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

Abstract

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.