The Separation Ratio

The capacity ratio of a solute, (k ), was introduced to develop a chromatographic measurement, simple to calculate, independent of flow-rate and one that could be used in solute identification. Although helpful, the capacity ratio is so dependent on the accurate measurement of extra column volume and on very limited solute exclusion by the support and stationary phase, that it is less than ideal for solute identification. An alternative measurement, the separation ratio (a) was suggested where, for two solutes (A) and (B), 

It is seen that the separation ratio is independent of all column parameters and depends only on the nature of the two phases and the temperature. Thus providing th sam phase system is used on two columns, and the solutes are chromatographed at the same temperature, then the two solutes will have the same separation ratio on both columns, The separation ratio will be independents the phase ratios of the two columns and the flow-rates. It follows, that the separation ratio of a solute can be used reliably as a means of solute identification.  

A standard substance is often added to a mixture and the separation ratio of the substance of interest to the standard is used for identification. In practice the separation ratio is taken as the ratio of the distances in centimeters between the dead point and the maximum of each peak. If computer data processing is being employed replace distances by corresponding times. 

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It is clear that the separation ratio is simply the ratio of the distribution coefficients of the two solutes, which only depend on the operating temperature and the nature of the two phases. More importantly, they are independent of the mobile phase flow rate and the phase ratio of the column. This means, for example, that the same separation ratios will be obtained for two solutes chromatographed on either a packed column or a capillary column, providing the temperature is the same and the same phase system is employed. This does, however, assume that there are no exclusion effects from the support or stationary phase. If the support or stationary phase is porous, as, for example, silica gel or silica gel based materials, and a pair of solutes differ in size, then the stationary phase available to one solute may not be available to the other. In which case, unless both stationary phases have exactly the same pore distribution, if separated on another column, the separation ratios may not be the same, even if the same phase system and temperature are employed. This will become more evident when the measurement of dead volume is discussed and the importance of pore distribution is considered. 

This equation allows the temperature to be calculated at which the separation ratio between the solutes would be (a). From the preceding equation, in addition. 

Thus, the separation ratio that will be obtained for the solute pair can be calculated for any temperature. The results of Heng Liang Jin not only confirm the existence of a... 

Figure 22. A 3-D Set of Curves Relating the Separation Ratio of the Two Enantiomers of 4-Phenyl-2-oxazolidinone to the Composition of a Ternary Solvent Mixture...

Although it is often possible to predict the effect of the solvent on retention, due to the unique interactive character of both the solvents and the enantiomers, it is virtually impossible to predict the subtle differences that control the separation ratio from present knowledge. Nevertheless, some accurate retention data, taken at different solvent compositions, can allow the retention and separation ratios to be calculated over a wide range of concentrations using the procedure outlined above. From such data the phase system and the column can be optimized to provide the separation in the minimum time, a subject that will be discussed later in the treatment of chromatography theory. 

It is seen that at about 45 °C the separation ratio appears to be independent of the solvent composition. This remarkable relationship can be examined theoretically. 

Consequently, if or when a g/ w2-) = — = —, then the separation ratio will be independent of the composition of the solvent mixture. 

Thus, from equation (19) the condition for the independence of the separation ratio from the solvent composition will be when... 

It is seen from equation (22) that there will, indeed, be a temperature at which the separation ratio of the two solutes will be independent of the solvent composition. The temperature is determined by the relative values of the standard free enthalpies of the two solutes between each solvent and the stationary phase, together with their standard free entropies. If the separation ratio is very large, there will be a considerable difference between the respective standard enthalpies and entropies of the two solutes. As a consequence, the temperature at which the separation ratio becomes independent of solvent composition may well be outside the practical chromatography range. However, if the solutes are similar in nature and are eluted with relatively small separation ratios (for example in the separation of enantiomers) then the standard enthalpies and entropies will be comparable, and the temperature/solvent-composition independence is likely be in a range that can be experimentally observed. 

It is seen that the curves in Figure (24) become horizontal between 40°C and 45 °C as predicted by the theory. It is also clear that there is likely source of error when exploring the effect of solvent composition on retention and selectivity. It would be important when evaluating the effect of solvent composition on selectivity to do so over a range of temperatures. This would ensure that the true effect of solvent composition on selectivity was accurately disclosed. If the evaluation were carried out at or close to the temperature where the separation ratio remains constant and independent of solvent composition, the potential advantages that could be gained from an optimized solvent mixture would never be realized. 

In addition, if the program is run for the second enantiomer, then the ratio of the retention times of the two isomers can be calculated (the separation ratio) for a range of different solvent program rates. 

Figure 11. Graph of the Separation Ratio of the Two Enantiomers against Program Rate...

It is seen that the separation ratio must be greater than about 1.055 for a low efficiency column (2500 theoretical plates) before accurate retention measurements can be made on the composite curve. On the high efficiency columns (10,000 theoretical plates), the separation ratio need only be in excess of about 1.035 before accurate retention measurements can be made on the composite curve. It will be seen later in this chapter that to optimize a column for a difficult separation, accurate retention data must be obtained over a range of temperatures and solvent compositions. It follows that ... 

Equation (5) was examined by Scott and Reese [1] employing mixtures of nitrobenzene and fully deuterated nitrobenzene as the test sample. Their retention times were 8.927 min. and 9.061 min., respectively, giving a difference of 8.04 seconds. The separation ratio of the two solutes was 1.023 and the efficiencies of the front and rear portions of the peaks were 5908 and 3670 theoretical plates, respectively. The detector was, not surprisingly, found to have the same response to both solutes, i.e., a = (3. Thus, inserting these values in equation (5),... 

Now (a), the separation ratio between the two solutes, has been defined... 

Figure 14, shows curves relating (n) and (k A) for a range of solute pairs having separation ratios of 1.02, 1.03, 1.05 and 1.07 calculated using equation (16). It is seen that as the separation becomes more difficult (i.e., the separation ratio (aA/e)... 

As a secondary consideration, the chromatographer may also need to know the minimum value of the separation ratio (a) for a solute pair that can be resolved by a particular column. The minimum value of (a) has also been suggested [8] as an alternative parameter that can be used to compare the performance of different columns. There is, however, a disadvantage to this type of criteria, due to the fact that the value of (a) becomes less as the resolving power of the column becomes greater. Nevertheless, a knowledge of the minimum value of (cxa/b) can be important in practice, and it is of interest to determine how the minimum value of (aA/B) is related to the effective plate number. 

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. 

It is seen from equation (46) that, as would be expected, the maximum sample volume decreases as the separation ratio decreases, i.e., with difficulty of the separation. 

Equation (13) is the first important equation for open tubular column design. It is seen that the optimum radius, with which the column will operate at the optimum velocity for the given inlet pressure, increases rapidly as an inverse function of the separation ratio (cc-1) and inversely as the square root of the inlet pressure. Again it must be remembered that, when calculating (ropt)5 the dimensions of the applied pressure (P) must be appropriate for the dimensions in which the viscosity (r)) is measured. 

It is clear that the major factor controlling the particle diameter will be the separation ratio (a), which reflects the difficulty of the separation. The more... 

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. 

It must be emphasized that equation (4) only applies to the separation and conditions defined in Table 1. The effect of the magnitude of the separation ratio on the minimum plate height is shown in Figure 4. 

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... 

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