoted by §. The u

Figure 1 Contributions to plate height in (A) a pressure-driven system (HPLC) and (B) an electrically driven system (electro-chromatography). HETP, height equivalent to one theoretical plate. (Reprinted from Dittmann MM and Rozing GP (1996) Capillary electrochromatography - a high efficiency micro-separation technique. Journal of Chromatography A 744: 63-74 with kind permission from Elsevier-NL.)

Figure 2 Electrical double layer. Origin of electroosmotic flow (EOF) in a fused silica capillary. (By permission of the author.)

Figure 1 Contributions to plate height in (A) a pressure-driven system (HPLC) and (B) an electrically driven system (electro-chromatography). HETP, height equivalent to one theoretical plate. (Reprinted from Dittmann MM and Rozing GP (1996) Capillary electrochromatography - a high efficiency micro-separation technique. Journal of Chromatography A 744: 63-74 with kind permission from Elsevier-NL.)

equation describing 5 is as follows:

gr£oRT1/2

where sr is the dielectric constant or relative permittivity of the medium; s0 is the permittivity of a vacuum (8.85 x 10"12 C2 N"1 m2); R is the gas constant (8.314 J K"1 mol"1); T is the temperature in Kelvin; c is the molar concentration of the electrolyte; and F is the Faraday constant (96 500 C mol"1).

Using the above equation with water (sr = 80), the thickness of the electrical double layer for a 1:1 electrolyte at a concentration of 0.001 mol L"1 in water would be 10 nm, while at a concentration of 0.01 mol L" 1 it would be 1 nm.

Electroosmotic flow (EOF) in a capillary arises when an electric filed is applied tangentially along the length of the column. This causes the ions in the diffuse (Goiiy) layer that are not absorbed into the Stern layer to migrate towards the cathode. Shearing will occur within this region and electroosmosis will result because the core of liquid within this sheath

Figure 2 Electrical double layer. Origin of electroosmotic flow (EOF) in a fused silica capillary. (By permission of the author.)

will also be transported to the cathode. Because shearing only occurs within the diffuse layer, the resulting flow profile is plug-like and its velocity is independent of the capillary diameter (d), provided that d > 105 (d is usually > 205).

If d approaches 5, then double layer overlap will occur and the elctroosmotic flow will be considerably reduced, taking on a parabolic profile. In the case of packed capillaries, the capillary diameter is replaced in the equation by the mean channel diameter. Thus for aqueous electrolytes between 0.001 mol L" 1 and 0.01 mol L" 1 there would be no double layer overlap as long as dp > 405.

If we assume a value of 10 nm for 5 in a 0.001 mol L"1 aqueous solution, then dp = 0.4 |im and use of these small-diameter particles should give a dramatic increase in column efficiency. Since typical silica-based reversed-phase packing materials also contain silanol groups, these also contribute to the overall EOF, as illustrated in Figure 3.

Another important consideration in CEC is the relationship between the linear velocity and concentration of the electrolyte. Since u is directly propor-

tional to the zeta potential, which itself decreases with increasing electrolyte concentration, it is an important variable to consider during method development. The effect of electrolyte concentration on the zeta potential has been measured using 5 |m Hypersil ODS. The results showed that 10"4 mol L"1 NaNOa had a zeta potential of ~50mV, while at 10"3molL_1 the potential was ~45mV and at 10"2 mol L"1 it was ~ 25 mV. When plate height and linear velocity were plotted against NaH2PO4 concentration, the reduced plate height was lowest at 10"3molL_1 and the linear velocity altered little over the range 4 x 10"5 mol L"1 to 2 x 10"2 mol L"1. The best overall performance, i.e. the lowest values of plate height (H), at high EOF would be achieved at electrolyte concentrations of c. 0.002 mol L"1.

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