Capillary electrophoresis

Put 25 kV across a fused-silica capillary 50 μm wide and the ions in the solution race towards the electrodes, each at its own speed. Within minutes ions of remarkably similar properties separate, with hundreds of thousands of theoretical plates: this is capillary electrophoresis. Arrays of capillaries sequenced DNA in the later years of the Human Genome Project; analytical labs use them for ions in drinking water, drug enantiomers and proteins. There is no stationary phase — separation rests entirely on each ion’s mobility in the field.

An ion in a field E drifts at v = μE; the proportionality constant μ is its electrophoretic mobility. Conductivity measures the same thing — how fast a mole of charge moves in unit field — so the limiting ionic conductivity λ° (per equivalent) from the conductometry lesson divided by the Faraday constant is the mobility. The same table gives diffusion coefficients too: the Nernst–Einstein relation ties mobility to diffusion, because the friction that sets how fast an ion migrates also sets how fast it diffuses.

Silanol groups on the silica wall ionise to $\ce{SiO-}$ above pH 3 and hold a layer of cations against the wall. With the voltage on, that layer moves towards the cathode and drags the whole column of solution with it: electro-osmotic flow. It pushes the liquid like a piston, with nearly the same speed across the bore — not fast in the middle and slow at the wall as in pressure-driven liquid chromatography — so the flow itself does not broaden the zones. The flow is usually faster than the electrophoresis of most ions, so cations, neutral molecules and slow anions are all carried to a detector near the cathode end; fast inorganic anions need a cationic surfactant to reverse the wall charge, and a reversed voltage. For a wall zeta potential of −50 mV the electro-osmotic mobility is $\mu_\text{eo} = -\varepsilon\zeta/\eta \approx 3.9\times10^{-4}\ \text{cm}^2\,\text{V}^{-1}\,\text{s}^{-1}$.