Neural net formulations for organically modified, hydrophobic silica aerogel
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Neural net formulations for organically modified, hydrophobic silica aerogel David Noever Biophysics Branch, Mail Code ES-76, George C. Marshall Space Flight Center, National Aeronautics and Space Administration, Huntsville, Alabama 35812
Laurent Sibille Universities Space Research Association, Huntsville, Alabama 35806
Raymond Cronise Biophysics Branch, Mail Code ES-76, George C. Marshall Space Flight Center, National Aeronautics and Space Administration, Huntsville, Alabama 35812
Subbiah Baskaran Institut fuer Molekulare Biotechnologie, e.V., Beutenbergerstr. 11, DO-7745, Jena, Germany
Arlon Hunt Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720 (Received 3 April 1996; accepted 26 December 1996)
Organic modification of aerogel chemical formulations is known to transfer desirable hydrophobicity to lightweight solids. However, the effects of chemical modification on other material constants such as elasticity, compliance, and sound dampening present a difficult optimization problem. Here a statistical treatment of a 9-variable optimization is accomplished with multiple regression and an artificial neural network (ANN). The ANN shows 95% prediction success for the entire data set of elasticity, compared to a multidimensional linear regression which shows a maximum correlation coefficient, R 0.782. In this case, using the Number of Categories Criterion for the standard multiple regression, traditional statistical methods can distinguish fewer than 1.83 categories (high and low elasticity) and cannot group or cluster the data to give more refined partitions. A nonlinear surface requires at least three categories (high, low, and medium elasticities) to define its curvature. To predict best and worst gellation conditions, organic modification is most consistent with changed elasticity for sterically large groups and high hydroxyl concentrations per unit surface area. The isocontours for best silica and hydroxyl concentration have a complex saddle, the geometrical structure of which would elude a simple experimental design based on usual gradient descent methods for finding optimum.
I. INTRODUCTION
Aerogel presents attractive material qualities including low density, high porosity, and good thermal and electrical insulation.1–4 Organic modification of silica precursors to include short chain hydrophobic moieties adds considerable water resistance to the final product. A generic formula for such modifications is R0.2 Si(OME)y (OH)z O[1.9 2 0.5sy 1 zd], where R is an organic substituent [R Me, Pr, Ph, Bu] as described by Schwertfeger et al.4 While many properties such as density and porosity vary only slightly upon these substitutions, aerogel elasticity as measured ultrasonically shows a strong variation by 2–3 orders of magnitude depending on the R value. The elasticity depends less on concentration of the groups R, but varies with the steric bulk.4 A statistical method is developed here to formulate chemical substitutions and proce
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