(377f) Modeling the Optical Properties of Silica Aerogel

Silica aerogel is a highly porous, low density material which absorbs light and scatters it in all directions of propagation. It is also optically transparent and thermally insulating due to these intrinsic properties of the molecular structure. This makes silica aerogel an excellent material to bond to windows to make glass structures more energy efficient by lowering heating and cooling costs. Before modelling transmittance and reflectance, we must understand that because of the high porosity of silica aerogel, we witness the multiple scattering effect, so to model the optical properties, we must model hemispherical transmittance and reflectance as the sum of forward and backward scattering intensities of the incident light beam through the material. To obtain the total intensity field, we call upon the radiative transfer equation (RTE) which states that the cosine of the polar angle with respect to the incident direction times the partial derivative of wavelength dependent intensity with respect to optical depth is equal to the negative intensity field over the optical depth and cosines of the polar angles to the incident directions plus one half albedo times the integral of the intensity field from negative one to one. We can solve the integro-differential equation for the intensity field by Gaussian-Legendre Quadrature, a method of numerical integration. I have written a program in python which computes the intensity field using the method of numerical integration, and then solving for hemispherical transmittance and reflectance. After plotting transmittance with albedo and optical depth and reflectance with albedo and optical depth, we super impose the images to see the curves intersect at one point, giving an albedo and optical depth we can use to model the coefficients of scattering and absorption.