# Capillary Chromatography - The Optimum Velocity

### The Optimum Velocity

It is seen from equation (8) that the optimum velocity is directly proportional to the diffusivity of the solute in the mobile phase (gas) and inversely proportional to the column radius (r). Consequently, for fast separations and short analysis times, hydrogen or helium should be used as the mobile phase (carrier gas) to provide the highest diffusivity. In practice, however, due to perceived fire hazards, hydrogen is not often used unless the FID detector is employed which preempts the use of hydrogen anyway.

**Figure 18. Graph of Function of (k') that Determines the Magnitude of the Optimum Velocity and Capacity Ratio**

The optimum mobile phase velocity being inversely proportional to the column radius suggests the use of the smallest possible column for fast separations. However, there is a limit to which the radius can be reduced due to coating difficulties and, more important, sampling difficulties. It can be very difficult to introduce a *representative* sample into columns of very small radii. Columns 100 mm in diameter appear to be, in general the smallest diameter that is practical although column 50 mm in diameter are available and can be used effectively under certain circumstances. It is also seen from equation (8) that the optimum velocity is a function of the capacity ratios (k') of the solutes separated. A graph relating the function of (k') that determines the magnitude of the optimum velocity and the capacity ratio is shown in figure 18.

It is seen that the highest optimum velocities are realized for solutes eluted close to the column dead volume so that for very fast separations the stationary phase should be chosen to elute the solutes below a capacity ratio of 2. However, the curve flattens at a (k') value of about 4, and subsequently the optimum velocity remain constant and is virtually independent of the capacity ratio of the eluted solute