The Reduced Chromatogram

Any chromatogram that represents the separation of a complex mixture of solutes can be reduced to a relatively simple separation that will concisely and accurately represent the limits and extent of the separation problem. The simple separation can be depicted in the form of a reduced chromatogram, an example of which is given in figure (2). 

The reduced chromatogram consists of four peaks, the first the dead volume peak, (which has been shown previously must be the fully excluded peak determined from the retention volume of a salt or solute of large molecular 

However, it should be pointed out that any given column, operated at a specific flow rate, can exhibit a range of efficiencies depending on the nature 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 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 contains solutes, for example, of widely different molecular weight. However, the possibility of this situation arising, in practice, is extremely remote 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 efficient laboratory manager will also require the maximum throughput of samples from the equipment and thus, the second criterion is that the analysis must be achieved in the minimum time. It should be pointed out 

Another aspect of cost reduction would be the need to employ the minimum amount of solvent per analysis and this would be the third performance criteria. Finally, to conserve sample and to have the capability of determining trace contaminants, the fourth criterion would be that the the combination of column and detector should provide the maximum possible mass sensitivity. The performance criteria can therefore be summarized as follows, 

A satisfactory chromatographic analysis demands, a priori, on an adequate separation of the constituents of the sample that will permit the accurate quantitative evaluation of each component of interest. To achieve this, an appropriate phase system must be chosen so that the individual components of the mixture will be moved apart from one another in the column. In addition, their dispersion must be constrained sufficiently to allow all the solutes of interest to be eluted discretely. At this stage it is necessary to introduce the concept of the Reduced Chromatogram. 

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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. 

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The selection of the mobile phase and the conditions of development. Having chosen the solvent(s) the following are defined from the reduced chromatogram,... 

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)). 

The chromatographic challenge associated with a particular sample can be summarized by the reduced chromatogram. The reduced chromatogram consists of three peaks and is represented in figure 6. 

All samples can be reduced to such a chromatogram and if the reduced chromatogram can be resolved then, almost without exception, so can the sample. In the following discussion it is assumed that all the components of the mixture have equal importance and must be isolated and quantitatively estimated. The analyst will, at times, be presented with samples for which a full analysis is not required and such samples will be discussed subsequently. 

The time that the last peak is eluted in the reduced chromatogram represents the total analysis time after which, the analysis can be terminated. The two peaks that are eluted closest together are the most difficult to separate and which, for obvious reasons, are called the "critical pair". 

The columns must be designed or chosen such that the critical pair are separated and, as a second priority, the last peak must be eluted in a reasonable time. The first peak in the chromatogram is not considered part of the reduced chromatogram and is included as the dead volume marker from which the capacity factors of each solute can be calculated, together with the separation ratio of the critical pair. 

The above columns were calculated for a sample where the first peak of the critical pair in the reduced chromatogram was eluted at a (k ) of 2.5 and the last peak was eluted at a (k ) of 5.0. The method of calculation is given in (1). 

It is seen that, although the dimensions and particle sizes may not be precisely matched, all three columns are of a size closely similar to those commercially available with, perhaps, the exception of the long high efficiency column. The small 3 cm column is excellent for the preliminary assessment of a sample. As a result of its size it does not use large volumes of solvent and can be quickly reconditioned after a separation in readiness for the next run. It is very convenient for choosing the best phase system in method development. The other columns would be chosen on a basis of the efficiency required to separate the critical pair in the reduced chromatogram of the sample for analysis. 

Figure (6) allows the solvent consumption of any analysis to be compared with which would be obtained from a fully optimized column. The data used is obtained from the reduced chromatogram and the extra column dispersion of the respective apparatus. It should be bourne in mind that the extra column dispersion assumed in the above calculations was equivalent to a standard deviation of 2.5 microlitres. This value for (oe) could be expected from a well designed chromatographic system. 

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