Iso-eluotropic mixtures

Acetonitrile shows in mixtnres with water, a better solnbility for salts. It is therefore recommended in ion-pair chromatography [52], Basic analytes also show better peak shapes in acetonitrile-buffer mixtures than with methanol. The proper selection, whether acetonitrile or methanol, should be used as the organic component in the mixtnre with a bnffer, however, the type of RP column used classical RP or a shielded RP column is also important. For demonstration with basic analytes, a standard mixture of anti depressives is used. Iso-eluotropic mixtures of methanol and acetonitrile are used. For standardization, the concentration of buffer components are also be kept constant. The analyte structures and the eluent mixtures are summarized in Table 2.2. As selectivity is worse in acidic eluents, a pH value of 7 has been used. Two phases... 

Within the framework of the given polarity of a phase, its composition may still be varied for optimization purposes (see the discussion about iso-eluotropic mixtures in section 3.2.2). However, the mutual solubility of the two phases is not only determined by their polarity, so that changes need to be considered carefully. In conventional LLC systems, changes to the stationary phase are hard to make, because they may require a lengthy re-coating procedure. 

To a first approximation (eqn.3.29) we may expect mixtures of the same polarity to yield the same capacity factors. In other words, mixtures with the same solubility parameters are expected to have the same eluotropic strength, and therefore they might be called iso-eluotropic mixtures. If we use THF (T) instead of methanol in a binary mixture with water, the following equation relates two iso-eluotropic mixtures... 

Due to specific effects, the corresponding compositions of methanol and THF will not be exactly the same for all solutes. Conversely, when the iso-eluotropic composition is taken as the average of that observed for many solutes (or from solubility parameter theory), some solutes will be eluted later than with the original methanol/water mixture, and some will be eluted earlier. The relative differences may amount to a factor of two for certain solutes. This should not be seen as an error in establishing iso-eluotropic mixtures. Rather, it enables us to exploit iso-eluotropic mixtures to enhance selectivity, whilst keeping retention roughly constant. This principle is widely used for the optimization of selectivity in LC. 

We can easily extend the above treatment to iso-eluotropic mixtures that contain more than one modifier. Let us rewrite eqn.(3.51) in a simplified form... 

According to the simple solubility parameter model any mixture of two iso-eluotropic mixtures (same value for 5) would yield a mixture that is iso-eluotropic to the original two (eqn.3.34). It then follows from eqn.(3.52) that for any ternary mixture of two iso-eluotropic binaries the following equation holds... 

Eqns.(3.54) and (3.55) are very convenient for the definition of iso-eluotropic mixtures and for the calculation of the eluotropic strength of multicomponent mobile phases, in terms of a corresponding binary methanol/water mixture. 

The solubility parameter model appears to work very well for the prediction of iso-eluotropic mixtures in LLC and RPLC. However, in LSC the retention mechanism is very different from the one that was assumed at the outset of this section, and hence a different model should be applied to allow the description and possibly prediction of the eluotropic strength in LSC. This model will be described in section 3.2.3. 

The vertical dashed line illustrates how a series of iso-eluotropic mixtures can be located. Mixtures of about 75% methylene chloride in n-hexane, 49% diethyl ether in n-hexane, 50% methylene chloride in 2-chloropropane, 46% diethyl ether in n-hexane, 1.5% acetonitrile in 2-chloropropane and 0.1% methanol in 2-chloropropane all show similar solvent strengths (e° = 0.30). 

As in RPLC, these iso-eluotropic mixtures are expected to yield similar capacity factors, but may give rise to certain specific effects towards certain (types of) solutes, which may be exploited to enhance separation. 

Eqn.(3.73) suggests that any mixture of two solvents with the same ° value (iso-eluotro-pic solvents) will also have the same eluotropic strength. This would allow the application of a similar strategy for the definition of iso-eluotropic multicomponent mobile phase mixtures as was used for RPLC in section 3.2.2.1. In practice, the situation in LSC has proved to be more complicated, because an effect described as solvent localization limits the validity of eqns.(3.72) and (3.73) if polar components (such as acetonitrile or methyl t-butyl ether) are present in the mobile phase. This makes it difficult to calculate the composition of iso-eluotropic mixtures for LSC with sufficient accuracy for optimization purposes [360-363]. 

Table 3.10d lists the parameters for LSC. Again, most separations may be optimized by optimizing the eluotropic strength (primary parameter) and the nature (secondary parameter) of the mobile phase. The latter parameter involves the preparation of different iso-eluotropic mixtures containing different solvents, or small quantities of very polar components ( modulators ). As in the case of RPLC, there are several additional parameters that are not frequently exploited. 

If we limit ourselves to iso-eluotropic mixtures, a one-parameter optimization problem remains. As was described in section 3.2.2, a binary mixture of 60% methanol and 40% water corresponds approximately to 48% acetonitrile in water or 37% THF in water. We may proceed with the optimization procedure by considering these binary mixtures as pure solvents (e.g. solvent A equals 60/40 methanol/water) and refer to them as pseudosolvents [537] or pseudocomponents [538]. 

