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Figure 5.1. Schematic of different orders of analytical measurements. Orders: (A) zero; (B) rst; (C) second; (D) third.
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Figure 5.2. Example of a zero-order measurement of combinatorial materials. Abrasion resistance of coatings from measurements of scattered light from each organic coating in a 48-element array at a single wavelength upon abrasion test. (A) Re ected-light image of the coatings array; (B) representative data from a single material in the array.
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Variable Parameter I
2500 2000 1500 1000 500 0 300
400 500 600 Wavelength (nm)
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Normalized Fluorescence
1.2 1 0.8 0.6 0.4 0.2 0 200 300 400 500 600 700 800 Wavelength (nm)
Figure 5.3. Example of a rst-order measurement of combinatorial materials. Polymer branching from measurements of uorescence spectra from each polymerized material in a 96element microreactor array at a single excitation wavelength. (A) Re ected-light image of the microreactor array; (B) representative uorescence spectrum from a single microreactor in the array.
Absorbance
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 450
Reaction progress
550 650 750 Wavelength (nm)
Figure 5.4. Example of a second-order measurement of combinatorial materials. Sensor materials as a 48-element sensor materials array. (A) general view of the sensor materials array in a gas ow-through cell; (B) representative absorption spectra from a single material in the array collected over a period of time of reaction of this sensor material with a vapor of interest.
capabilities and applicability, of each type of the instrument for the analysis of combinatorial samples. A measurement system that generates a single data point for each combinatorial sample is a zero-order instrument, as shown in Figure 5.1A. A single number is a zero-order tensor, the same as is known in mathematics.56 First-order measurement systems generate a string of multiple measurements for each combinatorial sample (see Figure 5.1B). For example, optical measurements can be done at a single wavelength over the course of a reaction in monitoring the reaction s progress. The variable parameter
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2.5 2.5 2.5
2 Absorbance 1.5 1 0.5 0 350 450 550 650 750 850 Wavelength (nm)
2 Absorbance
1.5 1 0.5 0
Temperature T1
2 Absorbance 1.5 1 0.5 0
Temperature T2
Temperature T3 Reaction Progress 1 7
1 2 3 4 5 6 7
T3 T2 T1
350 450 550 650 750 850 Wavelength (nm)
350 450 550 650 750 850 Wavelength (nm)
Figure 5.5. Example of a third-order measurement of combinatorial materials. Oxidative stability of polymers from measurements of UV-VIS re ection spectra from each polymeric composition in a materials array as a function of reaction temperature and time. (A) General view of the materials array on a gradient temperature heater; (B) representative UV-VIS spectra from a single material in the array as a function of reaction time and temperature. Reaction temperatures: T1 > T2 > T3. Reaction progress is shown as spectra changes from spectrum 1 to spectrum 7.
is the time to complete the reaction. Alternatively, an optical spectrum of the nal combinatorial material can be produced by the rst-order measurement system. The variable parameter in this case is the wavelength. As may be seen, measurements provided by the rst-order measurement system are of the same nature, whether, for example, temporal or spectral in response. Second-order measurement systems generate a second-order tensor of data for each sample. This is a matrix of the instrument s response upon a change of the two independent variables (see Figure 5.1C). Depending on the particular need in the combinatorial screening, higher-order measurement systems are also possible. For example, Figure 5.1D shows a response of the third-order system, where a matrix of an instrument response upon the change of the two independent variables is further modulated by a third independent variable. Clearly, the complexity of measurement systems increases dramatically with an increase in the measurement order. However, despite instrument complexity, the higher order instruments have obvious advantages for reaction monitoring and optimization. These advantages are illustrated below with real examples in the combinatorial screening of materials in our laboratories. An example of combinatorial screening using a zero-order measurement approach is illustrated in Figure 5.2. Abrasion resistance of organic protective coatings was determined from measurements of scattered light from each coating in a 48-element array.57 A simple zero-order measurement approach was useful because it provided the required information about