Thus, more theoretical plates will be required to resolve the enantiomers and thus a longer column will be necessary. At a temperature of 5˚C and at an ethanol concentration of 5%v/v, the column need only be about 5 mm long(a length of column that is impractical to pack and operate). Contemporary columns, shorter that 2 cm are extremely difficult to operate efficiently.     Figure 24 The Minimum Column Length that will Produce the Required Efficiency The minimum column length that will provide the minimum analysis time for this particular separation is not in the practical range of column lengths normally available. Consequently, the optimum column length must be a compromise between, that which is theoretically desirable, and that which is practically possible, and thus the shortest column available would be chosen.    

The Effect of Temperature and Solvent Composition on the Minimum Variance/Unit  Column Length (Hmin) Taking the values for the capacity ratios and separation ratios derived from equations (47), (48) and (49) in equation (40) the manner in which (Hmin) changes with temperature and solvent composition can be identified. The minimum variance per unit length of the column is solely a function of the capacity factor of the solute, the particle diameter and the packing factors (see Book 9). Thus, the influence of temperature and solvent composition on (Hmin) can only result from the effect of these variables on the magnitude of (k'). Curves relating (Hmin) to temperature for different solvent compositions are shown in figure 23. The magnitude of (Hmin) is seen to be strongly dependent on the solvent composition. At 50˚C by decreasing

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')

the column length divided by the number of theoretical plates in the column) has, for obvious reasons, become termed the Height Equivalent to the Theoretical Plate (HETP) and has been given the symbol (H). However, it is seen that (H) is numerically equal to, , which is, in fact, the variance per unit length of the column. Thus, the function, , is the variance that the Rate Theory will provide an explicit equation to define and can be experimentally calculated for any column from its length and column efficiency. It follows that the equations that give a value for, (H), the variance per unit length of the column, have been termed HETP equations

. The equation for the variance per unit length of a capillary column was developed by Golay (1) and the equation he derived took the following form,     (1)   Where (H) is the variance per unit length of the column , (k)' is the capacity factor of the solute, (DM) is the diffusivity of the solute in the mobile phase, (DS) is the diffusivity of the solute in the stationary phase, (r) is the radius of the column, and (u) is the average linear velocity of the mobile phase.   In the development of equation (1), Golay did not take into account that, due to the compressibility of the mobile phase (a gas), the linear velocity changed significantly along the length of the column. Due to the velocity change not being linear the average velocity can not be used in equation (1) to accurately described (H) (the variance of the dispersion that takes pace in the column

matter. Sometimes it is inevitable that the detector sensor must be a significant distance from the column exit and, thus, a relatively long length of connecting tube will be necessary. Under these conditions, low dispersion tubing, such as serpentine tubing, may be the solution. Dispersion in the detector sensor is the second largest source of extra-column dispersion and can only be reduced to a satisfactory level by reducing the volume of the sensor cell to 2 ml or less. Reducing the cell length will reduce its response but maintain the same or similar noise level, thus, reducing the sensitivity (minimum detectable concentration). Maintaining the same length, but reducing the cell radius, will maintain the same response, but increase the noise level, also reducing the overall sensitivity. It is clear a compromise is necessary and this compromise will depend on the type of detector, UV absorption, fluorescence, etc., that is employed. Nevertheless, to realize the maximum column