Neural net formulations for organically modified, hydrophobic silica aerogel

Abstract

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.