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Table 1 Typical Parameters Considered for the Optimization of Selectivity in Liquid Chromatographic Separations
Type of organic solvent
Percentage of organic solvent or gradient profile Column type (stationary phase)
Type and concentration of ion-pair reagent Concentrations of additives (buffer, salt, amine modifier)
in Fig. 8 is defined to include surfactant concentrations from 0.04 to 0.12 mM, and organic modifier concentrations from 0 to 10% of isopropanol. These limits are based on practical considerations, such as the minimum required elution strength, the critical micelle concentration of the surfactant, the solubility of the surfactant, and the viscosity of the mobile phase.
The next aspect of computer-assisted optimization procedures is evaluation of the observed or predicted chromatograms. To use the results of experiments and to advise the user on the direction in which to adjust the conditions, the computer requires that the chromato-grams be assessed in quantitative terms. It is often very difficult to establish that one chromatogram is “better” than another, let alone to derive a quantitative measure for the term better. This complication is partly because several considerations, such as resolution and analysis time, are considered. The measure for quality is generally referred to as a criterion, and the goal of the optimization procedure is to find those conditions that correspond to the maximum (or minimum) criterion value.
For instance, an often-applied criterion is the minimum resolution, Rsmin. This is the lowest resolution value encountered in the chromatogram. To optimize the separation, the process is aimed at maximizing /?s min. The observed or expected criterion value is referred to as the response for a given set of chromatographic conditions. The collection of criterion values as they are located in the parameter space is called the response surface.
The top window of Fig. 7 shows the value of 7?s min as a function of the fraction of mobile-phase 2, which represents a one-dimensional response surface. The complete coelution of compounds will give rise to an /?s-min value of 0; consequently, to a minimum in the response surface. The top half of Fig. 8 displays a two-dimensional response surface for part of the parameter space of the MLC separation. Again, well-separated peaks result in a high criterion value, whereas coelution results in a minimum in the response surface.
The foregoing considerations are valid for every optimization procedure applied in liquid chromatography. The differences between the various approaches can be traced to how the response surface is estimated and to how the response surface is searched for either an acceptable separation or for the global optimum. The global optimum on a response surface is that set of conditions that corresponds to the maximum criterion value throughout the parameter space, as opposed to a local optimum, which corresponds to an optimal criterion value in a limited section of the parameter space. Because the elution order of the analytes often varies with the experimental conditions, local optima are a frequently encountered phenom-enon in method development for liquid chromatography.
Some optimization procedures require a substantial amount of experimental work, which includes grid-search methods and sequential optimization procedures (see Sec. IV. D). The more versatile strategies applied for the optimization of liquid chromatographic separations require less experimental input. These are known as interpretive strategies. As indicated earlier, the order of peaks will change frequently when varying the experimental conditions. This results in local optima and minima on the response surface. However, the retention behavior of the individual analytes is much more regular and, therefore, is more amenable to modeling. The result is a retention surface for each analyte, as opposed to a response surface for the separation as a whole. If the retention of the components can be predicted at every point in the parameter space, it is possible to predict the chromatogram at every point. From the chromatogram the corresponding criterion value can be calculated. Thus, the response surface is estimated indirectly. Because of the regular nature of the retention surfaces, interperative strategies require far fewer experiments to obtain accurate estimates. The trade-off is the need to record (“interpret”) the retention times of every analyte in every chromatogram. Because it is essential that the peaks in the various chromatograms are matched to each other, but it is not necessary to identify each analyte, this process is generally referred to as peak tracking. Some techniques for peak tracking will be discussed in Section VI.
The implementation of interpretive strategies is illustrated in Fig. 7 and 8. The window in the center of Fig. 7 shows the retention behavior of each individual analyte as a function of the mobile-phase composition. Because this is a one-parameter optimization, each analyte