Generalized 1D photopyroelectric technique for optical and thermal characterization of liquids

Abstract

The analytical solution for the one-dimensional heat diffusion problem for a three-layer system, in the Beer–Lambert model for light absorption, is used for the implementation of a photopyroelectric (PPE) methodology for thermal and optical characterization of pigments in liquid solution, even for those ones potentially harmful to the pyroelectric sensor, taking the liquid sample's thickness as the only variable. Exponential decay of the PPE amplitude followed by a constant PPE phase for solutions at low pigment concentration, and exponential decay of the PPE amplitude but a linear decrease of the PPE phase for the concentrated ones are theoretically shown, allowing measurements of the optical absorption coefficient (at the wavelength used for the analysis) and the thermal diffusivity for the liquid sample, respectively. This PPE methodology was tested by measuring the thermal diffusivity of a concentrated solution of methylene blue in distilled water and the optical absorption coefficient, at two wavelengths (658 and 785 nm), of water solutions of copper sulfate at various concentrations. These optical parameters were used for measuring the molar absorption coefficient of this last pigment in water solution at these two wavelengths. This last optical property was also measured using a commercial spectrometer, finding very good agreement with the corresponding ones using this PPE technique.