Quantitative diffusion and swelling kinetic measurements using large-angle interferometric refractometry

Abstract

The uptake and release of sorbates into films and coatings is typically accompanied by changes of the films' refractive index and thickness. We provide a comprehensive model to calculate the concentration of the sorbate from the average refractive index and the film thickness, and validate the model experimentally. The mass fraction of the analyte partitioned into a film is described quantitatively by the Lorentz–Lorenz equation and the Clausius–Mosotti equation. To validate the model, the uptake kinetics of water and other solvents into SU-8 films (d = 40–45 μm) were explored. Large-angle interferometric refractometry measurements can be used to characterize films that are between 15 μm to 150 μm thick and, Fourier analysis, is used to determine independently the thickness, the average refractive index and the refractive index at the film–substrate interface at one-second time intervals. From these values the mass fraction of water in SU-8 was calculated. The kinetics were best described by two independent uptake processes having different rates. Each process followed one-dimensional Fickian diffusion kinetics with diffusion coefficients for water into SU-8 photoresist film of 5.67 × 10⁻⁹ cm² s⁻¹ and 61.2 × 10⁻⁹ cm² s⁻¹.