Modelo teórico para a técnica de dois feixes aplicado a amostras de duas camadas

Abstract

Many physical devices can be approached as a two-layer system and many interesting properties of such are of interest. Heat conduction studies in layered samples are very common in this days, optical absorption and thermal diffusion are among others physical properties of particular interest when one deal with coatings on substrates, with thin or thick films on semiconductors as well as dye diffusion on polymeric films and fungus on modified surfaces and membranes. These are some of good examples of two-layer materials. In this way, the present work proposes to develop an extension of the well known "Two-Beam Phase Lag Method", but with suitable adjustment for two-layer samples. The model starts with the standard Rosencwaig and Gersho photoacoustic modeling, considering both light incidences, one frontal and another from the back (rear). Expressions for both illumination geometries are derived to the temperature on the interface sample-gas, obtained upon suitable boundary conditions, mainly considering different optical absorption coefficient and thermal diffusivity for each layer. Expressions for the temperature on the interface sample-gas are simulated for some limiting cases and in the limit of one single-layer condition, Rosencwaig and Gersho equation is recovered and it validates the model. Further, simulation are made upon samples properties ranging from typical cases of interest for two layer materials such as for semiconductor, polymeric and ceramic. Simulations were made with the ratio "frontal/rear" amplitudes and for the phase difference between front and rear expressions. The amplitude ratios and phase-lag can be used for deriving effective thermal properties from fitting parameters and also frequency scanning may allow one to find out thickness of the layer. The model is essentially theoretical and experiments should be performed soon in order to validate it for homogeneous sample.