(699c) Analytic Design Formulae for Homogeneous Reactive Barrier Membranes

Membranes with immobile and irreversibly reactive sites can be effective barrier materials for packaging applications, for example, for oxygen sensitive foodstuffs or organic electronics. Often the application of interest focuses on situations where one side of the barrier material is exposed to a high concentration of an unwanted mobile species and the other side is exposed to a vanishingly small concentration of it. The reactive term that consumes the mobile species in the governing transport equations for such membranes usually is a function of both the mobile species and the immobilized reactive sites, leading to non-linear partial differential equations that typically have to be solved numerically. Here we present analytic design formulae developed to estimate the time varying flux, kill time and time lag through homogeneous reactive membranes, obviating the need to numerically solve the model's non-linear equations for a large number of cases.

Modeling reveals three regimes for the time varying flux. For early times most reactive sites are still present, and an initial flux plateau is observed. For intermediate times, a moving reaction front is found to travel across the film coupled with an increasing flux of the mobile species. Finally, for long times when most reactive sites are consumed, the transient flux approaches its steady value. Analytic design equations characterizing the flux in these three regimes are developed based on perturbation theory and matched asymptotic expansions. They agree closely with the exact numerical solutions. In addition algebraic formulae for the kill time, time lag and speed of the reaction front are presented and also correspond to the full numerical solutions. We also briefly discuss how the results presented here for homogeneous reactive membranes can be extended to composite films.

Anticipated barrier properties of reactive barrier films make complete experimental characterization impractical due to the long time scales involved; a viable barrier material for oxygen should prevent significant flux for months or years. The design formulae presented here are a key component for understanding these materials and confidently extrapolating limited experimental data for product design purposes.