# Capillary Chromatography - The Minimum Variance/Unit Length of the Column

### The Minimum Variance/Unit Length of the Column

The minimum value of (H) is given by equation (9) and it is seen that it is directly proportional to the column radius and a function of the capacity ratio of the solute but, unlike the optimum velocity (H(min.)) is independent of the solute diffusivity. A graph relating the function of the capacity ratio (k') that controls the magnitude of (H(min.)) to the actual value of (k') is shown in figure 19.

(H(min.)) increases as the capacity ratio becomes greater, leveling out to a constant value at a (k') value of about 7. This means that the column efficiency will decrease as the value of (k') increases tending to a constant efficiency at high values of (k'). This means that efficiency decreases along the chromatogram till eventually all late eluting peaks have the same or very similar efficiencies. However, this does not mean, necessarily, that the resolution will decrease with increasing (k') values (see book 9 of this series). As the resolution equation or Purnell (11) shows, more theoretical plates are necessary at low (k') values to achieve a given resolution than those required at high (k') values.

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It is seen that, as a result of the expression containing (k'), the value of Equations (8) and (9) and the curves shown in figures 18 and 19 demonstrate the general conclusion that smaller diameter columns give higher efficiencies and faster separations. However, this also assumes that there is adequate inlet pressure available to provide the necessary exit velocity, and that the apparatus is designed to cope safely with that pressure. In addition, faster separations are obtained using gasses that provide higher solute diffusivities.