Program parameters

Figure A2.1 Waters ProMonix On-Line HPLC analyzer. The upper compartment door contains a keypad for programming and operation of the analyzer. The upper window allows viewing of indicator lights and a liquid crystal display that provides the operator with analyzer interface, programmed parameters, and instrument status results. The lower chamber contains the pumps, valves, injector, and detector(s) required for the chromatographic separation. The sample conditioning plate for online process monitoring is to the right of the analyzer. This is a typical process HPLC. (From Cotter, R.L. and Li, J.B., Lab Rob Autom., 1, 251,1989. With permission of VCH Publishers.)...

Relative and absolute MIP gap mixed integer programming parameter for controlling optimization accuracy e g. MIP gap of 1% leads to an algorithm stop, if the objective value cannot be improved within a tolerance interval of 1%. 

Basic to the entire exercise is the issue of how much alternative fuel development can be reasonably expected over the next twenty years. Given the previous synfuel program parameters, sulfur output then depends on both the characteristics of the original fuel source and the specific method of processing. These also serve to determine the location of the sulfur output. 

In this chapter we will take a look at some aspects of programmed analysis, particularly those which bear relation to the chromatographic selectivity. The parameters involved in the optimization of programmed analysis will be divided into primary or program parameters and secondary or selectivity parameters. These parameters will be identified for different chromatographic techniques and procedures will be discussed for the optimization of both kinds of parameters. 

If the program is optimized so that all sample components are eluted under optimal conditions, then other (secondary) parameters may be used for the optimization of the selectivity. However, changes in the secondary parameters may imply that the parameters of the program need to be re-optimized. For example, if the selectivity in a temperature programmed GC analysis is insufficient, then another stationary phase may be used to enhance the separation. However, the optimum program parameters obtained with one stationary phase cannot be transferred to another column that contains another stationary phase. The re-optimization of the temperature program for the other column will require at least one additional experiment to be performed. 

It can be seen in table 6.3 that the optimization of selectivity in programmed temperature GC involves variation of the (nature or composition) of the stationary phase. To vary this parameter, a different column and re-optimization of the (primary) program parameters will be required. This is clearly not a very attractive proposition and therefore the optimization of programmed temperature GC is usually restricted to optimizing the program. 

Parameters for the optimization of programmed analyses in various chromatographic techniques. Primary parameters may be used to optimize the program parameters (initial and final conditions, slope and shape). Secondary parameters may be used to optimize the selectivity. 

Because this optimization only concerned program parameters and not selectivity parameters, the response surface will have been relatively simple. Therefore, the probability that the Simplex procedure would arrive at the global optimum rather than at a local one was greater than it was in section 5.3, where we described the use of the Simplex method for selectivity optimization. 

For the interpretive optimization of the primary (program) parameters in the programmed analysis of complex sample mixtures it may well be sufficient to optimize for the major sample components. This may be done if it is assumed that the primary parameters do not have a considerable effect on the selectivity, so that if the major sample components are well spread out over the chromatogram, the minor components in between these peaks will follow suit automatically, and if it is assumed that the minor peaks are randomly distributed over the chromatogram. The major chromatographic peaks can be separated to any desired degree if optimization criteria are selected which allow a transfer of the result to another column. 

If we leave out of account the delay that both the column and the packing material may cause in the temperature program inside the column relative to the program followed in the column oven [615], then the program parameters are naturally known. 

Simplex optimization of the primary (program) parameters in programmed temperature GC analysis has been demonstrated [612]. A systematic sequential search [613] may be used as an alternative. The Simplex method may be used to optimize a limited number of program parameters, whereas the latter approach was developed for the optimization of multisegment gradients. The use of interpretive methods has so far only been suggested [614,615]. 

The (primary) program parameters may be used to optimize the separation in programmed solvent LC in a non-selective way. Since this involves optimization of the... 

Of course, the simultaneous optimization of different (primary) program parameters (initial and final composition, slope and shape of the gradient) and secondary parameters (nature and relative concentration of modifiers) may involve too many parameters, so that an excessive number of experiments will be required to locate the optimum. This problem may be solved by a separate optimization of the program (primary parameters) and the selectivity (secondary parameters) based on the concept of iso-eluotropic mixtures (see section 3.2.2). This will be demonstrated below (section 6.3.2.2). However, the transfer of... 

Systematic optimization of program parameters Optimization without solute recognition... 

If the retention vs. composition plots of all solutes are known, then it is in principle possible to calculate the optimum program parameters for a simple, continuous gradient (figure 6.2a-d). In such a procedure an appropriate optimization criterion can be selected such that the distribution of all the peaks over the chromatogram, as well as the required analysis time, can be taken into account (see chapter 4). 

However, the calculations required for such an optimization are quite involved. This is caused by the requirement to calculate the retention times of each solute (and the resolutions of each pair of adjacent peaks) from the isocratic retention vs. composition relationships. In order to characterize the response surface, these calculations need to be performed a number of times. Finally, the optimum needs to be found on the response surface. If all four program parameters (initial and final concentration, slope and shape) are considered, the number of calculations would be large, even though the response surface may be simple compared with those encountered in selectivity optimization (see the discussion in section 6.3.2.1). 

Without knowing much about the sample, the Snyder approach may also be used to optimize the program parameters. This is an empirical approach in which the sample properties are largely disregarded, but it does lead to the formulation of reasonable working conditions after only one or two chromatograms have been obtained. 

A second reason not to become involved in extensive calculations for the complete mathematical optimization of the (primary) program parameters is that a more powerful way to optimize the separation of all sample components in the mixture may be to optimize the selectivity of the gradient by varying the nature of the mobile phase components (secondary parameters). 

The characteristics of the different methods for gradient optimization are summarized in table 6.5. In table 6.5a, the different methods for the optimization of the program parameters are compared. Bearing in mind that a large effort is generally not warranted for the optimization of programmed analysis (see section 6.3.2.4), we should conclude that the Simplex method is not suitable because of the large experimental effort required, and... 

Summary of the characteristics of gradient optimization methods, a. Optimization of primary (program) parameters... 

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