Monitoring of a batch organic synthesis by near‐infrared spectroscopy: modeling and interpretation of three‐way data

Abstract

Three-way data of the type batch  time  NIR wavelength were obtained by NIR spectroscopic multivariate monitoring of an organic synthesis as a batch process. The model synthesis, an ester synthesis, was carried out as an experimental design. Unexpected technical problems caused a blocking effect that forced a modification of the design. After preprocessing of a reduced three-way array, the spectral data in the three-way array were subjected to parallel factor analysis (PARAFAC). The loadings from this analysis could be interpreted and explained as a function of the synthesis studied. For the spectral interpretation, spectra of pure chemicals were needed. The paper is an illustration of what can be done with three-way modeling in order to increase the understanding of a reaction, and it attempts to show how the results can be interpreted and presented. The data sets are available from the authors.

Scatter plotting in multivariate data analysis

“…Equation (4) means that in PARAFAC models for threeway data any pair of loadings may be mirrored, leaving the remaining loading unchanged [17][18][19]. This can really cause confusion in the interpretation of loading plots, because moving in one direction in one loading plot may correspond to moving in the opposite direction in another.…”

“…It gives Euclidean distances between variables and Mahalanobis distances between objects. Equations (19) and (21) give scores and loadings that fit the SVD model, but for pure plotting purposes it is also possible to choose exponents that do not exactly sum to one in equation (21) [30]. Good examples of biplots are shown in Reference [29].…”

“…Good examples of biplots are shown in Reference [29]. Equation (19) works well when the number of objects and variables is almost equal. With 1000 variables and 10 objects, all variables would end up close to the origin of the biplot, and the objects would be more spread out.…”

“…After mean-centering, PCA was done, giving two components explaining 96% and 2% of the total sum of squares. The plot according to Equation (19) is shown in Figure 8. A plot according to Equation (21) with c ¼ 1 is shown in Figure 9.…”

“…PCA on mean-centered data gave three to four meaningful components explaining 97.4%, 2.1%, 0.28% and 0.16% SS, for a total of 99.9%. Figure 10 shows a biplot according to Equation (19). This is the quickest way to get objects and variables in the same plot.…”