A model of the optical properties of a non-absorbing media with application to thermotropic materials for overheat protection

Thermotropic materials offer the potential to provide overheat protection for polymer absorbers. These materials are composed of a matrix material in which a second material, referred to as the scattering domain, is dispersed. Temperature control is accomplished by a reduction in transmittance at a desired temperature corresponding to the phase change temperature of the scattering domain. The phase change is accompanied by a change in refractive index. This paper describes a numerical model to predict the transmittance and reflectance of a polymer based thermotropic material as a function of the relative index of refraction m between the matrix and scattering domains, the scattering domain size and volume fraction f_v, and the sheet thickness. The thermotropic material is modelled as a non-absorbing sheet comprised of discrete anisotropic scattering spherical particles embedded in a matrix material. Under the assumption that the particles scatter incident radiation independently, the direction of scattered radiation is determined by Mie theory. A Monte Carlo numerical technique is used to predict the transmittance and reflectance for thermotropic materials in which the matrix index of refraction is 1.5 (representative of polymers) and the incident wavelength is 550 nm. Model results are validated by comparison to measured transmittance for 0.3 mm thick polymer samples containing particles with 200 nm radius at m ranging from 0.97 to 1.09 and f_v ranging from 5 to 18.2%. As the mismatch in refractive indices and volume fraction increase, the transmittance is reduced. For example, the transmittance is reduced from 83% for m=1.02 and f_v = 9.6 to approximately 50% for m=1.09 and f_v =13.5% (200 nm radius and 0.3 mm thick).