Of course, the simultaneous optimization of different (primary) program parameters (initial and final composition, slope and shape of the gradient) and secondary parameters (nature and relative concentration of modifiers) may involve too many parameters, so that an excessive number of experiments will be required to locate the optimum. This problem may be solved by a separate optimization of the program (primary parameters) and the selectivity (secondary parameters) based on the concept of iso-eluotropic mixtures (see section 3.2.2). This will be demonstrated below (section 6.3.2.2). However, the transfer of... 

Fig. 4.4.1S. Chromatograms illustrating the variations in selectivity obtained by eluting with some iso-eluotropic mixtures of methanol, tetrahydrofuran and water. Reprinted from Ref. 27 with permission.

These very simple relationships can be verified experimentally as is shown in figure 3.16. The iso-eluotropic compositions of binary mixtures of THF and acetonitrile with water have been plotted against the binary methanol-water composition. The thin straight lines indicate the theoretical relationships from solubility parameter theory (eqns. 3.50 and 3.51). The thick lines correspond to average experimental data over large numbers of solutes [335]. An (average) experimental data point can be found as follows. 

Figure 3.16 Iso-eluotropic compositions for binary mixtures of THF and acetonitrile in water, relative to methanol/water mixtures. The solid lines represent the average experimental compositions for a large number of solutes. The thin lines represent calculated compositions from solubility parameter theory (eqns.3.50 and 3.51). Figure taken from ref. [311]. Reprinted with permission.

It follows from eqn.(3.54) that iso-eluotropic ternary mixtures fall on a straight line in a figure where the two variables three-dimensional space, and so on. 

Of the many different iso-eluotropic solvent mixtures, not all are equally attractive from... 

Figure 3.20 Nomogram illustrating the solvent strength of various binary solvent mixtures for LSC. Vertical (dashed) line illustrates a series of iso-eluotropic solvents (see text). Figure taken from ref. [358]. Reprinted with permission.

In practice, as a first approximation, it may be assumed that mixtures of iso-eluotropic solvents can be used. If the resulting solvent strength is either too high or two low, it may be corrected by the addition of more or less n-hexane. 

The latter was also the case for the optimization of the composition of a ternary mobile phase in RPLC by Issaq et al. [554]. The ternary mixture was formed by mixing two limiting (non iso-eluotropic) binary mixtures and a fourth order polynomial equation was fitted through five equally spaced data points. 

The points on the sides of the triangle (A, B, and C) represent three iso-eluotropic binary mixtures (solvents A, B and C). The composition of one of the three binary mixtures (i.e. the appropriate eluotropic strength) should be determined by either a scanning gradient or a stepwise series of isocratic scans (see section 5.4). Once one of the compositions is known, the compositions of the two iso-eluotropic binary mixtures can be calculated using the conversion factors given in table 5.4b. 

So far, an empirical approach that neglects the specific problems of LSC has appeared more feasible. Antle [572] demonstrated the applicability of the Sentinel method to LSC, using mixed mobile phases corresponding to table 5.4a, i.e. mixing the individual binary mixtures according to their volume fractions. This yielded some success, although admittedly not all solvents were iso-eluotropic. 

The parameter space in the original Sentinel method is restricted to a series of iso-eluotropic solvents, which means that only a very small fraction of all possible quaternary mixtures is considered. This is illustrated in figure 5.27a. 

The reason for this is that the linear relationship between In k and composition (mixing ratio of two iso-eluotropic binary mixtures) is not rigorously valid. A careful examination shows that the observed lines for In k vs. composition are slightly and systematically curved [576,577]. 

Methods used to estimate the correct eluotropic strength (methanol-water ratio) have been described in section 5.4. Methods used to calculate corresponding compositions of other (iso-eluotropic) binary mixtures were discussed in section 3.2. 

Naturally, the number of initial experiments required to start the optimization procedure will increase if either the number of parameters considered or the complexity of the model equations increases. As far as the number of parameters is concerned, we have seen this to be true with any optimization procedure, and hence the number of parameters should be carefully selected. In order to avoid a large number of initial experiments, the complexity of the model equations may be increased once more data become available during the course of the procedure. For example, retention in RPLC may be assumed to vary linearly with the mixing ratio of two iso-eluotropic binary mixtures at first. When more experimental data points become available, the model may be expanded to include quadratic terms. However, complex mathematical equations, which bear no relation to chromatographic theory (e.g. higher order polynomials [537,579]) are dangerous, because they may describe a retention surface that is much more complicated than it actually is in practice. In other words, the complexity of the model may be dictated by experimental... 

Next, the concept of iso-eluotropic mobile phases is used to determine the binary acetonitrile-water and THF-water mixtures that correspond to the initial and the Final composition. For example, 20% methanol corresponds [627] to 17% acetonitrile and to 12% THF, whereas 100% methanol corresponds to 84% acetonitrile and to 59% THF. 

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