Pairs, critical

Equation (22) allows the maximum sample volume that can be used without seriously denigrating the performance of the column to be calculated from the retention volume of the solute and the column efficiency. In any separation, there will be one pair of solutes that are eluted closest together (which, as will be seen in Part 3 of this book, is defined as the critical pair) and it is the retention volume of the first of these that is usually employed in equation (22) to calculate the maximum acceptable sample volume. 

The second and third peaks will be the pair of peaks in the mixture that are eluted closest together and, thus, the most difficult to separate (usually given the term the critical pair as they define the severity of the separation). Finally, the fourth peak will be that which is eluted last from the mixture and will determine when the analysis is complete and establishes the total analysis time. The chromatographic system must be designed to separate the critical pair and, as this is the pair that is eluted closest together, all other peaks should also be resolved... 

However, any given column operated at a specific flow rate will exhibit a range of efficiencies depending on the nature and capacity ratio of the solute that is chosen for efficiency measurement. Consequently, under exceptional circumstances, the predicted conditions for the separation of the critical pair may not be suitable for another pair, and the complete resolution of all solutes may still not be obtained. 

This could occur if the separation ratio of another solute pair, although larger, was very close to that of the critical pair but contained solutes, for example, of widely different molecular weight (and, consequently, very different diffusivities). Fortunately, the possibility of this situation arising is remote in practice, and will not be considered in this discussion. It follows that the efficiency required to separate the critical pair, numerically defined, is the first performance criterion. 

The choice of variables remaining with the operator, as stated before, is restricted and is usually confined to the selection of the phase system. Preliminary experiments must be carried out to identify the best phase system to be used for the particular analysis under consideration. The best phase system will be that which provides the greatest separation ratio for the critical pair of solutes and, at the same time, ensures a minimum value for the capacity factor of the last eluted solute. Unfortunately, at this time, theories that predict the optimum solvent system that will effect a particular separation are largely empirical and those that are available can be very approximate, to say the least. Nevertheless, there are commercially available experimental routines that help in the selection of the best phase system for LC analyses, the results from which can be evaluated by supporting computer software. The program may then suggest further routines based on the initial results and, by an iterative procedure, eventually provides an optimum phase system as defined by the computer software. 

The capacity ratio of the first solute of the critical pair. 

The separation of the critical pair would require a minimum column efficiency and, so, the number of theoretical plated produced by the column must be reported. The... 

Column design involves the application of a number of specific equations (most of which have been previously derived and/or discussed) to determine the column parameters and operating conditions that will provide the analytical specifications necessary to achieve a specific separation. The characteristics of the separation will be defined by the reduced chromatogram of the particular sample of interest. First, it is necessary to calculate the efficiency required to separate the critical pair of the reduced chromatogram of the sample. This requires a knowledge of the capacity ratio of the first eluted peak of the critical pair and their separation ratio. Employing the Purnell equation (chapter 6, equation (16)). 

Starting with the same basic equation of Purnell (chapter 6) which is applicable to all forms of chromatography, and allows the number of theoretical plates required to separate the critical pair of solutes to be calculated. 

Capacity Ratio (first eluted peak of the Critical Pair) (k ) Capacity Ratio (first eluted peak of the Critical Pair) (k") Viscosity of the Mobile Phase (r])... 

Figure 2. Curve Relating Optimum Particle Diameter to the Separation Ratio of the Critical Pair...

Table 1, values for the optimum velocity can be calculated for different values of the separation ratio of the critical pair. The results are shown in Figure 3. 

The column length will actually increase as (l/(a-l)3). This means that the column length is extremely sensitive to the separation ratio of the critical pair and explains... 

Taking a value for (oe) of 2.5 pi (which would be typical for a well-designed column detector system) and using equation (8), values for (ropt) are shown plotted against separation ratio in Figure 7. It is seen that the optimum column radius increases linearly with the separation ratio of the critical pair (ranging from 0.1 mm... 

Capacity Ratio (first eluted peak of the Critical Pair) (k ) 2.5... 

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