Optimization peak separation 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. 

Rather than the separation function, resolution between individual peak pairs is used in most automated optimization procedures because it is easier to calculate, although non-Gaussian pe2dcs and overlapping peaks can present problems due to the difficulty of estimating peak widths. A simple objective function would be to consider only the separation between the worst separated peak pair, ignoring all others. If a set of... 

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. 

Cation exchange chromatography with a methanesulfonic acid eluant is a much simpler alternative. For optimizing peak efficiencies, 1 % (v/v) methanol is added to the mobile phase. As an alternative to the lonPac CSIO, an OmniPac PCX-100 (see Section 6.7) can also be used. The latter one has very similar separation properties, but it is characterized by a lower hydrophobicity of the cation exchange functionality, which improves peak efficiency for choline and its derivatives even more. 

In practice, it is more difficult to optimize resolution as a function of the relative retentlvity than to optimize retention. Thus, unless the mixture is very complex or contains components that are particularly difficult to separate it may be possible to optimize a particular separation using the linear equation (1.72) as demonstrated by Bttre [177]. Figure 1.13 illustrates the relative change in peak position for a polarity test mixture with two identical, serially coupled open tubular columns, coated with a poly(dimethylslloxane) and Carbowax 20 M stationary phases, as a function of their relative retentlvity on the second column. The linear relationship predicted by equation (1.72) effectively predicts the relative peak positions and indicates that a nearly... 

The non-BO wave functions of different excited states have to differ from each other by the number of nodes along the internuclear distance, which in the case of basis (49) is r. To accurately describe the nodal structure in aU 15 states considered in our calculations, a wide range of powers, m, had to be used. While in the calculations of the H2 ground state [119], the power range was 0 0, in the present calculations it was extended to 0-250 in order to allow pseudoparticle 1 density (i.e., nuclear density) peaks to be more localized and sharp if needed. We should notice that if one aims for highly accurate results for the energy, then the wave function of each of the excited states must be obtained in a separate calculation. Thus, the optimization of nonlinear parameters is done independently for each state considered. 

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... 

A similar argument holds for the influence of the peak shape on the separation criterion. In the non-linear part of the distribution isotherm, the shape of the peak will be a function of the injected quantity. Hence, once again, the location of the optimum may be affected by the composition of the sample. Also, the effect of column dimensions on the peak shape may be hard to predict, and the peak shape may to a large extent be determined by the characteristics of the instrument, rather than of the column. Therefore, if the composition (or the concentration) of the sample can be expected to vary considerably, and if it is desirable that the result of an optimization process can be extrapolated to different columns (of the same type) and to different instruments, then it is advisable to use criteria that are not affected by the relative peak areas, nor by the shape of the peaks. 

Hie typical output from method optimization software is a resolution map, as shown in Figure 10-1. The map shows resolution of the critical pair (two closest eluting peaks) as a function of the parameter(s). The example shows resolution as a function of gradient time (slope of the gradient). The resolution map has several advantages as an experimental display tool It forms a concise summary of experiments performed, it allows the chromatographer to select areas of interest and communicate the expected result, and it facilitates the viewing of data that would allow for a more robust separation. 

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