Development of a differential photoacoustic system for the determination of the effective water diffusion and water vapor permeability coefficients in thin films

This paper focused on developing a methodology and metrology using a differential photoacoustic (PA) system to determine the effective water vapor diffusion coefficient $(Deff)$ and the effective permeability coefficient $(Π)$ in thin films as a piece of paper and standard polystyrene for a controlled relative humidity. The methodology proposes a new differential photoacoustic system, including the water reservoir, relative humidity, and temperature detectors. Two cells, reference/sample, were used to obtain the instrumental function to reduce the electronic and environmental noises. A method based on the study of $ln[1−(S−S0)/ΔS]=t/τD$ and the behaviors of R² as a function of the number of data was proposed to assess the region in which the photoacoustic signal should be processed to determine each effective coefficient. S is the amplitude of the PA signal, $S0$ is the initial amplitude value, $ΔS$ is the change, t (time), and $τD$ is the water vapor diffusion time. The effective water diffusion coefficient $(Deff)$ for water and polystyrene was 1.90 × 10⁻¹¹ m²/s and 3.09 × 10⁻¹¹ m²/s, respectively. The permeability coefficient value for the piece of paper was 4.18 × 10⁻⁹ mol kg⁻¹ cm⁻² s⁻¹ Pa⁻¹, while for polystyrene, it was 6.80 × 10⁻⁹ mol kg⁻¹ cm⁻² s⁻¹ Pa⁻¹ for 70% of relative humidity. This methodology can be extended by changing the moisture content on the chamber to obtain the dependence of $Deff$ as a function of relative humidity.