Partial Analytical Solution of a Model Used for Measuring Oxygen Diffusion Coefficients of Polymer Films by Luminescence Quenching

Many aspects of optical chemical sensor design would benefit from a better knowledge of the diffusion properties of the analyte in the polymer host. The response times of such sensors to a step change of analyte concentration are of vital interest for many applications of fast-responding sensors. Further, the diffusion properties govern their quenching behavior and their sensitivity. A method for determination of the diffusion constant of oxygen in polymers has been developed and used by several groups in the past. The underlying mathematical model for luminescence quenching by molecules of a gas in a single sensing layer on an impermeable support has not yet been completely derived in an analytical form and still uses tedious numerical methods. We present a partial analytical solution to the problem of modeling the time dependence of luminescence generated by in- or outdiffusion of a gaseous quencher in a polymer film in which a luminophor is immobilized and offer a suitable method to predict sensor response times.