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array reaction parameters as illustrated in Table 5.3. The combinations of these parameters were provided from design of experiments. Ranges of these parameters were selected to preserve the rank order of a variety of control catalysts from a lab-scale to combinatorial reactors.86,98 All parameters described in Table 5.3 are considered process conditions because once chosen they are not altered throughout screening of new catalysts.98 Replicates (n = 8) of similar conditions in each 96-microreactor array are randomized in groups of four to reduce possible effects of any positioninduced variability. In addition one set of eight microreactors in each microreactor array is always left blank and one of the microreactors contains a thermocouple (see Figure 5.3A). The experimental setup for the automated acquisition of uorescence spectra from materials in 96-microreactor arrays is shown in Figure 5.6. The uorescence measurements of polymers in each microreactor were performed through the glass bottom of the microreactors using a white light source, a monochromator, a portable spectro uorometer, and a translation stage. The white light source was coupled to the monochromator for selection of the excitation wavelength and further focused into one of the arms of a six-around-one bifurcated ber-optic re ection probe. Emission light
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Figure 5.6. Automated multifunctional high-throughput screening system: (1) spectro uorometer; (2) data acquisition computer; (3) ber-optic probe; (4) combinatorial array; (5) translation stage; (6) in-line optical lter.
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from the polymeric material in each microreactor was collected when the common end of the ber-optic probe was positioned near the bottom of the reactor at a 45 angle to the normal to the surface. The second arm of the probe was coupled to the portable spectro uorometer through an inline optical lter holder. The holder contained a long-pass optical lter to block excitation light from entering the spectro uorometer. The spectro uorometer was equipped with a 200-mm slit, 600-groove/mm grating blazed at 400 nm and covering the spectral range from 250 to 800 nm, and a linear CCD-array detector. The uorescence spectra reported here were not corrected by the spectral response of the optical system. For uorescence analysis of solid polymers, each microreactor array was arranged on an X-Y translation stage, and the common end of the beroptic probe was held stationary to measure emission spectra. The size of the excitation beam of the ber-optic probe was in the range from 1 to 4 mm, depending on the probe-microreactor distance. Data acquisition and automatic control of the X-Y translation stage were achieved with a computer using a program that also provided adequate control of the data acquisition parameters and real-time communication with the translation stage. Prior to PCA, uorescence spectra from ve 96-microreactor arrays were appropriately preprocessed. The preprocessing included a baseline subtraction, normalization of spectra by the uorescence intensity at 500 nm, selection of an appropriate spectral range for the PCA, and meancentering the spectra. The spectra from the empty and thermocouplecontaining microreactors were excluded from the spectral descriptor analysis. Principal components analysis was used to extract the desired spectral descriptors from the spectra. PCA is a multivariate data analysis tool that projects the data set onto a subspace of lower dimensionality with removed collinearity. PCA achieves this objective by explaining the variance of the data matrix X in terms of the weighted sums of the original variables with no signi cant loss of information. These weighted sums of the original variables are called principal components (PCs). In applying PCA, we express the data matrix X as a linear combination of orthogonal vectors along the directions of the principal components:
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T X = t1p1 + t 2 pT + + t A pT + E, 2 K
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(5.1)
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where ti and pi are, respectively, the score and loading vectors, K is the number of principal components, E is a residual matrix that represents random error, and T is the transpose of the matrix. PCA determines a spectral descriptor for each uorescence spectrum. The spectral descriptor is represented as a vector in PCA space. This vector
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