Example Fractional Factorial Design for Exploring the Reaction Space

7 Example Fractional Factorial Design for Exploring the Reaction Space [22] 

The Willgerodt-Kindler reaction was studied for a series of para substituted acetophenones with different amines in different solvents. 

The selection of test items by such a design can be accomplished as follows For each constituent of the reaction system, two principal property axes should be considered. The columns of a two-level fractional factorial design matrix contain an equal number of minus and plus signs. If we let the columns pairwise define the selection of test systems, four combinations of signs are possible [(—),(—)], [(-), (+)]. [(+), (—)]. and [( + ), (+)]. These combinations of signs correspond to different quadrants in the score plots. Hence we can use the sign combinations of two columns to define from which quadrant in the score plot a test item should 

If we let columns in the design matrix define the constituents as follows 1, 2 define the substrate, columns 3, 4 define the amine co-substrate, and columns 5, 6 define the solvent, the first row in the design matrix in Table 11 would thus correspond to a selection of a substrate projected in the [( — ),( — )] quadrant, an amine from the [(—),( + )] quadrant, and a solvent from the [( + ),( + )] quadrant. The other rows define other combinations. The test items selected accordingly are shown in Table 13. To permit fair comparisons as to the performance of the reaction, it is necessary to adjust the experimental conditions for each system to yield an optimum result. The danger of using standardized conditions has been emphasized [1] and the arguments against such a technique are not repeated here. The conditions which afforded a maximum yield were determined by response surface techniques and these results are also shown in Table 13. 

It is realized that it would be quite cumbersome to carry out elaborate optimizations for every new reaction system considered. Fortunately, this is not necessary since it is possible to use the technique of PLS modelling, described below, for determining quantitative relations between the properties of a reaction system and the performance of the system. The PLS model can then be used to 

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