Chromatographic optimizing

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... 

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. 

Figure 4.3S. (a) Simplex lattice design for reversed-phasc chromatographic optimization showing relative proportions of each... 

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 ... 

A more formal approach is to use t-tests or analysis of variance. In most practical cases of chromatographic optimization, this is not necessary and we will therefore refer the reader to the general literature on experimental design [21-271. The r-test is more important in the screening designs and some additional information is therefore given in Section 6.4.2. 

Chromatographic optimizations are usually performed at a preselected pH. However, a simultaneous consideration of the three factors (i.e., surfactant, organic solvent, and pH) expands the separation capability for some problems. The retention can be predicted from (see below) where Kas, Kam, Kad, md, and sd are the equilibrium constants associated to the basic species and T has. HAM. HAD HMD, and Thsd Correspond to the acidic species. is the protonation constant in the aqueous-organic bulk solvent, and [//] is the proton concentration. 

Fiprc 4.35. (a) Simplex lattice design for reversed-phase chromatographic optimization showing relative proportions of each solvent to be used, (b) Individual resolution maps for the live pairs of solutes in a 6-componcnt test mixture, (c) Overlapping, resolution map (ORM) for the 6-componcnt test mixture. 

As a rule, chromatographic optimizations are based on the trial-and-error approach, relying on experimentation, and the basic relationships of chromatographic theory. In HPLC [58-62] is used the well-known expression for the resolution... 

The most simple criteria used in chromatographic optimization are based on properties that only depend on the retention of solutes [11], such as the modified selectivity ... 

There are yet further sophistications such as the supermodifled simplex, which allows mathematical modeling of the shape of the response surface to provide guidelines as to the choice of the next simplex. Simplex optimization is only one of several computational approaches to optimization, including evolutionary optimization, and steepest ascent methods, however, it is the most commonly used sequential method in analytical chemistry, with diverse applications ranging from autoshimming of instruments to chromatographic optimizations, and can easily be automated. 

Chromatographic optimization is usually performed at a preselected pH. However, the simultaneous consideration of the three factors (i.e., surfactant, organic solvent, and pH) expands the separation capability for some problems. The retention can be predicted from (see below)... 

Various computer-assisted chromatographic optimization methods have been developed to optimize separation selectivity It should be pointed out that most of the method development strategies, as well as many types of chromatography softwares, have been focused on... 

Optimization of gas chromatographic separations requires careful attention to a number of important variables and their interactions. In this chapter we will approach gas chromatographic optimization from the top down. First we will consider major options that have profound effects on a given separation, and which limit subsequent choices for many of the column variables, both physical—length, inner diameter, stationary phase—and parametric—temperature and flow or velocity. Then we will examine in more detail the questions of how to... 

The ensuing discussion of gas chromatographic optimization primarily addresses goal-oriented modification of column dimensions and operating conditions. Column selection, particularly of the stationary phase, has been addressed in Chapter 3. Here we focus on the effects of changing the column operating conditions and the column dimensions. 

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