Chromatographic optimization function

In the literature many different terms are used for such criteria (chromatographic) response functions, objective functions or (chromatographic) optimization functions. Throughout the rest of this chapter, the neutral term optimization criteria will be used. 

The optimization results for different criteria may be conflicting in the sense that they show optima at different values of the factors. One does not need to find the optimum of the two (or more) responses separately, but rather an adequate compromise. There are several ways of doing this. The most usual, but not necessarily the best is to combine (elemental) criteria in some way to obtain what have been called global criteria. Again several such criteria have been propo.sed. for instance the COF (chromatographic optimization function) 5] given by ... 

For manual optimization methods the peak separation function, P, is easy to determine and can be calculated as shown in Figure 4.30 (479). The chromatographic response function for the chromatogram is then simply the sum of the In P values for the n adjacent peak pairs. 

Chromatographic response and optimization functions Experimental variables Optimization method Ref... 

Simplex Optimization Criteria. For chromatographic optimization, it is necessary to assign each chromatogram a numerical value, based on its quality, which can be used as a response for the simplex algorithm. Chromatographic response functions (CRFs), used for this purpose, have been the topics of many books and articles, and there are a wide variety of such CRFs available (33,34). The criteria employed by CRFs are typically functions of peak-valley ratio, fractional peak overlap, separation factor, or resolution. After an extensive (but not exhaustive) survey, we... 

Optimization Criteria for Interpretive Methods. As noted earlier in our discussion of the simplex methods, there are many chromatographic response functions (CRFs) for the evaluation and comparison of chromatograms during an optimization process. Here we discuss two CRFs that we employed successfully with this interpretive method of optimization. Since the retention behavior of every solute must be modeled prior to optimization, the number of sample components is known beforehand it is thus unnecessary to include the number of peaks in these CRFs as was done in CRF-3 (equation 8) for the simplex. 

It has also proven advantageous to use a combination of individual responses in order to optimize as many parameters as possible (39-43). The two performance goals for a separation of bisphenols by MEKC were good resolution among five peaks and short total analysis time (42). Thus, a chromatographic response function (CRF) was employed that was a product of two types of desirability functions, as used by Divjak et al. (30-33, 44). Resolution (R) between two adjacent peaks in an electropherogram was calculated using... 

FIGURE 5.2. Representative electropherograms for three of the experiments of a Box-Behnken design and corresponding CRF (chromatographic response function) values. Used to optimize a separation of Bisphenols E, A, AP, and P, and Tetramethyl bisphenol A. Extracted from Reference 42. 

Different aggregations of objective criteria have been developed for particular analytical methods. Table 4.2 gives examples of objective functions for chromatography and spectroscopy. The objective function for chromatography, the chromatographic response function (CRF) accounts for all m peaks of the chromatogram, the time t for elution of the last peak, the noise, Af , at the measurement point of peak i, and the selectivity of peak separation based on Kaiser s measure for peak separation fig (see Figure 4.5). For optimal separations, the CRF is maximized. 

Planar response function (PRF) has been used in the statistical approach to solvent selectivity [40] that is a modified form of the chromatographic response function (CRF) used by Morgan and Deming in GC optimization studies [42]. PRF is defined by... 

Column chromatographic separations depend on the relative affinity of different proteins for a given stationary phase and for the mobile phase. Association between each protein and the matrix is weak and transient. Proteins that interact more strongly with the stationary phase are retained longer. The length of time that a protein is associated with the stationary phase is a function of the composition of both the stationary and mobile phases. Optimal separation of the protein of interest from other proteins thus can be achieved by careful manipulation of the composition of the two phases. 

FIGURE 6.14 (a) Principle of SBCD, elution with five interstitial volumes on 4-cm distance (5x4 cm) is faster than single development on 20-cm distance (thick line), (b) Rp values of sample components plotted as a function of modifier concentration. Optimal concentration (Y) for SBCD (5x4 cm) is lower than for development on the full distance of 20 cm (X). (Modified from Soczewinski, E., Chromatographic Methods Planar Chromatography, Vol. 1, Ed., Kaiser R.E., Dr. Alfred Huetig Verlag, Heidelberg, Basel, New York, 1986, pp. 79-117.)... 

Bourguignon, B., and Massart, D. L. (1991). Simultaneous optimization of several chromatographic performance goals using Derringer s desirability function.. Chromatogr. A 586, 11—20. 

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