Combinatorial Materials Development using Gradient Arrays. Sphere Covering Lattice Designs
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Combinatorial Materials Development using Gradient Arrays. Sphere Covering Lattice Designs Designs for Efficient use of Experimental Resources. James N. Cawse (GE Corporate Research and Development, 1 Research Circle, Niskayuna NY 12309)
Abstract Gradient arrays are now common tools in combinatorial chemistry for discovery of new leads to commercial materials. Although the cost per sample has dropped markedly with new high throughput methods, efficient use of experimental resources is still important. Examination of gradient arrays from an informational standpoint suggests that designs which use the concepts of sphere packing and covering will be more efficient than simple gradients. This is especially true in higher dimensional systems.
Background In a combinatorial search for new materials having an improved or new property, an extremely large number of samples may be needed to locate leads toward new compositions. This is because the search is frequently done in high dimensional space where the property of interest is not a simple continuous function of the factors. This is in contrast to the assumptions of conventional Design of Experiments (DOE). In conventional DOE, the response is a linear function of the factors, their interactions, and perhaps quadratic terms (Figure 1). In combinatorial search, the response may be a phase space with irregular boundaries (Figure 2) or a highly jagged landscape (Figure 3). These response surfaces become even harder to search in high dimensional space, which is more “spacious” than the two or three dimensional spaces that we can visualize and intuit.
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Figure 2. Phase space with irregular boundaries
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Figure 1. Relatively smooth linear/quadratic space
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Figure 3. Jagged landscape with isolated local maximum
JJ11.8.2
Search of multidimensional compositional space has been done using gradient arrays which may be either continous [1] or discrete [2]. These arrays are often made using methods derived from semiconductor manufacture, in which components of the system are projected (either directly or through a mask system) onto all the appropriate points of an array simultaneously. The design of the experiment[3] then becomes far more a function of the geometric limitations of the masking or the analysis equipment. These methods are very effective for making up samples with three variable components, but more complex systems become more difficult. Weinberg [4] has published a very complex multidimensional system which is essentially an array of arrays. In other systems, the array is made up by making discrete samples and applying them to a substrate, usually with a formulation robot. The resources required for making up the samples then become more significant and increase in proportion to the number of samples. This robotic equipment can easily make up arrays with three or more variable components. Four and five com
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