Chromatographic response function

Equation 4.32 expresses the difference between the retention parameters Ai p of two solutes as a chromatographic response function ... 

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. 

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... 

Figure 2. Measurement of the peak valley ratio used in several chromatographic response functions (equations 6 and 7).

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. 

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. 

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. 

By input compounds names or chemical formulas to RPS, suitable descriptors for the compounds group desired are calculated with the same procedures as in the main function of RPS by the computer and then capacity factor s for the solutes at v u ious mobile phase compositions are predicted by step-by-step with the interval of X=0.01 for both aqueous acetonitrile and methanol mobile phases. The range available in this procedure is from 0.3 to 0.7 of X-values for acetonitrile system and from 0.4 to 0.8 for methanol system, respectively. After calculations of capacity factors for the desired solutes, Rgand Tp, for each step are estimated according to the equation-9 and 10, at five different flow rates of the mobile phase such as 1, 2, 4, 8 and 16 uL/min (because we use microcolumns) and then quality of the separation is Judged using a simple numerical chromatographic response function (CRF) defined as follows ... 

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... 

ANRF area norm2ilization with response factors CRF chromatographic response function... 

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