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nbsp;     The Effect of Temperature and Solvent Composition on the Required Column Efficiency Using the values for the capacity ratios and separation ratios derived from equations (47), (48) and (49) in equation (39) the efficiency necessary to ensure a separation of (6s) for the two enantiomers can be calculated over a range of temperatures and solvent compositions. Figure 22. Graphs of Required Efficiency against Temperature for Each Solvent Composition Curves relating required efficiency against temperature for each solvent composition, calculated in this manner, are shown in figure 22. As would be expected, the minimum efficiency is required at the lowest temperature and lowest ethanol concentration. As either the separation ratio and/or the capacity ratios decrease, the necessary efficiency to achieve a separation increases (as predicted by equation (39)). At one extreme

.02, an efficiency of 360,000 theoretical would be required if the (k') value was 0.5. GC Capillary columns can provide such efficiencies but, in LC, such efficiencies would be extremely difficult and costly to produce. It follows that the phase system should be chosen so that the closest eluted solutes are not eluted at low (k') values. Less efficiency will be needed and, thus, shorter columns and consequently, shorter analysis times will be achieved. At (k') values that exceed 10, the requiredefficiency changes little as the capacity ratio increases. Thus, for fast analyses, the phase system provide a large separation ratio, but the first peak should elute at a (k') of 10 or more. The phase system should have high selectivity and retentive capacity so that minimum efficiency is required and the column can be as short as possible. 

column design. It is clear that increasing radius and length of the column increases both the maximum sample volume and the maximum sample mass. It is also seen that increasing the column length will also increase the column efficiency (unless it is accompanied by an corresponding increase in the particle diameter). However, increasing the column efficiency will have the opposite effect, as seen by equation (1), it will reduce the maximum sample load. Consequently, if the necessary efficiency to achieve the required separation has been obtained, then if the column is lengthened to increase the loading capacity for optimum performance, either the flow rate will need to be increased to reduce the efficiency and thus maintain the maximum loading, or the particle size will need to be increased to reduce the efficiency to its required value. However, an increased flow rate will also reduce separation time and thus increase sample throughput. Conversely, the alternative use of

5 m. The mobile phase consisted of 26.5% v/v of methanol, 16.5%v/v acetonitrile and 57.05v/v of  0.1M ammonium acetate adjusted to a pH of 6.0 with glacial acetic acid and the flow-rate was 2 ml/min. The column efficiency available at the optimum velocity would be about  15,000 theoretical plates. The retention time of the last peak is about 12 minutes (i.e., a retention volume of 24 ml). At a flow rate of 2 ml/min., the mobile phase velocity will be well above the optimum and so the maximum efficiency has not been realized. The general technique used when there are more theoretical plates available than required is to increase the flow rate until the separation required is just realized. This procedure trades efficiency for time and allows the separation to be achieved in the minimum time given the column and phase system that has been chosen

product of the required efficiency (figure 22) and (Hmin) (figure 23) which is shown for different temperatures and solvent compositions in figure 24. The dependence of the minimum theoretical plates on temperature and solvent composition dominates the magnitude of the product and, thus, the curves in figure 24 take a form similar to those in figure 22. The higher the temperature and the stronger the ethanol concentration, the smaller the magnitude of (k'). 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

' for the solute to achieve equilibrium at that point in the column and the process of distribution could be considered as incremental. This approach has been discussed in Plate Theory and Extensions . Employing this concept an equation for the elution curve can be easily obtained and, from that basic equation, others  can be developed that describe the various properties of a chromatogram. Such equations have permitted the calculation of efficiency, the number of theoretical plates required to achieve a specific separation and among many applications, elucidate the function of the heat of absorption detector. The Plate Theory, however, does little to explain how the efficiency of a column may be changed or, what causes peak dispersion in a column in the first place. It does not tell us how dispersion is related to column geometry, properties of the packing, mobile phase flow-rate, or the physical properties of the distribution system. Nevertheless, it was not so much