NEURAL-NET FORMULATIONS FOR ORGANICALLY MODIFIED, HYDROPHOBIC SILICA AEROGEL

Organic modification of aerogel chemical formulations is known to tran sfer desirable hydrophobicity to lightweight solids. However, the effe cts of chemical modification on other material constants such as elast icity, compliance, and sound dampening present a difficult optimizatio n problem. Here a statistical treatment of a 9-variable optimization i s accomplished with multiple regression and an artificial neural netwo rk (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, usi ng the Number of Categories Criterion for the standard multiple regres sion, traditional statistical methods can distinguish fewer than 1.83 categories (high and low elasticity) and cannot group or cluster the d ata to give more refined partitions. A nonlinear surface requires at l east three categories (high, low, and medium elasticities) to define i ts 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 comp lex saddle, the geometrical structure of which would elude a simple ex perimental design based on usual gradient descent methods for finding optimum.