A Parametric Numerical Study of Radiative Transfer in Thermotropic Materials

A thermotropic material is modeled as an absorbing, thin slab containing anisotropic scattering, monodisperse, spherical particles. Monte Carlo ray tracing is used to solve the governing equation of radiative transfer. Predicted results are validated by comparison to the measured normal-hemispherical reflectance and transmittance of samples with various volume fraction and relative index of refraction. A parametric study elucidates the effects of particle size parameter, scattering albedo, and optical thickness on the normal-hemispherical transmittance, reflectance, and absorptance. The results are interpreted for a thermotropic material used for overheat protection of a polymer solar absorber. For the preferred particle size parameter of 2, the optical thickness should be less than 0.3 to ensure high transmittance in the clear state. To significantly reduce the transmittance and increase the reflectance in the translucent state, the optical thickness should be greater than 2.5 and the scattering albedo should be greater than 0.995. For optical thickness greater than 5, the reflectance is asymptotic and any further reduction in transmittance is through increased absorptance. A case study is used to illustrate how the parametric study can be used to guide the design of thermotropic materials. Low molecular weighted polyethylene in poly(methyl methacrylate) is identified as a potential thermotropic material. For this material and a particle radius of 200 nm, it is determined that the volume fraction and thickness should equal 10% and 1 mm, respectively.